experiment for force and acceleration

Check Your Understanding

1. Determine the accelerations that result when a 12-N net force is applied to a 3-kg object and then to a 6-kg object.

A 3-kg object experiences an acceleration of 4 m/s/s . A 6-kg object experiences an acceleration of 2 m/s/s .

2. A net force of 15 N is exerted on an encyclopedia to cause it to accelerate at a rate of 5 m/s 2 . Determine the mass of the encyclopedia.

Use F net = m * a with F net = 15 N and a = 5 m/s/s.

So (15 N) = (m)*(5 m/s/s)

And m = 3.0 kg

3. Suppose that a sled is accelerating at a rate of 2 m/s 2 . If the net force is tripled and the mass is doubled, then what is the new acceleration of the sled?

Answer: 3 m/s/s

The original value of 2 m/s/s must be multiplied by 3 (since a and F are directly proportional) and divided by 2 (since a and m are inversely proportional)

4. Suppose that a sled is accelerating at a rate of 2 m/s 2 . If the net force is tripled and the mass is halved, then what is the new acceleration of the sled?

Answer: 12 m/s/s

The original value of 2 m/s/s must be multiplied by 3 (since a and F are directly proportional) and divided by 1/2 (since a and m are inversely proportional)

Force, Mass & Acceleration: Newton's Second Law of Motion

Isaac Newton's First Law of Motion states, "A body at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force." What, then, happens to a body when an external force is applied to it? That situation is described by Newton's Second Law of Motion. 

According to NASA , this law states, "Force is equal to the change in momentum per change in time. For a constant mass, force equals mass times acceleration." This is written in mathematical form as F = m a

F is force, m is mass and a is acceleration. The math behind this is quite simple. If you double the force, you double the acceleration, but if you double the mass, you cut the acceleration in half. 

Newton published his laws of motion in 1687, in his seminal work " Philosophiæ Naturalis Principia Mathematica " ( Mathematical Principles of Natural Philosophy ) in which he formalized the description of how massive bodies move under the influence of external forces. 

Newton expanded upon the earlier work of Galileo Galilei , who developed the first accurate laws of motion for masses, according to Greg Bothun, a physics professor at the University of Oregon. Galileo's experiments showed that all bodies accelerate at the same rate regardless of size or mass. Newton also critiqued and expanded on the work of Rene Descartes, who also published a set of laws of nature in 1644, two years after Newton was born . Descartes' laws are very similar to Newton's first law of motion.

Acceleration and velocity

Newton's second law says that when a constant force acts on a massive body, it causes it to accelerate, i.e., to change its velocity, at a constant rate. In the simplest case, a force applied to an object at rest causes it to accelerate in the direction of the force. However, if the object is already in motion, or if this situation is viewed from a moving inertial reference frame, that body might appear to speed up, slow down, or change direction depending on the direction of the force and the directions that the object and reference frame are moving relative to each other.

The bold letters F and a in the equation indicate that force and acceleration are vector quantities, which means they have both magnitude and direction. The force can be a single force or it can be the combination of more than one force. In this case, we would write the equation as ∑ F = m a

The large Σ (the Greek letter sigma) represents the vector sum of all the forces, or the net force , acting on a body. 

It is rather difficult to imagine applying a constant force to a body for an indefinite length of time. In most cases, forces can only be applied for a limited time, producing what is called impulse . For a massive body moving in an inertial reference frame without any other forces such as friction acting on it, a certain impulse will cause a certain change in its velocity. The body might speed up, slow down or change direction, after which, the body will continue moving at a new constant velocity (unless, of course, the impulse causes the body to stop).

There is one situation, however, in which we do encounter a constant force — the force due to gravitational acceleration, which causes massive bodies to exert a downward force on the Earth. In this case, the constant acceleration due to gravity is written as g , and Newton's Second Law becomes F = mg . Notice that in this case, F and g are not conventionally written as vectors, because they are always pointing in the same direction, down.

The product of mass times gravitational acceleration, mg , is known as weight , which is just another kind of force. Without gravity, a massive body has no weight, and without a massive body, gravity cannot produce a force. In order to overcome gravity and lift a massive body, you must produce an upward force m a that is greater than the downward gravitational force mg . 

Newton's second law in action

Rockets traveling through space encompass all three of Newton's laws of motion.

If the rocket needs to slow down, speed up, or change direction, a force is used to give it a push, typically coming from the engine. The amount of the force and the location where it is providing the push can change either or both the speed (the magnitude part of acceleration) and direction.

Now that we know how a massive body in an inertial reference frame behaves when it subjected to an outside force, such as how the engines creating the push maneuver the rocket, what happens to the body that is exerting that force? That situation is described by Newton’s Third Law of Motion . 

Additional reporting by Rachel Ross, Live Science contributor.

• Newton's Laws of Motion
• Inertia & Newton's First Law of Motion

Additional resources

• HyperPhysics: Newton's Laws
• The Physics Classroom: Newton's Laws
• NASA: Newton's Laws of Motion

Sign up for the Live Science daily newsletter now

Get the world’s most fascinating discoveries delivered straight to your inbox.

The Higgs particle could break physics throughout the universe. Here's why it hasn't.

Huge cosmological mystery could be solved by wormholes, new study argues

'Final parsec problem' that makes supermassive black holes impossible to explain could finally have a solution

Most Popular

• 2 Why is a 'once-in-a-decade' Supermoon Blue Moon happening twice in 2 years?
• 3 'Banana apocalypse' could be averted thanks to genetic breakthrough
• 4 The sun might've just had a record-breaking number of visible sunspots
• 5 'Spectacular silver treasure' from Viking Age unearthed by college student on farm in Denmark

Sciencing_Icons_Science SCIENCE

Sciencing_icons_biology biology, sciencing_icons_cells cells, sciencing_icons_molecular molecular, sciencing_icons_microorganisms microorganisms, sciencing_icons_genetics genetics, sciencing_icons_human body human body, sciencing_icons_ecology ecology, sciencing_icons_chemistry chemistry, sciencing_icons_atomic & molecular structure atomic & molecular structure, sciencing_icons_bonds bonds, sciencing_icons_reactions reactions, sciencing_icons_stoichiometry stoichiometry, sciencing_icons_solutions solutions, sciencing_icons_acids & bases acids & bases, sciencing_icons_thermodynamics thermodynamics, sciencing_icons_organic chemistry organic chemistry, sciencing_icons_physics physics, sciencing_icons_fundamentals-physics fundamentals, sciencing_icons_electronics electronics, sciencing_icons_waves waves, sciencing_icons_energy energy, sciencing_icons_fluid fluid, sciencing_icons_astronomy astronomy, sciencing_icons_geology geology, sciencing_icons_fundamentals-geology fundamentals, sciencing_icons_minerals & rocks minerals & rocks, sciencing_icons_earth scructure earth structure, sciencing_icons_fossils fossils, sciencing_icons_natural disasters natural disasters, sciencing_icons_nature nature, sciencing_icons_ecosystems ecosystems, sciencing_icons_environment environment, sciencing_icons_insects insects, sciencing_icons_plants & mushrooms plants & mushrooms, sciencing_icons_animals animals, sciencing_icons_math math, sciencing_icons_arithmetic arithmetic, sciencing_icons_addition & subtraction addition & subtraction, sciencing_icons_multiplication & division multiplication & division, sciencing_icons_decimals decimals, sciencing_icons_fractions fractions, sciencing_icons_conversions conversions, sciencing_icons_algebra algebra, sciencing_icons_working with units working with units, sciencing_icons_equations & expressions equations & expressions, sciencing_icons_ratios & proportions ratios & proportions, sciencing_icons_inequalities inequalities, sciencing_icons_exponents & logarithms exponents & logarithms, sciencing_icons_factorization factorization, sciencing_icons_functions functions, sciencing_icons_linear equations linear equations, sciencing_icons_graphs graphs, sciencing_icons_quadratics quadratics, sciencing_icons_polynomials polynomials, sciencing_icons_geometry geometry, sciencing_icons_fundamentals-geometry fundamentals, sciencing_icons_cartesian cartesian, sciencing_icons_circles circles, sciencing_icons_solids solids, sciencing_icons_trigonometry trigonometry, sciencing_icons_probability-statistics probability & statistics, sciencing_icons_mean-median-mode mean/median/mode, sciencing_icons_independent-dependent variables independent/dependent variables, sciencing_icons_deviation deviation, sciencing_icons_correlation correlation, sciencing_icons_sampling sampling, sciencing_icons_distributions distributions, sciencing_icons_probability probability, sciencing_icons_calculus calculus, sciencing_icons_differentiation-integration differentiation/integration, sciencing_icons_application application, sciencing_icons_projects projects, sciencing_icons_news news.

• Share Tweet Email Print
• Home ⋅
• Science ⋅
• Physics ⋅
• Mechanics (Physics): The Study of Motion.

Second Law of Motion Experiments

Kinetic Energy Experiments for Kids

Sir Isaac Newton's second law of motion states that the force exerted by a moving object is equal to its mass times its acceleration in the direction from which it is pushed, stated as the formula F=ma. Because force is proportional to mass and acceleration, doubling either the mass or acceleration while leaving the other constant will double the force of impact; the force of impact increases when an object of constant weight is subject to greater acceleration. You can explore several different experiments that demonstrate this principle.

Crater Experiment

Collect a rock and a wadded up piece of paper. Because gravity's acceleration is constant, all objects fall at the same rate regardless of their mass. Test this law by dropping both items simultaneously and watching them fall at the same speed. Now place a bowl filled with powdered sugar or flour underneath the rock, and drop it from a fixed height into the powder. Set the bowl to the side, being careful not to disturb the powder in it. Drop the ball of paper from the same height into a bowl with the same amount of the same powder. Compare the craters in the powder created by each impact. Because acceleration was constant, the difference in size between the crater made by the rock and the one made by the paper illustrates that an increase in mass directly increases the force of the impact into the flour.

Softball Experiment

Screw an eyelet into a softball and another into the lintel of a door frame. Hang the softball from the door frame by a piece of string tied through the eyelets so that it hangs a few centimeters above the floor. Mark the spot directly underneath the softball's resting position. Move the hanging softball and place another softball on the marked spot. Pull the hanging softball back so it is three feet from the ground and release it so it swings and hits the softball on the floor. Measure the distance the softball on the floor travels. Repeat the experiment, substituting a plastic Wiffle ball for the softball on the floor, and measure how far it rolls after impact. This experiment illustrates that when force is held constant, the acceleration is greater in objects with less mass.

Hot Wheels Experiment

Construct a simple ramp 18 inches high and about 24 inches long using a piece of thin plywood and bricks. Place a toy car at the top of the ramp. Release it and measure how far it rolls. Tape two metal washers to the car, release it from the ramp and measure how far it rolls. Repeat the experiment with five washers taped to the top of the car. This experiment shows that as mass increases with gravity's constant acceleration, the force pushing the car along the floor increases, making heavier cars travel farther.

Wagon and String

Obtain a child's wagon, some light cotton string or thread, and two or three small volunteers. Tie the string around the wagon handle and leave 2 or 3 feet of string hanging off the handle to pull with. Begin with an empty wagon. On flat, level ground such as a sidewalk, and from a standing start, pull the string until you reach a comfortable walking speed. Note the effort it takes to pull the wagon. Next, have one of your volunteers sit in the wagon and once again pull the string until you reach walking speed. Note the effort needed to pull the wagon. The string can take only a small amount of force before it breaks; the more riders in your wagon, the more force you need to pull it, until you pass the string's breaking point. With this experiment, your acceleration is about the same each time, though you need to pull with more force due to the additional mass of each new passenger. How many passengers can you pull before the string breaks?

Related Articles

Science project: the effect of mass on the distance..., science projects on newton's second law of motion, how to calculate catapult force, science project on gravity and motion for third graders, toy car experiments, how to demonstrate newton's laws of motion, science projects on amusement park rides, how to build a newton car, ball drop science projects, paintball science fair project ideas, science experiments on bouncing & rolling, fun science activities for force & motion, how to make a compound machine for a school project, how to make a simple machine project for school, how to create a justice scale, background information on egg drop experiments, acceleration lab activities in physical science, soccer science fair ideas, how to determine the strength of an electromagnet.

• Home Science Tools: Newton's Laws of Motion

About the Author

Wilhelm Schnotz has worked as a freelance writer since 1998, covering arts and entertainment, culture and financial stories for a variety of consumer publications. His work has appeared in dozens of print titles, including "TV Guide" and "The Dallas Observer." Schnotz holds a Bachelor of Arts in journalism from Colorado State University.

Find Your Next Great Science Fair Project! GO

• Sign in / Register
• Administration
• Edit profile

The PhET website does not support your browser. We recommend using the latest version of Chrome, Firefox, Safari, or Edge.

24 Elementary Force and Motion Experiments & Activities

Get teaching with these  force and motion  experiments, activities and videos to use in the elementary classroom. This collection of  force and motion activities and resources should help you cover the topics like  texture, gravity, incline and simple machines .

If you’re looking for helpful ideas and lesson plans – then this is the place to start!

Do you need a refresher as the teacher before planning your simple machines unit? This simple machines facts page is an excellent (and easy) way to jog your memory.

Force and Motion Experiments

Let’s plan some force and motion experiments for all elementary grades. Some of these can be adapted for different grade levels.

Set up ramps with different textures and send toy cars down. Use lots of questions to guide young students to extend their exploration.

Create catapults to explore how to make simple machines. With plastic utensils and marshmallows you’re set to build.

Take what you learned about building catapults in the above experiment to build a STEM engineering challenge. Students have to build a basketball hoop with classroom objects and recycled materials.

Skip the cars on an incline and go for liquids! Create a viscosity race with stuff from your fridge. Talk about how resistance to flowing is called viscosity and have fun.

Create a simple machines challenge . Students must create 3 ways to move a lion (or another small toy) using simple machines. Perfect to accompany the (affiliate) book How Do You Lift a Lion ?

Explore Newton’s first law together – the law of inertia – by seeing it in action. Create towers with note cards, string and a tower to feel the law as you take out each card separately, quickly or try to pull them all out at once!

Explore how to move the fulcrum on a lever to experiment how it impacts ease of use. All you need are some simple tools like rulers, a semi-heavy object and something to be the fulcrum.

A video explaining how a lever works is included.

Conduct trials with toy cars to see how you can make them go faster. Record the distance, time and speed with a free recording sheet.

Save a few water bottles and fill them with dry rice. Your students will love exploring friction in this floating rice experiment .

Aren’t those fun and clever force and motion experiments? Let’s move onto activities to help reinforce what you’ve taught.

Force and Motion Activities

After learning about how friction and force moves a roller coaster , set up your classroom to bring the concept to life.

Don’t be afraid to get messy! Combine art with science in this  force and motion marble painting activity .

Work on note taking. Use free simple machine notebooking pages and have students describe the lever, pulley, inclined plane, wedge, screw and wheel and axle. This would be a good resource for upper elementary.

Build a winch with paper towel tubes, spool and a straw. Students could make this recycled materials winch in pairs or small groups.

Attempt to lift heavier objects (by adding pennies to the object being lifted) feeling the change in force it takes to pull it up.

Make a foldable to summarize Sir Isaac Newton’s Laws of Motion . Write each law and illustrate on the flap.

Force and Motion Free Games Online

Experiment online (for kindergarten and first grade ) with this push and pull online activity. [no longer available]

Try this forces and movement interactive game for first and second grade . [no longer available]

Experiment with forces in action with this online activity for 10-11 year olds. [no longer available]

While it’s tricky to build flying contraptions in the classroom – use this how do things fly online simulator to design your own airplanes can make it happen – virtually.

Learn about drag, lift, thrust and weight in this interactive activity.

Your students will totally get into this online simple machines game . This game can be challenging – but your students will learn! Reading skills are needed.

Explore forces, loads, materials and shapes with this interactive  force and motion building big activity . This is neat for upper elementary students to see simulated (but interactive) examples of what they are learning about – with more options than you can explore in the classroom.

Force and Motion Videos for Elementary

Here is a list of more force and motion videos for 4th and 5th grade.

Ready for more force and motion activities for the classroom? Check out these 19 Fun Ideas & Resources for Force and Motion .

More Science

• 28 Awesome STEM Challenges for the Elementary Classroom
• Clouds Science for Kids: 23 Smart Ideas for the Classroom
• 21 Super Activities for Teaching Moon Phases
• Rocks for Kids – 15 Fun Activities and Ideas

Teach Junkie

Leslie {aka the original Teach Junkie} loves learning new things to make teaching easier and more effective. She enjoys featuring creative classroom fun when she's not designing teacher shirts, making kindergarten lesson plans or planning her family's next trip to Disney World.

• UK GCSE (Age 14-16)
• UK A-level (Age 16-18)
• UK Higher Ed. (Age 18+)

Tensile Testing (lite)

Structural materials are required to withstand a variety of applied loads in use. Understanding how these materials respond to applied loads is vital for informed materials selection. Here you can investigate how materials behave under tensile loading (loads applied along the length of a material to cause stretching).

This is only the LITE version, the full version (wtih all materials) is availabe via log-in.  Press GO to launch the experiment!

• Application
• Quick Guide
• Full Instructions

What is ‘Tensile Testing’?

The ‘tensile’ properties of a material describe its most basic mechanical behaviour – how much does a material stretch when it is pulled and how much of the stretching is permanent? ‘Tensile Testing’ is the process of measuring a material’s tensile properties. 

Why are tensile properties important?

Understanding of tensile properties is vital for any application that uses materials structurally, i.e. to withstand or apply force. The range of uses this covers is enormous.  Strong  and  stiff  structures are used in vehicles (cycles, cars, trains, aeroplanes, spacecraft), bridges and buildings, sports equipment and bio-implants (e.g. hip joint replacements).  Flexible  materials are also used in many of these applications.  Thin  but  robust  materials are used in touchscreens.  Hard  materials are used in machines and robots that process and shape other materials and as durable coatings that improve the performance and lifetime of aerospace and bio-implant components.  Elastic  materials can be stretched enormously before any permanent change is made and are used in springs and high performance fabrics. And it’s not just how a component is used – many manufacturing processes involve changing a component’s shape or response to applied forces, e.g.  extrusion  to make tubes, beams and bottles;  drawing  to make springs or wires; or  forging  and  rolling  to shape and harden metals.

Use this experiment to find out more!

​Download the file below for the quick guide for the  Tensile Testing  experiment (requires login) or follow these brief instructions:

To select a sample:

• Click the lower jaw to go to the sample view.
• Open the calliper jaws, drag a sample of choice between the jaw and fully close the jaws around it. (In this LITE version you can only select one of the samples).
• Use the Vernier scale to measure the sample width.
• Click the sample held in the callipers to use it in the tensile testing machine.
• Or open the callipers, return the sample to its original position and choose another sample. (Only available in the full version).

To set the strain increment:

• Click the Set button (display starts to flash).
• Use the keypad and the Del button to enter the desired Step value.
• Click the Set button again (display stops flashing).

To apply strain to samples:

• Set the strain increment value as described above.
• Click the up arrow to increase the applied strain by the Step increment value.
• Click the down arrow to decrease the applied strain by the Step increment value.
• Measure (and record) the applied load (force) using the needles on the Load dial.
• Turn off the strain control unit and click on the lower sample holder to select a new sample.

Download the file below for full instructions for the Tensile Testing experiment (requires login).

Structural materials are required to withstand a variety of applied loads in use. Understanding how these materials respond to the applied loads is vital for informed materials selection. Here we investigate how materials behave under  tensile loading  (loads applied along the length of a material to cause stretching).

The Tensile Test experiment allows a number of mechanical tests to be performed on materials, including:

• Determination of full stress-strain curve to fracture, using either ‘engineering’ or ‘true’ value
• Observation of elastic behaviour and calculation of Young’s modulus
• Observation of the onset of plastic behaviour and permanent deformation
• Calculation of moduli of resilience and toughness
• Calculation of strain energy in a system
• Calculation of work done in deforming a sample

Download the file below for activities for the Tensile Testing experiment (requires login). 

• QUICK ACTIVITIES: 9 quick activities to try
• ACTIVITY 1: Elastic deformation
• ACTIVITY 2: Plastic deformation
• ACTIVITY 3: Fracture

(Available as separate downloads or all activities)

*NEW* Now also available in editable Microsoft Word format

We have also provided a spreadsheet file to allow you to enter your SAMPLE WIDTH, STRAIN and APPLIED LOAD data and obtain stress-strain plots. (HINT: to investigate the general form of stress-strain curves with younger students, use a default sample width of, say, 7 mm)

Watch the video above and download the file below for the background science behind the Tensile Testing experiment (requires log in).

Ohm's Law

Ohm's law is a fundamental equation that shows how voltage, electrical current and electrical resistance are related in simple conductors such as resistors. This experiments allows you to explore Ohm's law and how the coloured bands on resistors codes their resistance. In doing this you will also learn how to use a power supply and 'digital multimeters'.

Press GO to launch the experiment!

Ohm’s law

Voltage , current and resistance are the most fundamental quantities for describing the flow of electricity . Ohm’s law shows how these three quantities are related and so is a powerful way of understanding the basic nature of electricity.

This is relevant to vast areas of technology today, including national electricity grids, power generation, design of all electronic devices and all electronic circuits, heating, electrical safety and understanding of natural phenomena such as lightning. This experiment will allow you to explore Ohm’s law by making measurements of voltage, current and resistance.

Resistors are the simplest and most commonly used electronic component and almost all electronic circuits contain them. They can be used to change the properties of any circuit they are part of, such as current flow , how voltage is distributed across components, the speed of a circuit , the amount of amplification from a circuit, the response of a sensor or the amount of electrical heating from a circuit.

The simplest resistors are made of a thin film or wound wire of carbon or metal . They usually have a series of coloured bands that represents both their target resistance value and how much the actual value might vary from this (the ‘ tolerance ’). This experiment lets you practise selecting the appropriate colour bands on a resistor to achieve a certain resistance value.

Digital Multimeters

Digital multimeters (DMMs) are versatile pieces of equipment commonly found in electronics, physics and engineering labs. In this experiment you’ll learn how to use a DMM to measure voltage , current and resistance . You’ll see this piece of equipment in many other FlashyScience experiments!

Download the file below for the quick guide for the  Ohm's Law  experiment (requires login) or follow these brief instructions:

To measure resistance:

• On the right-hand Digital Multimeter (DMM), rotate the switch to resistance measurement.
• Click and drag the clips on the wires attached to the right-hand DMM so that they snap to the wires either side of the resistor (make sure the power supply is turned off).
• Note the resistance value shown on the DMM screen.

To change the resistor:

• Click the resistor you wish to change to move to the  Selection  screen.
• Click on the colour band you wish to change.
• Click on the palette colour you wish to select.
• Click on the resistor wire to return to the main screen.

To use voltage and current:

• Turn on the power supply (right hand side of screen) and turn the dial to set the voltage.
• To measure  current through the resistor  – turn the  left-hand DMM  dial to DC current.
• To measure the  voltage across the resistor  – turn the  right-hand DMM  dial to DC voltage.
• NOTE: in this experiment the power supply voltage is also shown directly on its display.

​Download the file below for full instructions for the Ohm's Law  experiment (requires log in).

Download the files below for activities for the Ohm's Law  experiment (requires login).

• ACTIVITY 1: Investigate what the different coloured bands on resistors mean
• ACTIVITY 2: Learn how to use a DMM to measure electrical resistance
• ACTIVITY 3: Explore the effect of the tolerance band (band 4) on resistors
• ACTIVITY 4: Explore the statistics of resistance values from resistors with the same band colour coding
• ACTIVITY 5: Investigate Ohm’s law by measurement of voltage and current with a resistor
• ACTIVITY 6: Investigate Ohm’s law by measurement of current for different resistors with a fixed voltage
• ACTIVITY 7: Investigate Ohm’s law by measurement of voltage for different resistors with a constant current
• ACTIVITY 8: Investigate the power consumption due to electricity flowing in a single resistor
• ACTIVITY 9: Investigate the power consumption due to electricity flowing through different resistances

Download the file below for the background science behind the Ohm's Law  experiment (requires log in).

Free-fall due to Gravity

Gravity is a fundamental force in nature, without which we would not have galaxies, stars, the Earth, oceans, life on Earth... or golf. This experiment allows you to measure the acceleration due to gravity by measuring the time taken for a ball to fall through different heights. You can choose between two ways of timing the free fall, and you can even travel through space to measure the strength of gravity on different objects of the Solar system!

It is safe to say that gravity is important to us! Without gravity there would be no life on Earth and, in fact, without gravity, the Earth would never have existed.

Gravity is responsible for stars forming in the first place, keeping the Sun from exploding from the heat it generates, and for the structure of galaxies. It also keeps the Earth in orbit around the Sun, keeps our atmosphere and oceans in place and means we don’t float off into space. Gravity even allows plants to detect which way is ‘up’ so they send their roots and shoots in the right directions. You can see more at this  NASA web page .

So, why does it matter that we know how strong gravity is?

Well, for lots of reasons.

The strength of gravity is essential to know in  Civil Engineering  projects such as design of buildings and bridges so we can  calculate the stresses materials are under .

Aircraft and space rocket designers  must know the strength of gravity that must be overcome and satellite technology is based upon a certain strength of gravity to maintain orbits at particular heights above the Earth.

Hydroelectric power generation  also relies on gravitational potential energy, either through energy ‘storage’ in dams or from the water flow or tides in rivers or oceans.

Our quality of life would be very different too. Most  sports rely on gravity  (we’re not counting chess as a sport here!) and gravity even keeps food in a saucepan while it cooks!

​Download the file below for the quick guide for the  Free-fall due to Gravity  experiment (requires login) or follow these brief instructions:

• Choose between using a Pressure Pad sensor and Light Gate sensors using switch on side of timer.
• Click and drag the electromagnet 
• Read the height of the ball on the electromagnet using the magnified view of the ruler
• Press the Start/Reset button to release the ball from the electromagnet
• Read the time (from the timer) for the ball to drop to the pressure pad
• Press the Start/Reset button to return the ball to the electromagnet and reset the timer to zero
• Click and drag the electromagnet and both light gates to adjust their height on the ruler but ensure the separation of the electromagnet and first light gate is constant throughout your experiment
• Measure the distance between light gates using the magnified view of the ruler
• Read the time for the ball to fall between the light gates

Measured Earth’s gravity? Click on the poster to explore gravity elsewhere in the Solar System too!

Download the file below for full instructions for the Free-fall due to Gravity experiment (requires log in).

Download the files below for activities for the Free-fall due to Gravity  experiment (requires login).

• ACTIVITY 1: Measurement of g using pressure pad sensor
• ACTIVITY 2: Measurement of g using light gate sensors
• ACTIVITY 3: Travel the Solar System!
• ACTIVITY 4: Uncertainty in g based on uncertainty in individual measurement

Download the file below for the background science behind the Free-fall due to Gravity  experiment (requires log in).

Radioactivity

Radioactive materials are used by us in lots of ways. This experiment allows you to explore alpha, beta and gamma radiation and how they are absorbed by various materials. You can also measure the change in radioactive signal with distance from the radiation source and even time travel to measure the halflife of radioactive decay for different elements!

Radioactive elements (radionuclides or radioactive isotopes) produce high energy particles and are used in a huge range of applications. Most people know about  nuclear power , which converts the energy of radiation from uranium-238 or plutonium-239 into heat and then electrical power, even in small-scale form for remote applications (e.g. spacecraft). There are far more widespread uses all around us though.

Radionuclides are used in many  medicinal applications . They can be used as  tracers  to follow fluid flow inside the body by detecting the radionuclide emitted radiation (e.g. technetium-99, thallium-201, iodine-131 and sodium-24).  Medical   imaging  can use radioactive elements that naturally collect in particular parts of the body and image the radioactive emission. For example, iodine-131 is used to image the thyroid and other isotopes can be used for other organs, such as bones, heart, liver and lungs. Larger doses of the radionuclides (e.g. cobalt-60) are used to create a targeted  radiotherapy  treatment of cancer in these organs. It is even possible to detect the presence of Heliobacter pylori (an unwanted bacterium that can be in stomachs) with a simple breath test that uses carbon-14.

You may have radioactive materials in your home, school or workplace.  Smoke detectors  use alpha radiation from americium-241 to ionise smoke particles for detection.  Glow-in-the-dark inks  on clocks, watches and emergency signs that convert radioactive particle energy from promethium-147 into light.

You may also have food that has been treated with radiation. Many foods (including tomatoes, mushrooms, berries, cereals, eggs, fish and some meat products) are irradiated with gamma rays from cobalt-60 to kill micro-organisms and  improve the food’s shelf life  (without making the food radioactive!). Similarly, gamma radiation from caesium-137 is used to  sterilise medical products  such as syringes, heart valves, surgical instruments and contact lens solutions.

Radioactive elements are used in industry too. For example, the absorption of different types of radiation mean it can be used to  monitor  the thickness  of manufactured components and sheets. Radionuclides are also used for detecting  leaks from pipes , the  direction of underground pipes  and  waste dispersal  in the environment. Radioactive sources are also used in  industrial imaging , with the sample placed between the radiation source and a detector. Certain isotopes are used as chemicals in order to trace  chemical  reaction routes , e.g. carbon-14 in photosynthesis. Similar approaches are used in biology to test when proteins undergo important ‘ phosphorylation ’ reactions (using phosphorus-32) to learn when their function is activated by other proteins or small chemicals.

Radioactive elements can also be used for  historical dating  of objects, e.g. carbon-14 dating for estimating the age of organic matter and uranium-238 for rocks. Similarly, radioactive decay from vintage drinks such as wine can be used to prove their age, since radionuclides were released into the atmosphere by nuclear explosion tests after World War II and are present in all food and drink produced since then.

With so many uses, it’s no wonder that radioactive decay is an important aspect of science and engineering!

​Download the file below for the quick guide for the  Radioactivity  experiment (requires login) or follow these brief instructions:

Select the radiation source:

• Click on the  Source holder.
• Click on one of the radiation sources in the tray and then in the holder.

Detecting radiation:

• Click the power  switch  on the Geiger-Müller  counter .
• Read the needle position on the dial to measure level of radiation.

Changing the filter material and thickness:

• Click on the  filter holder.
• Click on the material of choice to increase its thickness in the holder by 1 mm.
• Click on the material in the holder to reduce its thickness by 1 mm.
• Measure the filter thickness using the markings inside the holder.

Change the source-detector separation:

• Click and drag the holder mount to move it along the ruler.
• Measure the mount’s position using the magnified ruler view seen while clicked on the holder mount.

Time travel!

• Move time forward by one minute, hour, day, month or year by clicking on the appropriate value on the clock .

Download the file below for full instructions for the Radioactivity  experiment (requires log in).

Download the file below for activities for the Radioactivity  experiment (requires login).

• ACTIVITY 1: Radioactive half-life… and time travel! (used in GCSE Physics)
• ACTIVITY 2: Inverse square law (used in A-level Physics)
• ACTIVITY 3: Which materials absorb different types of radiation?
• ACTIVITY 4: Radiation absorption strength
• ACTIVITY 5: Alpha radiation (advanced experiment)
• ACTIVITY 6: Mixed radiation sources

Or see if you can do some of the following:

• Measure the half-life of different sources (GCSE)
• Measure how detected gamma radiation varies with source-detector separation
• Find out how alpha, beta and gamma radiation is absorbed by various materials
• Explore multi-decay type radioactive sources

Download the file below for the background science behind the Radioactivity  experiment (requires log in).

Resistivity of a Wire

The electrical resistivity of a wire tells us how well the wire material conducts electricity. This is crucial information for any application that involves conducting electricity, including wind turbines, electric vehicles, household electrical goods and computers. Here you can measure the resistivity of wires of different materials and widths, and consider which would be best suited for conducting electricity.

Electronic materials are crucial to our life today , and electrical ‘resistivity’ tells us how good or poor a material is at conducting electricity.

We use materials with low electrical resistivity to transmit electrical power from generators, across grid distribution networks , and to homes and workplaces for use . Designers of electrical devices rely on knowing the resistivity of wire used in order to calculate the resistance of components.

These devices range in size from enormous machines such as wind turbines or industrial lifting equipment ; motors or engines in electric vehicles and all-new electric aircraft ; consumer products such as washing machines, hair dryers and ovens ; and the nanoscale components within the computer chips found in smart devices, laptops, and mobile phones .  

In fact, modern computing is based on controlling the resistivity of semiconductor materials in a type of transistor (known as ‘field effect transistors’ using ‘CMOS’ technology).

Measuring electrical resistivity helps us to understand the properties of materials, to monitor manufacturing processes, and to select the best material for an application.

Download the file below for the quick guide for the  Resistivity of a Wire  experiment (requires login) or follow these brief instructions:

• Click on the right hand wire post to move to the  Select Wire  screen.
• Open the micrometer by dragging the thumbwheel down.
• Choose a material and drag the unlabelled wire into the micrometer.
• Close the micrometer and measure the wire's width.
• Click on the wire while it's in the micrometer to return to the  main screen .
• Click on the switch to turn it on.
• Measure voltage and current for a variety of contact positions on the wire.
• Calculate resistance for each contact position. 
• Plot resistance vs contact position and calculate the gradient of a line of best fit.
• Multiply the line's gradient by the wire's cross-sectional area to obtain the wire's electrical resistivity.

Download the file below for full instructions for the Resistivity of a Wire  experiment (requires log in).

Download the file below for activities for the Resitivity of a Wire  experiment (requires login).

• QUICK ACTIVITIES: 5 quick activities to try
• ACTIVITY 1: Different wire lengths

(Available as separate downloads or all activities)

Download the file below for the background science behind the Resitivity of a Wire  experiment (requires log in).

Hooke's Law

Hooke's law describes how springs respond to having forces applied. This experiment allows you to apply force using weights and measure how springs of different stiffness extend in response. You can calculate the stored elastic potential energy in the springs and even go to different parts of the Solar System to see how changing the strength of gravity changes the weight applied to the springs!

Stretching – the truth!

You may wonder why we study springs and why questions about stretching springs appear on exams. Sure, springs are used in the world, but are they really so important? Why is it important to know how springs stretch when they are pulled?

Well, first, springs are incredibly useful . When made from elastic materials, such as most metals, springs stretch when pulled and return to their original size when released . They can also be compressed and, again, return to their original size when released. The stretching or compression stores energy that is then returned when the spring is released. This energy storage and return is the key reason springs are useful. Springs use this capability in all sorts of applications, including in high tech areas such as automotive, industrial tools and robotics, to more everyday items such as trampolines, mattresses, children’s play equipment, door handles and retractable pens. 

The second reason is that the way that springs respond to force being applied to them (i.e. being pulled or mass added to one end of them) is identical to how materials in general behave. If materials are pulled, then they stretch. The coiled shape of a spring, though, means that the ends tend to move large distances compared to a regular shape of the same material (e.g. a simple rod). This means that studying what happens to springs when they are pulled allows simple measurements to be performed that give us understanding of how all materials behave when they are pulled. Materials behave this way in any application where they have force applied to them, e.g. in construction, vehicles, heart valves, body implants, plants, rocks, furniture, tools, footwear – the list goes on and on. And don’t forget this includes your body too!

Download the file below for the quick guide for the  Hooke's Law  experiment (requires login) or follow these brief instructions:

• Click on 50 g or 100 g masses to add them to the mass holder.
• Click on the ruler to go to a zoomed view (centimetre scale).
• Click on the masses on the holder to move them back to their boxes.
• To change to a different spring:
• Remove all mass from the holder.
• Click on the spring.
• Select from Low, Medium, High or Unknown Stiffness.
• Click again on the spring to return to main screen. 

5. To change to a different part of the Solar System: 

• Click on the poster to choose where to do the experiment.

6. Click the Information button to see the controls.

Use this experiment to:

• Test Hooke’s law.
• Measure spring constants.
• Test the ‘limit of proportionality’ for springs.
• Calculate the stored energy of a spring.
• See how different strengths of gravity affect the weight added to a spring.

Download the file below for full instructions for the Hooke's Law  experiment (requires log in).

Download the files below for activities and associated worksheets for the Hooke's Law  experiment (requires login).

• ACTIVITY 1: Testing Hooke’s law
• ACTIVITY 2: Measurement of the stiffness of a spring
• ACTIVITY 3: Energy stored in a spring
• ACTIVITY 4: Limit of proportionality of a spring
• ACTIVITY 5: Travel the Solar System!

Download the file below for the background science behind the Hooke's Law  experiment (requires log in).

Specific Heat Capacity: Solids

Specific heat capacity of solids is important to understand in lots of applications that deal with heat energy and changes in temperature. This experiment allows you to control the electrical heating power applied to a choice of six different materials and measure the rate at which the sample temperature changes. You can then calculate the specific heat capacity of the chosen material. Compare the different materials, investigate the effect of having thermally insulated or uninsulated samples, and see if different heating powers change the measurements.

There are lots of ways that we use materials that see them change temperature. Some examples include heating systems in buildings (especially storage heaters ), simple household appliances such as an iron or an oven , combustion engines in cars, jet engines in aircraft, high speed machines such as drills, and industrial furnaces ; however, examples also include applications where the temperature is reduced, for example in refrigerators , freezers and heat sinks , which are used to help cool another component.

A change in a material’s temperature will also result in a change in its heat energy . Different materials, however, will have a different change in heat energy for a given change in temperature.

The material's property we use to show this difference is called specific heat capacity . This property is key to allowing us to understand how components will perform in thermal applications and help us to choose the most appropriate material. If you go to study Physics or Engineering at university you will probably also learn how specific heat capacity values depend on a material’s types of atom, atomic bonding and electrical properties.

Download the file below for the quick guide for the Specific Heat Capacity: Solids  experiment (requires login).

Download the file below for full instructions for the Specific Heat Capacity: Solids  experiment (requires log in).

Download the files below for activities and associated worksheets for the Specific Heat Capacity: Solids experiment (requires login).

• ACTIVITY 1: Measurement of specific heat capacity of a material
• ACTIVITY 2: Comparison of specific heat capacity for different materials
• ACTIVITY 3: Measurement of specific heat capacity using different heating powers
• ACTIVITY 4: Effect of insulation on measuring specific heat capacity

(Available as separate downloads or all activities/all worksheets)

Download the file below for the background science behind the Specific Heat Capacity: Solids  experiment (requires log in).

Acceleration and Force

Understanding the relationship between force, acceleration and mass is key to starting to understand the physics of changing motion. This experiment allows you to change the mass of a tabletop car and the force applied to it before timing how long it takes the car to move various distances. Analysis of your results will allow you to see the relationship between acceleration and force.

The FlashyScience Acceleration and Force experiment might use a toy car on a table top but the science you can learn from it helps us to understand the world around us, to design all sorts of new vehicles and machines, and even to understand our bodies better.

At the largest of scales, knowing the huge forces involved with galaxies, stars and planets show us how these huge objects move and even how they form. We use our knowledge of force and acceleration to launch objects into space using rockets and to put satellites into stable orbits. This knowledge also allows us to calculate the acceleration of high performance cars (e.g. F1 cars) and aircraft , to design and build machines with moving parts, and to understand the forces parts of our bodies experience through an area of science called biomechanics . Force and acceleration can even be used to measure the mass of atoms and molecules through scientific techniques called mass spectrometry , and help us to understand how atoms interact in gases.

You can see that knowledge of force and acceleration is essential to lots of areas of science, engineering and our lives in general.

Download the file below for the quick guide for the Acceleration and Force  experiment (requires login).

Download the file below for full instructions for the Acceleration and Force  experiment (requires log in).

Download the files below for activities and associated worksheets for the Acceleration and Force  experiment (requires login).

• ACTIVITY 1: Investigating acceleration, F = ma (mass transfer between car and mass holder)
• ACTIVITY 2: Investigating acceleration, F = ma (constant holder mass, increasing car mass)
• ACTIVITY 3: Distance versus time graphs

Download the file below for the background science behind the Acceleration and Force  experiment (requires log in).

Density of Solids & Liquids

Density is an 'intrinsic' property of materials and liquids, which means its value doesn't change when the amount of material or liquid changes. This experiment allows you to find the density of various materials with regular and irregular shapes, as well as several liquids, using three methods of determining mass and volume. 

Density is a basic property of materials and liquids. It is important in all sorts of areas of science , engineering and medicine . Density (mass per unit volume) is related to the type of atoms within the material or liquid and how they are arranged . Changing the temperature of a solid or liquid often changes its volume , which also changes its  density . Different processing treatments of materials can lock in some of these changes, resulting in materials made of the same atoms but with different densities. Many materials can be ‘ porous ’ (contain lots of holes) and being able to measure density is a simple way of finding the level of porosity of a material.

The buoyancy of a solid in a liquid depends upon the density of the solid and liquid. Ice floats in liquid water because ice molecules are more widely spaced than those in water, and so the density of ice is lower than that of water.

The density of solids and liquids is also related to a substance’s refractive index and how it interacts with X-rays. For example, your bones are denser than your muscle tissue and so absorb X-rays more; this allows medical images to be created that show the different regions inside your body.

Density is vital to the efficient design of physical objects, particularly for structural and transport applications. There is a huge demand for engineers and materials scientists to create lighter vehicles and aircraft to reduce their power requirements and help reduce our use of fossil fuels .

Download the file below for the quick guide for the  Density of Solids & Liquids  experiment (requires login).

Download the file below for full instructions for the Density of Solids & Liquids experiment (requires log in).

Download the files below for activities and associated worksheets for the Density of Solids & Liquids  experiment (requires login).

• ACTIVITY 1: Density of regularly shaped objects – cubes and rectangular cuboids
• ACTIVITY 2: Density of regularly shaped objects – spheres
• ACTIVITY 3: Density of irregularly shaped objects
• ACTIVITY 4: Density of liquids

Download the file below for the background science behind the Density of Solids & Liquids  experiment (requires log in).

Thermal Insulation

Heat is transmitted by conduction, convection or radiation. This experimental allows you to investigate thermal conduction by measuring the time for thermal energy to pass through different materials.

The thermal conductivity of materials is hugely important for how we live today.

Thermally-insulating materials are found in lots of places around the home. This includes safety items such as oven gloves or fire blankets and inside ovens and refrigerators to stop them heating or cooling the rest of your kitchen! Your hot water pipes and water heating system will probably have thermal insulation around them to stop unwanted heat loss. Houses and other buildings usually have thermal insulation around them to reduce heat loss when it is cold outside and reduce heat entering when it is very hot outside. This is important as we try to reduce CO2 emissions from energy use as part of our fight against climate change . Insulating materials are also used around industrial furnaces , in refrigerated vehicles and packages (e.g. for transporting food or medical supplies ) in aircraft to keep crew and passengers warm in the cold air, and in spacecraft to stop the insides reaching temperature extremes and protecting the spacecraft itself from burning up if it re-enters Earth’s atmosphere.

Thermally-conducting materials are also very important to heating and cooling systems, such as heating elements in kettles and furnaces, radiators , high speed industrial machines and heat-sinks found in electronic devices.  

Heat conduction is also really important in many renewable energy technologies, such as solar cells (photovoltaics), which work less efficiently if they heat up, and ‘ thermoelectric generators ’ (TEGs), which are most efficient if they conduct electricity well but conduct temperature weakly.

This huge range of applications means there is a lot of research and development of materials with new thermal conduction properties. How materials conduct heat is also related to their atomic-scale structure – this means that we can learn about the materials from how they conduct heat and change their structure in order to create new properties that are better suited for particular applications.

Download the file below for the quick guide for the Thermal Insulation  experiment (requires login).

Download the file below for full instructions for the Thermal Insulation   experiment (requires log in).

Download the files below for activities and associated worksheets for the Thermal Insulation  experiment (requires login).

• ACTIVITY 1: Effect of a material as thermal insulation
• ACTIVITY 2: Comparison of different materials as thermal insulation
• ACTIVITY 3: Effect of material thickness on heat conduction
• ACTIVITY 4: Effect of temperature difference on its rate of change (Advanced experiment)

Download the file below for the background science behind the Thermal Insulation  experiment (requires log in).

Leslie Cube (IR emission)

This experiment allows you to measure the infrared emission from the four different surfaces of a Leslie cube. You can choose which surface to measure, see what happens as temperature changes, and adjust the signal strength by changing the detector position and the level of signal amplification. Advanced activities involve calculations of emissivity, how signal varies with source-detector separation, and the temperature-dependence of infrared emission.

Any object emits electromagnetic radiation due to having a temperature above absolute zero (about -273.15°C), although different surfaces emit the radiation to different levels. This might seem like a curiosity created just for lab measurements but it has lots of real-world relevance.

The hotter an object is, the stronger this thermal emission is. Objects with different temperatures emit different parts of the electromagnetic spectrum too. Objects close to room temperature (like us!) only emit infrared radiation (‘IR radiation’), which we feel as warmth. Objects at hundreds of degrees Celsius start to emit visible radiation (wavelength from 400 – 700 nm), those at thousands of degrees Celsius emit ultra-violet (UV) radiation (wavelength from 100 – 400 nm), while the hottest objects in the galaxy (e.g. regions around black holes) emit X-ray radiation (wavelengths shorter than 100 nm).

The most important aspect of thermal emission is that life on our planet would not exist without it! Our nearest star, the Sun , is so hot its IR emission reaches across over 140 million kilometres (that’s over 90 million miles) of space to warm our planet . The Sun’s visible light also allows us to see. The Earth’s ozone layer plays an important role in absorbing most of the UV light from the Sun, which would otherwise reach us at harmful levels.

Astronomers also use the thermal emission from other stars and astronomical objects to learn about how they were formed, their lifecycle, and the processes that go on within them.

Climatologists and meteorologists (scientists who study the Earth’s climate and weather) use satellites to map the IR emission of the Earth’s atmosphere and land to help predict future weather events and trends. The surface of the Earth can also be imaged to locate underground heat sources, objects and water flows .

In smaller-scale applications, surface materials are often chosen to help either cool or insulate an object by either maximising or minimising IR emission, depending on what is needed. IR emission is used in some household or industrial heaters and to measure temperature in areas such as industrial manufacturing processes and medical applications , e.g. measuring the temperature of a patient.

‘Thermal imaging’ cameras create images from IR emission for a huge range of applications, including night vision (e.g. for security systems or non-invasive imaging of wild animals), analysing heat sources in electronic circuits , industrial monitoring (e.g. web servers , aircraft engines ), and analysing the thermal efficiency of objects from miniature devices to houses .

Download the file below for the quick guide for the Leslie Cube (IR emission)  experiment (requires login).

Download the file below for full instructions for the Leslie Cube (IR emission)   experiment (requires log in).

Download the files below for activities and associated worksheets for the Leslie Cube (IR emission)  experiment (requires login).

• ACTIVITY 1: Infrared emission from different surfaces (basic)
• ACTIVITY 2: Infrared emission at different surface temperatures (basic)
• ACTIVITY 3: Detected infrared emission versus distance from source (advanced)
• ACTIVITY 4: Measurement of emissivity of different surfaces (advanced)
• ACTIVITY 5: Temperature dependence of infrared emission (advanced)

Download the file below for the background science behind the Leslie Cube (IR emission)   experiment (requires log in).

Reflection and Refraction of Light

Use either a prism or a hemicylinder of material to discover how light interacts with materials when it pass through of reflects off of materials. You will be able to measure the refraction index of materials along with the angle requried for total internal reflection.

We use light in all sorts of ways. You are probably using a screen that emits light to read these words now and might be in a room that is lit by artificial light from a lightbulb.

This experiment deals with how light interacts with transparent materials. The fact that you can read this is down to how transparent materials in your eyes interact with and redirect light to create images . If you wear glasses or contact lenses , you are relying on these effects even more!

In fact, there are lots of types of imaging systems that work by redirecting light. These include a wide variety of microscopes and telescopes for making the very small or very large parts of our world and universe visible to us. These work by refracting light through lenses or by reflecting light from mirrors , or a combination of both.

Light scanners use light refraction or reflection in all sorts of applications, from barcode readers to laser display systems to laser machining tools used to process materials. 

Vast amounts of information are sent worldwide every minute of every day using packets of light travelling down transparent fibre optic cables. This vital technology depends on how light interacts with interfaces between two types of material. The future might see super-fast all-optical computers that use light to process information.

The way light interacts with a material can also tell us a lot about the material. Lots of scientific techniques use light to probe the nature of all sorts of materials.

The FlashyScience Reflection & Refraction of Light experiment allows you to learn about the way light behaves at surfaces and through transparent materials – this is a great starting point to understanding many of the ways we use light in the world around us!

Download the file below for the quick guide for the Reflection & Refraction of Light  experiment (requires login).

Download the file below for full instructions for the Reflection and Refraction of Light  experiment (requires log in).

Download the files below for activities and associated worksheets for the  Reflection and Refraction of Light  experiment (requires login).

• ACTIVITY 1: Reflection from a surface
• ACTIVITY 2: Refraction in materials: air-to-glass
• ACTIVITY 3: Refraction in materials: glass-to-air
• ACTIVITY 4: Transmission of light

Download the file below for the background science behind the Reflection and Refraction of Light  experiment (requires log in).

Properties of waves (ripple tank)

Waves are incredibly important across science, engineering, technology, and medicine. Learning about them from waves on the surface of a liquid is a great way of starting to understand them. Here, you can change the frequency of waves on water and measure their wavelength, and then change to different liquids, use different depths of liquid, and even perform the experiment around the Solar System!

Most people are familiar with waves on the surface of water from looking at ripples created by, for example, dropping stones into the water. This might seem to have little to do with how we live but this couldn’t be further from the truth – waves are essential for our existence and there is a huge range of applications of them in our world.

Understanding waves on water Is essential for understanding important topics like coastal erosion and how to reduce it, using renewable electricity from wave poower , designing ships, and even calculating the speed of tsunami events.

We find all sorts of other waves, too, though. Light is a kind of electromagnetic wave , together with all parts of the electromagnetic spectrum, including radio waves, microwaves, infrared radiation, ultra-violet, X-rays, and even gamma rays. The range of applications from these is immense, and includes, among many other areas, optics (do you wear glasses or contact lenses?), communications , displays , sensors , telescopes and microscopes , imaging techniques , medical diagnostics and therapies , radar , cooking , heating , energy applications , and manufacturing techniques (e.g. laser-selective melting 3D printing), and all sorts of scientific methods of measurements or controlling matter, e.g. measuring the distance between atoms in a material, finding the structure of a protein molecule, or even laser-cooling and trapping of atoms.

The vibrations in materials are waves, too, and these allow us to make all sorts of musical instruments with different sounds. Sound then travels through the air and materials as a wave, and this allows us to design soundscapes and tones using acoustics . These effects also allow sonar to map below the surface of the sea, acoustic imaging to visualise underground structures, and ultrasound imaging to show us inside the human body, for example, to check the health and development of a growing foetus through to visualising damage to a bone joint.

At a larger scale, seismology uses how wave vibrations travel through the Earth to understand its structure and why events like earthquakes happen. Understanding waves then also helps us to design buildings that can withstand earthquakes. Seismology is now even being applied to other planets in the Solar System to understand their structures, too. Believe it or not, the Sun’s surface shows ripples due to pressure waves inside it, and scientists study these to learn more about what happens inside the Sun. And, within the last few years, scientists have detected gravitational waves that travel through the universe!

Zooming back to the smallest scales, atoms and subatomic particles such as electrons often behave like waves (if you continue to study science will learn more about this in the coming years). These properties have been incredibly important for us to understand fundamental physics and have given us new areas of science such as ‘ quantum mechanics ’. This helps to explain the nature of atoms, how they interact, and why different elements have such different properties – these were huge questions for humankind for centuries. Indeed, all chemistry comes from electrons having wave properties, while the electrical properties of metals, semiconductors, and insulators, as well as most magnetic properties of materials, come from the wave properties of electrons.  Today, we’re seeing new technologies based on quantum mechanics, such as unbreakable codes ( cryptography ) and super-powerful ‘quantum computing' . These same wave properties of electrons lie behind crucial biological processes such as photosynthesis , without which there would be no life on Earth.

What’s great news is that waves have many common properties, whatever type they and wherever they are found.

The FlashyScience Properties of Waves experiment will help you on the first steps of the journey to understand how waves travel and can be used!

Download the file below for the quick guide for the Properties of waves (Ripple tank)  experiment (requires login).

Download the file below for full instructions for the Properties of waves (Ripple tank)   experiment (requires log in).

Download the files below for activities and associated worksheets for the  Properties of waves (Ripple tank)  experiment (requires login).

• ACTIVITY 1: How wavelength changes with frequency
• ACTIVITY 2: Speed of waves on water
• ACTIVITY 3: Relationship between wavelength and frequency
• ACTIVITY 4: Effect of water depth on surface waves
• ACTIVITY 5: Waves on different liquids (advanced)
• ACTIVITY 6: Effect of gravity on surface waves on liquids (advanced)

Download the file below for the background science behind the Properties of waves (Ripple tank)  experiment (requires log in).

Reflection and Refraction of Light (Advanced)

This experiment deals with how light interacts with transparent materials.  You can explore the nature of the refraction of light by taking measurements using four different materials and applying Snell's law. Refraction is an important optical effect. The fact that you can read this is down to how transparent materials in your eyes refract light to create images . If you wear glasses or contact lenses , you are relying on refraction even more!

In fact, there are lots of types of imaging systems that work by refracting light. These include a wide variety of microscopes and telescopes for making the very small or very large parts of our world and universe visible to us. These work by refracting light through lenses or by reflecting light from mirrors , or a combination of both.

This experiment also allows you to investigate total internal reflection with the various materials provided. Vast amounts of information are sent worldwide every minute of every day using packets of light travelling down transparent fibre optic cables. This vital technology depends on  total internal reflection of light at the interface of two types of material to direct the light with minimal loss of intensity. The future might see super-fast all-optical computers that use light to process information.

Download the file below for the quick guide for the Reflection & Refraction of Light (Advanced)  experiment (requires login).

Download the file below for full instructions for the Reflection & Refraction of Light (Advanced)  experiment (requires login).

Download the files below for activities and associated worksheets for the Reflection & Refraction of Light (Advanced)  experiment (requires login).

• ACTIVITY 1: Snell's law (calculating refraction)
• ACTIVITY 2: Total internal reflection

Download the file below for the background science behind the Reflection & Refraction of Light (Advanced)  experiment (requires login).

The Young Modulus (Pre-release)

Measuring the Young Modulus of a piece of wire made from steel, aluminum, copper or nylon. NOTE: This is a beta version that is currently being tested but feedback is very welcome!

Simple Harmonic Motion (Pendulum) - Early release

Simple Harmonic Motion using a Pendulum - early release. 

Simple harmonic motion (SHM) is a type of oscillating motion. It is used to model many situations in real life where a mass oscillates about an equilibrium point.  Early release - while the experiment is fully functional not all documents and supporting material is available just yet. 

Simple harmonic motion can be seen all around us in objects and applications that improve our lives. However, it is also seen in the fundamental behaviour of molecules and materials, although this usually occurs at frequencies and length scales that require scientific instruments for us to observe them.

A child on a park swing will just be enjoying the ride, probably unaware that the swing’s movement is an example of simple harmonic motion , or SHM.

The same child might go on a larger ride, such as a Pirate Ship, at an amusement park. The ride’s designers will have used simple harmonic motion principles to calculate the frequency of the Pirate Ship, its maximum speed , and the forces involved, and use this to specify the construction materials and the electric motor that should be used.

Musical instruments often use simple harmonic motion. For example, the strings of stringed instruments such as a guitar or violin vibrate back-and-forth in a way that obeys simple harmonic motion.

Our understanding and measurement of time has been affected by simple harmonic motion. Pendulum clocks use the regular, simple harmonic motion of a pendulum mass to determine how fast the clock hands move, while this is done in quartz clocks and watches using the simple harmonic vibrations of a quartz crystal.

Shock absorbers , including those in cars, use springs in an oil that move with ‘damped’ harmonic motion to reduce vibrations and give the vehicle passengers a smoother ride.

Simple harmonic motion is important for hearing too. The cochlea in our ears is lined with hairs called stereocilia just 0.01 – 0.05 mm in length. These hairs vibrate when particular frequencies of sound are transmitted through the cochlea and give us our sense of hearing.

The electronic bonds that hold atoms together in molecules and solids create forces that try to return atoms to equilibrium positions. This results in simple harmonic motion, even at this atomic scale .

Different molecules have atoms and groups of atoms with different masses bonded in different ways (e.g., single or double bonds) that can also vibrate in different ways (e.g. three atoms bonded along a single axis can all vibrate along the axis or laterally to it). This means that molecules have different sets of vibrational frequencies that absorb light of the same frequencies, usually infrared light. Forms of infrared spectroscopy are therefore used to find what molecules are in a measured sample.

These vibrations are one of the main ways molecules and solids absorb thermal energy, and increasing the temperature of molecules or solids will increase the amplitude of their simple harmonic vibrations.  

There are also some sophisticated scientific effects that show simple harmonic motion. One example is electrons at the surface of some metals. A sea of conduction electrons can form, which then acts as a single object. This sea of electrons, known as a surface plasmon , can be made to oscillate across the metal using light. The simple harmonic motion of surface plasmons is currently being developed in research labs to create high sensitivity detectors (e.g., of molecules, proteins, and bacteria), computer chips thousands of times faster than those we have today, and even improved makeup !

Download the file below for the quick guide for the Simple harmonic motion (Pendulum)  experiment (requires login).

Download the file below for full instructions for the Simple harmonic motion (pendulum)   experiment (requires log in).

Download the file below for the background science behind the Simple harmonic motion (pendulum)  experiment (requires log in).

Teacher Resource Center

Pasco partnerships.

2024 Catalogs & Brochures

Force and acceleration.

Investigate the relationship between the net force applied to an object and the resulting acceleration of that object. A force is applied to a low friction cart using hanging masses over a pulley.

Grade Level: College

Subject: Physics

Student Files

Teacher Files

Sign In to your PASCO account to access teacher files and sample data.

Featured Equipment

Comprehensive 850 Mechanics Bundle

This bundle includes all the equipment and sensors needed to perform the experiments in the Comprehensive 850 Mechanics System Experiment Manual.

PASPORT High Resolution Force Sensor

The PASPORT High Resolution Force Sensor is designed to make very high resolution measurements of pulling and pushing forces.

PASPORT Motion Sensor

The PASPORT Motion Sensor accurately measures the position, velocity, and acceleration of a target. It can be used to track the motion of balls, carts, people, and more.

Basic PAScar Metal Track 1.2 m System

The Basic PAScar Metal Track 1.2 System includes plastic PAScar dynamics carts and a 1.2-m aluminum dynamics track. The accessories package is not included.

Many lab activities can be conducted with our Wireless , PASPORT , or even ScienceWorkshop sensors and equipment. For assistance with substituting compatible instruments, contact PASCO Technical Support . We're here to help. Copyright © 2018 PASCO

Source Collection: Lab #16

Comprehensive 850 Physics System

More experiments.

• Oscillation of Cart and Spring
• Light Intensity vs. Distance
• Electric Field Mapping
• Projectile Motion - Wireless

High School

• Acceleration
• Exploring a Rotating System

All Subjects

3.6 Centripetal Acceleration and Centripetal Force

1 min read • june 18, 2024

Kashvi Panjolia

Important Equations

The acceleration is equal to the rate of change of velocity with time, and velocity is equal to the rate of change of position with time.

Surprisingly, in uniform circular motion , in which an object has constant speed, there is an acceleration due to a  change in direction . Don’t forget, acceleration is a change in velocity, which is a  vector quantity that has both magnitude and direction!

Centripetal Acceleration

Centripetal acceleration is the acceleration that an object experiences when it moves in a circular path. This acceleration is directed toward the center of the circle. It is also known as  radial acceleration .

Imagine you are on a roller coaster and you experience the feeling of being pulled toward the center of the loop as you go through a loop-the-loop. This is an example of centripetal acceleration. The force that is pulling you toward the center of the loop is the centripetal force . 

Force and acceleration are both quantities that have both magnitude and direction. The direction of the net force acting on an object is the same as the direction of its acceleration. This means that if you want to change the direction of an object's acceleration, you need to change the direction of the net force acting on it. For example, if you want to change the direction of a car's acceleration so it is accelerating and turning right, you need to give it a rightward net force.

The  center of mass (COM) of a system is a point that represents the average position of all the mass in the system. Conceptually, it is the point where the entire mass of the system can be considered to be concentrated, which makes it the point at which the system would balance if it were suspended by a single point. The position of the center of mass depends on the distribution of mass within the system.

Consider a seesaw in a playground. The center of mass of a seesaw is located at the point where the board of the seesaw balances. This point is also known as the pivot point . If you place a heavier person on one side of the seesaw, the center of mass will shift closer to that side, and the seesaw will tilt in that direction.

The center of mass velocity is the velocity of the center of mass of the system, and it is equal to the rate of change of position of the center of mass with time. The acceleration of the center of mass is the rate of change of the center of mass velocity with time.

For example, if you want to know how fast a car is moving, you can measure its velocity. If you want to know how fast the car's velocity is changing, you can measure its acceleration. Similarly, if you want to know how fast the center of mass of a system is moving, you can measure its center of mass velocity, and if you want to know how fast the center of mass velocity is changing, you can measure the acceleration of the center of mass.

While the centripetal acceleration points towards the center of the circle, the velocity vector does not. A key element of uniform circular motion is that the velocity is kept constant, so in order to have acceleration due to a change in direction only, the velocity vector must be  tangent to the acceleration vector at all points along the circle. Tangent means that the velocity vector makes a  90-degree angle with the centripetal acceleration vector when the vectors are placed tail to tail.

Since the velocity and acceleration vectors make a 90-degree angle, there is no component of the centripetal acceleration that is acting in the same direction as the velocity vector, so the acceleration will not affect the magnitude of the velocity. However, the acceleration vector does affect the direction of the velocity vector. If you add the acceleration and velocity vectors using vector addition , you will find that the direction of the resultant vector is always pointing along the circle, causing uniform circular motion.

We can relate the centripetal acceleration to the tangential velocity using this equation:

where a is the centripetal acceleration, v is the velocity, and r is the radius of the circle.

Centripetal Force

The  centripetal force is defined as the force that is required to make an object move in a circular path. It is equal to the mass of the object multiplied by the centripetal acceleration. The formula for centripetal force is: F = m * a_c, where F is the centripetal force, m is the mass of the object and a_c is the centripetal acceleration.

Recall that the centripetal force is not a new force; it is just another name for the net force directed toward the center of the circle. This net force could be caused by the normal force, tension, gravitational force , friction , or another type of force.

For example, when a car takes a turn, the tires exert friction on the road, and the friction force is what provides the centripetal force to keep the car moving in a circular path. Similarly, when a planet is orbiting the sun, it is the gravitational force of the sun that acts as the centripetal force.

The direction of the centripetal force vector is always pointed toward the center of the circle, like the acceleration vector. This occurs because the accleration vector always points in the  same direction as the net force vector (in this case, the centripetal force) due to Newton's Second Law (F=ma).

It's also important to note that the greater the speed of an object, the greater the centripetal force required to keep it moving in a circular path. Similarly, the smaller the radius of a circular path, the greater the centripetal force required to keep an object moving in that path.

Practice Questions

1. What is the direction of the centripetal acceleration of an object undergoing uniform circular motion? A) Radial B) Tangential C) Perpendicular D) Horizontal

Answer: A) Radial

2. An object of mass 5 kg is moving in a circular path of radius 3 m with a constant velocity of 4 m/s. What is the centripetal acceleration of the object? A) 12 m/s^2 B) 16 m/s^2 C) 20 m/s^2 D) 5.33 m/s^2

Answer: D) 5.33 m/s^2 Explanation: To find the centripetal acceleration, we use the formula a_c = v^2/r, where a_c is the centripetal acceleration, v is the velocity of the object and r is the radius of the circular path. Substituting the given values, we get a_c = (4 m/s)^2 / 3 m = 16 m/s^2 / 3 m = 5.33 m/s^2

3. A ball of mass 1 kg is tied to a string and is moving in a circular path of radius 0.5 m. If the ball is moving with a velocity of 3 m/s, what is the centripetal force acting on the ball? A) 2.25 N B) 4.5 N C) 9 N D) 1.5 N

Answer: D) 1.5 N Explanation: The centripetal force acting on an object in uniform circular motion is given by the formula F = m * a_c, where F is the centripetal force, m is the mass of the object and a_c is the centripetal acceleration. To find the centripetal acceleration, we use the formula a_c = v^2/r, where a_c is the centripetal acceleration, v is the velocity of the object and r is the radius of the circular path. By substituting the given values, we get a_c = (3 m/s)^2 / 0.5 m = 9 m^2/s^2 / 0.5 m = 18 m/s^2Then we can use the formula F = m * a_c to find the centripetal force acting on the ball, we know the mass of the ball is 1 kg, so we substitute the values into the formula: F = m * a_c = 1 kg * 18 m/s^2 = 18 N

Key Terms to Review ( 17 )

© 2024 fiveable inc. all rights reserved., ap® and sat® are trademarks registered by the college board, which is not affiliated with, and does not endorse this website..

Core Practical: Investigating Force & Acceleration ( Edexcel GCSE Physics: Combined Science )

Revision note.

Core Practical 1: Investigating Force & Acceleration

Equipment list.

• Metre ruler = 1 mm
• Stopwatch = 0.01 s

Experiment 1: Investigating the Effect of Force on Acceleration

Aim of the experiment.

• The aim of this experiment is to investigate the effect of varying force on the acceleration of an object of constant mass
• Independent variable = force, F
• Dependent variable = acceleration, a

Force and acceleration apparatus setup

• Use the metre ruler to measure out intervals on the bench, e.g. every 0.2 m for a total distance of 1 m. Draw straight lines with pencil or chalk across the table at these intervals
• Attach the bench pulley to the end of the bench
• Tie some string to the toy car or trolley
• Pass the string over the pulley and attach the mass hanger to the other end of the string
• Make sure the string is horizontal (i.e. parallel to the bench) and is in line with the toy car or trolley
• Hold the toy car or trolley at the start point
• Attach the full set of weights (total = 1.0 N) to the end of the string
• Release the toy car or trolley at the same time as you or a partner starts the stopwatch. Press the stopwatch (in lap mode) at each measured interval on the bench and for the final time at 1.0 m
• Record the results in the table and repeat step 8 to calculate an average time for each interval
• Repeat steps 6-9 for decreasing weights on the weight hanger, e.g. 0.8 N, 0.6 N, 0.4 N, and 0.2 N. Make sure you place the masses that you remove from the weight stack onto the top of the car, using the Blu-tac, each time you decrease the weight
• A possible results table is illustrated as an example below:

Analysis of Results

• Use the table of results to determine the average speed of the trolley between intervals
• This is done using the equation:

• Compare the average speed between the first and last intervals for different weights
• Use the equation below to calculate the acceleration between the first and the last intervals:

• Do this for each different weight, comparing how the acceleration varies

Experiment 2: Investigating the Effect of Mass on Acceleration

• The aim of this experiment is to investigate the effect of varying mass on the acceleration of an object produced by a constant force
• Independent variable = mass, m
• Put a 200 g mass on the car
• Select a weight to put on the weight hanger that will gently accelerate the car along the bench. This provides the constant force on the car or trolley and will not change
• Hold the car at the start point
• Release the car at the same time as you or a partner start the stopwatch. Press the stopwatch (in lap mode) at each measured interval on the bench and for the final time at 1.0 m
• Repeat steps 6-9 for increasing mass on the car, e.g. 400 g, 600 g, 800 g and 1000 g

• As in Experiment 1, use the table of results to determine the average speed of the trolley between intervals
• This is done using the equation
• Do this for each different mass on top of the toy car or trolley, comparing how the acceleration varies

Evaluating the Experiments

• This is to ensure the total mass of the system remains constant
• Ensure to take repeat readings when timing intervals and calculate an average to keep this error to a minimum
• Ensure not to give it a 'push'

Safety Considerations

• Place a crash mat underneath the weight hanger just in case this happens
• If you need to use an equation to calculate something, start off by giving it as this will give you some hints about what you need to mention later
• List the apparatus that you need
• State what measurements you need to make (your equation will give you some hints) and how you will measure them
• Finally, state that you will repeat each measurement several times and take averages

You've read 0 of your 10 free revision notes

Get unlimited access.

to absolutely everything:

• Downloadable PDFs
• Unlimited Revision Notes
• Topic Questions
• Past Papers
• Model Answers
• Videos (Maths and Science)

Join the 100,000 + Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

Author: Katie M

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.

NTRS - NASA Technical Reports Server

Available downloads, related records.

Information

• Author Services

Initiatives

You are accessing a machine-readable page. In order to be human-readable, please install an RSS reader.

All articles published by MDPI are made immediately available worldwide under an open access license. No special permission is required to reuse all or part of the article published by MDPI, including figures and tables. For articles published under an open access Creative Common CC BY license, any part of the article may be reused without permission provided that the original article is clearly cited. For more information, please refer to https://www.mdpi.com/openaccess .

Feature papers represent the most advanced research with significant potential for high impact in the field. A Feature Paper should be a substantial original Article that involves several techniques or approaches, provides an outlook for future research directions and describes possible research applications.

Feature papers are submitted upon individual invitation or recommendation by the scientific editors and must receive positive feedback from the reviewers.

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

Original Submission Date Received: .

• Active Journals
• Find a Journal
• Proceedings Series
• For Authors
• For Reviewers
• For Editors
• For Librarians
• For Publishers
• For Societies
• For Conference Organizers
• Open Access Policy
• Institutional Open Access Program
• Special Issues Guidelines
• Editorial Process
• Research and Publication Ethics
• Article Processing Charges
• Testimonials
• Preprints.org
• SciProfiles
• Encyclopedia

Article Menu

• Subscribe SciFeed
• Recommended Articles
• Google Scholar
• on Google Scholar
• Table of Contents

Find support for a specific problem in the support section of our website.

Please let us know what you think of our products and services.

Visit our dedicated information section to learn more about MDPI.

JSmol Viewer

Development of a fast positioning platform with a large stroke based on a piezoelectric actuator for precision machining, 1. introduction, 2. conceptual design and analysis of the fpp mechanism, 2.1. conceptual design, 2.2. input and output characteristic of fpp, 2.3. structural design of flexible hinges, 3. finite element analysis of fpp, 3.1. static structure analysis, 3.2. modal analysis, 4. performance testing experiments, 5. conclusions, author contributions, data availability statement, conflicts of interest.

• Fang, F.Z.; Zhang, X.D.; Weckenmann, A.; Zhang, G.X.; Evans, C. Manufacturing and measurement of freeform optics. CIRP Ann. 2013 , 62 , 823–846. [ Google Scholar ] [ CrossRef ]
• Dow, T.A.; Miller, M.H.; Falter, P.J. Application of a fast tool servo for diamond turning of nonrotationally symmetric surfaces. Precis. Eng. 1991 , 13 , 243–250. [ Google Scholar ] [ CrossRef ]
• Patterson, S.; Magrab, E. Design and testing of a fast tool servo for diamond turning. Precis. Eng. 1985 , 7 , 123–128. [ Google Scholar ] [ CrossRef ]
• Ku, S.-S.; Larsen, G.; Cetinkunt, S. Fast tool servo control for ultra-precision machining at extremely low feed rates. Mechatronics 1998 , 8 , 381–393. [ Google Scholar ] [ CrossRef ]
• Kim, H.-S.; Lee, K.-I.; Lee, K.-M.; Bang, Y.-B. Fabrication of free-form surfaces using a long-stroke fast tool servo and corrective figuring with on-machine measurement. Int. J. Mach. Tools Manuf. 2009 , 49 , 991–997. [ Google Scholar ] [ CrossRef ]
• Bhokare, S.G.; Behera, B. Motion improvised miniaturized dual focus lens module based on piezoelectric actuator for the medical applications. Ferroelectrics 2022 , 598 , 68–78. [ Google Scholar ] [ CrossRef ]
• Delibas, B.; Koc, B.; Thielager, J.; Stiebel, C. A novel drive and control method for piezoelectric motors in microscopy stages. In Proceedings of the Euspen’s 21st International Conference & Exhibition, Copenhagen, Denmark, 7–10 June 2021. [ Google Scholar ]
• Mohith, S.; Upadhya, A.R.; Navin, K.P.; Kulkarni, S.; Rao, M. Recent trends in piezoelectric actuators for precision motion and their applications: A review. Smart Mater. Struct. 2020 , 30 , 013002. [ Google Scholar ] [ CrossRef ]
• Yuan, Y.; Zhang, D.; Jing, X.; Ehmann, K.F. Freeform surface fabrication on hardened steel by double frequency vibration cutting. J. Mater. Process. Technol. 2020 , 275 , 116369. [ Google Scholar ] [ CrossRef ]
• Brinksmeier, E.; Riemer, O.; Gläbe, R.; Lünemann, B.; Kopylow, C.; Dankwart, C.; Meier, A. Submicron functional surfaces generated by diamond machining. CIRP Ann. 2010 , 59 , 535–538. [ Google Scholar ] [ CrossRef ]
• Gao, W.; Aoki, J.; Ju, B.-F.; Kiyono, S. Surface profile measurement of a sinusoidal grid using an atomic force microscope on a diamond turning machine. Precis. Eng. 2007 , 31 , 304–309. [ Google Scholar ] [ CrossRef ]
• Gan, S.; Lim, H.; Rahman, M. A high precision piezoelectric fine tool servo system for diamond turning. In Proceedings of the 1st International Conference on Nanomanufacturing, Singapore, 15–31 March 2008. [ Google Scholar ]
• Zhu, Z.; Zhou, X.; Liu, Q.; Zhao, S. Multi-objective optimum design of fast tool servo based on improved differential evolution algorithm. J. Mech. Sci. Technol. 2011 , 25 , 3141–3149. [ Google Scholar ] [ CrossRef ]
• Das, T.K.; Shirinzadeh, B.; Al-Jodah, A.; Ghafarian, M.; Pinskier, J. A novel compliant piezoelectric actuated symmetric microgripper for the parasitic motion compensation. Mech. Mach. Theory 2021 , 155 , 104069. [ Google Scholar ]
• Wang, F.; Zhao, X.; Huo, Z.; Shi, B.; Liang, C.; Tian, Y.; Zhang, D. A 2-DOF nano-positioning scanner with novel compound decoupling-guiding mechanism. Mech. Mach. Theory 2021 , 155 , 104066. [ Google Scholar ] [ CrossRef ]
• Ding, B.; Li, Y. Design and analysis of a decoupled XY micro compliant parallel manipulator. In Proceedings of the 2014 IEEE International Conference on Robotics and Biomimetics (ROBIO 2014), Bali, Indonesia, 5–10 December 2014; pp. 1898–1903. [ Google Scholar ]
• Tian, Y.; Lu, K.; Wang, F.; Zhou, C.; Ma, Y.; Jing, X.; Yang, C.; Zhang, D. A Spatial Deployable Three-DOF Compliant Nano-Positioner with a Three-Stage Motion Amplification Mechanism. IEEE/ASME Trans. Mechatron. 2020 , 25 , 1322–1334. [ Google Scholar ] [ CrossRef ]
• Tang, H.; Gao, J.; Chen, X.; Yu, K.-M.; To, S.; He, Y.; Chen, X.; Zeng, Z.; He, S.; Chen, C. Development and repetitive-compensated PID control of a nanopositioning stage with large-stroke and decoupling property. IEEE Trans. Ind. Electron. 2017 , 65 , 3995–4005. [ Google Scholar ] [ CrossRef ]
• Gere, J.M.; Goodno, B.J. Mechanics of Materials , 5th ed.; Brooks Cole: Pacific Grove, CA, USA, 2001; Volume 780. [ Google Scholar ]
• Zhou, X.; Zuo, C.; Liu, Q.; Wang, R.; Lin, J. Development of a double-frequency elliptical vibration cutting apparatus for freeform surface diamond machining. Int. J. Adv. Manuf. Technol. 2016 , 87 , 2099–2111. [ Google Scholar ] [ CrossRef ]

Click here to enlarge figure

Share and Cite

Hu, G.; Xin, W.; Zhang, M.; Chen, G.; Man, J.; Tian, Y. Development of a Fast Positioning Platform with a Large Stroke Based on a Piezoelectric Actuator for Precision Machining. Micromachines 2024 , 15 , 1050. https://doi.org/10.3390/mi15081050

Hu G, Xin W, Zhang M, Chen G, Man J, Tian Y. Development of a Fast Positioning Platform with a Large Stroke Based on a Piezoelectric Actuator for Precision Machining. Micromachines . 2024; 15(8):1050. https://doi.org/10.3390/mi15081050

Hu, Gaofeng, Wendong Xin, Min Zhang, Guangjun Chen, Jia Man, and Yanling Tian. 2024. "Development of a Fast Positioning Platform with a Large Stroke Based on a Piezoelectric Actuator for Precision Machining" Micromachines 15, no. 8: 1050. https://doi.org/10.3390/mi15081050

Article Metrics

Article access statistics, further information, mdpi initiatives, follow mdpi.

Subscribe to receive issue release notifications and newsletters from MDPI journals

• Share full article

For more audio journalism and storytelling, download New York Times Audio , a new iOS app available for news subscribers.

• Apple Podcasts
• Google Podcasts

Biden Leaves the Stage

On president biden’s private pain since stepping aside, and his public message at the democratic national convention..

Hosted by Sabrina Tavernise

Featuring Katie Rogers and Peter Baker

Produced by Rob Szypko Lynsea Garrison Carlos Prieto Stella Tan and Jessica Cheung

Edited by Rachel Quester and Paige Cowett

Original music by Marion Lozano Dan Powell Rowan Niemisto and Corey Schreppel

Engineered by Chris Wood

Listen and follow ‘The Daily’ Apple Podcasts | Spotify | Amazon Music | YouTube | iHeartRadio

On the first night of the Democratic National Convention, the stage belonged to the man who chose to give it up.

Katie Rogers and Peter Baker, White House correspondents for The Times, discuss President Biden’s private pain since stepping aside, and his public message in Chicago.

On today’s episode

Katie Rogers , a White House correspondent for The New York Times.

Peter Baker , the chief White House correspondent for The New York Times.

Background reading

Biden defended his record and endorsed Kamala Harris : “America, I gave my best to you.”

Analysis: The speech Biden never wanted to give .

There are a lot of ways to listen to The Daily. Here’s how.

We aim to make transcripts available the next workday after an episode’s publication. You can find them at the top of the page.

The Daily is made by Rachel Quester, Lynsea Garrison, Clare Toeniskoetter, Paige Cowett, Michael Simon Johnson, Brad Fisher, Chris Wood, Jessica Cheung, Stella Tan, Alexandra Leigh Young, Lisa Chow, Eric Krupke, Marc Georges, Luke Vander Ploeg, M.J. Davis Lin, Dan Powell, Sydney Harper, Michael Benoist, Liz O. Baylen, Asthaa Chaturvedi, Rachelle Bonja, Diana Nguyen, Marion Lozano, Corey Schreppel, Rob Szypko, Elisheba Ittoop, Mooj Zadie, Patricia Willens, Rowan Niemisto, Jody Becker, Rikki Novetsky, Nina Feldman, Will Reid, Carlos Prieto, Ben Calhoun, Susan Lee, Lexie Diao, Mary Wilson, Alex Stern, Sophia Lanman, Shannon Lin, Diane Wong, Devon Taylor, Alyssa Moxley, Olivia Natt, Daniel Ramirez and Brendan Klinkenberg.

Our theme music is by Jim Brunberg and Ben Landsverk of Wonderly. Special thanks to Sam Dolnick, Paula Szuchman, Lisa Tobin, Larissa Anderson, Julia Simon, Sofia Milan, Mahima Chablani, Elizabeth Davis-Moorer, Jeffrey Miranda, Maddy Masiello, Isabella Anderson, Nina Lassam and Nick Pitman.

Katie Rogers is a White House correspondent. For much of the past decade, she has focused on features about the presidency, the first family, and life in Washington, in addition to covering a range of domestic and foreign policy issues. She is the author of a book on first ladies. More about Katie Rogers

Peter Baker is the chief White House correspondent for The Times. He has covered the last five presidents and sometimes writes analytical pieces that place presidents and their administrations in a larger context and historical framework. More about Peter Baker

Advertisement