rubber band mass experiment

April 5, 2012

Snappy Science: Stretched Rubber Bands Are Loaded with Potential Energy!

A fun physics problem from Science Buddies

By Science Buddies

Key concepts Physics Mathematics Energy Projectiles

Introduction If you've ever been shot with a rubber band then you know it has energy in it—enough energy to smack you in the arm and cause a sting! But have you ever wondered what the relationship is between a stretched rubber band at rest and the energy it holds? The energy the rubber band has stored is related to the distance the rubber band will fly after being released. So can you guess one way to test how much energy a stretched rubber band contains?

Background No mechanical contraption would be any fun if it did not work. But "work," in the physics sense, takes energy. Consider a rope and pulley that bring a bucket up a well. The energy that makes this mechanical system work is provided by a person who pulls up the rope.

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There are actually two different kinds of energy: potential energy, which is stored energy, and kinetic energy, which is energy in motion. A great example of the difference between kinetic and potential energy is from the classic "snake-in-a-can" prank. This is an old joke where you give someone a can of peanuts and tell them to open it, but inside is actually a long spring that pops out when the lid is twisted off. Because the spring is usually decorated to look like a snake, this prank usually causes the victim to jump back and shout in surprise! When the snaky spring is compressed and secured inside the unopened can, it has potential energy. But when the can is opened, the potential energy quickly converts to kinetic energy as the fake snake jumps out. Materials •    A long, wide concrete sidewalk, driveway or other hard surface that you can draw on with chalk (as an alternative, you can make distance markers out of paper and place them on a surface on which you cannot draw) •    Sidewalk chalk •    Metric ruler •    Rubber bands (all of the same length and kind) •    A helper •    Metric tape measure •    Paper and pencil or pen Preparation •    Find a helper, gather your supplies and go outside to do this activity. You will want a place with a lot of clearance that has a concrete or other hard surface on which you can draw with chalk. •    Your partner will draw circles around where the flying rubber bands land, so choose a person with a keen eye and some running shoes! •    Use caution to shoot the rubber bands out in front of you—and make sure no one is in the flight path! If necessary, have an adult do the rubber band launching. Procedure •    At the outside place you picked, stand where there is lots of clearance in front of you. With your chalk, draw a line in front of your toes. This is where you will line your feet up when you shoot your rubber bands. This is also the mark from where you will measure the distances your rubber bands have flown. •    Your helper can stand a few meters in front of you, but off to the side, not directly in the line of fire! Make sure he or she has a piece of chalk. •    Shoot a rubber band by hooking it on the front edge of the ruler, then stretching it back to 10 centimeters (cm) on the ruler and letting the rubber band go. Remember the angle and height at which you hold the ruler because you will need to keep it the same for each rubber band launch. •    Have your helper draw a small chalk circle where the rubber band landed. •    Shoot at least four more rubber bands in the same way, stretching them back to 10 cm on the ruler each time. Have your helper circle where each lands. •    Measure the distances from your line to the circles your helper made. Write these distances down under the heading "10 cm." Did all five rubber bands land close to each other or was there a lot of variation in where they fell? •    Shoot more rubber bands in the same way, except stretch them back to 15 cm, 20 cm, 25 cm or 30 cm. Shoot at least five rubber bands for each stretch length. After each launch, have your helper circle where they land. After launching five rubber bands at a given stretch length, measure the distances from your line to the circles. Write these distances under a heading for their stretch length (for example, "20 cm"). •    For each stretch length, did all five rubber bands land close to one another or was there a lot of variation? Did they land far from where the rubber bands landed that were launched using different stretch lengths? •    Average your results for each stretch length and make a graph of your results by putting "Stretch Length (cm)" on the x -axis (this will be 10 cm, 15 cm, 20 cm, 25 cm and 30 cm) and "Launch Distance (cm)" on the y -axis (this will be the distances you measured). Do your data follow any type of pattern or trend? What was the relationship between the stretch length and the launch distance? What do you think this indicates about the relationship between potential and kinetic energy when using rubber bands? •     Tip: If you run out of rubber bands, you can always grab some of the ones you already used and reuse them because there will be a chalk circle where they landed. •     Extra: In this activity you kept the angle and height of the launch the same from trial to trial. How do these variables affect the distance the rubber band travels? Design a separate activity to test each of these variables separately. •     Extra: You can do a very similar activity to this one by using other types of mechanical systems, such as springs and slingshots. How do the data collected using these other mechanical systems compare with that collected using rubber bands? •     Extra: For an advanced challenge, you can use linear regression to further analyze your data. Can you define an equation that expresses the relationship between potential and kinetic energy in this system? Observations and results Did the rubber bands stretched to 30 cm launch farther than the other rubber bands? Did you see a linear relationship between the launch distance and stretch length when you graphed your data?

You input potential (stored) energy into the rubber band system when you stretched the rubber band back. Because it is an elastic system, this kind of potential energy is specifically called elastic potential energy. Elastic potential energy (measured in the unit joules) is equal to ½ multiplied by the stretch length (" x ") squared, multiplied by the spring constant " k ." The spring constant is different for every rubber band, but can be figured out (see "Welcome to the Guide to Shooting Rubber Bands" below). When the rubber band is released, the potential energy is quickly converted to kinetic (motion) energy. This is equal to one half the mass (of the rubber band) multiplied by its velocity (in meters per second) squared.

Using these equations, you can calculate the velocity of the rubber band right when it is released, and find that the velocity has a linear relationship with the stretch length. (Because the amount of time that the rubber band spends in the air is dependent on its initial height and force of gravity, and these factors should not change between your trials, then how far the rubber band flies depends on its initial velocity.) Consequently, after you graph your data, you should see a roughly linear relationship between the stretch length and the launch distance.

More to explore What Is Energy? from Wisconsin K-12 Energy Education Program (KEEP) Energy Conversions: Potential Energy to Kinetic Energy from FT Exploring Science and Technology Welcome to the Guide to Shooting Rubber Bands: The Physics of Shooting by Tim Morgan Rubber Bands for Energy from Science Buddies This activity brought to you in partnership with Science Buddies  

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Stretching Rubber Bands

We can use common household objects to measure properties that match physical laws. This experiment takes a very common household item, the rubber band, and applies physical laws (Hooke’s Law and the Young’s Modulus) to them in a hands-on way.

To describe the stretching action of rubber bands, and explore the connection between Hooke’s Law and Young’s modulus.

Introduction:

Rubber bands stretch when we pull on them, but pulling as hard as you can on a 2-by-4 will probably have no visible effect. The stretchability of solid materials is expressed as their Young’s Modulus (a.k.a. “Elastic Constant”), $Y$. Here is the formula for Young’s modulus (Eqn.1):

$Y=\dfrac{\dfrac{F}{A}}{\dfrac{\ \Delta L\ }{L_0}} \tag{1}$

• $F$ = Force applied to solid [N]
• $A$ = Cross-sectional area of solid [m$^2$]
• $L$ = stretched length of solid [m]
• $L_0$ = original length of solid [m]

A simple way to understand this formula is $Y = \frac{\text{stress}}{\text{strain}}$. The stress is the amount of force applied to the object, per unit area ($F/A$). The strain is the relative change in the length of the solid ($\Delta L/L_0$). Therefore, a solid with a greater value of $Y$ will stretch less than a solid with a smaller $Y$, when the same force is applied.

Let’s return to rubber bands. Rubber bands are elastic solids and can be described with Hooke’s Law (Eqn.2). We can think of Hooke’s Law as a simplified version of Young’s Modulus, and it is classically applied to spring systems. However, it can also, to some extent, describe the stretch patterns observed for rubber bands.

$F=k \Delta L \tag{2}$

• $F$ = Force applied to elastic material [N]
• $k$ = spring constant [N/m]
• $ΔL$ = change in length of the elastic material [m]

If you compare the two equations, you will find (try this as an exercise) that the spring constant $k$ contains Young’s modulus $Y$ (which describes the material), the length $L_0$, and the cross-sectional area $A$ of the material, can be related as in Eqn.3.

$k=Y\dfrac{A}{L_0} \tag{3}$

This allows us now to make predictions before we do an experiment. For example, a thicker rubber band should have a larger spring constant due to its larger cross-sectional area. In this experiment you can check this prediction and investigate the way in which Hooke’s Law applies to rubber bands. You can also think about what happens if you use two rubber bands at the same time, either to hang an object from both bands in parallel or to create a longer band by knotting one band to the end of the other band. Write down your hypothesis and test it with an experiment.

The Challenge:

Design an experiment to measure the constant $k$ for rubber bands. Use items of known mass to provide the applied force. Measure the change in length and the original length for each rubber band; also record the physical properties of each band.

Key Concepts: • Young’s modulus is a measure of stress over strain. • Hooke’s Law takes only applied force and change in length into account. • Different rubber bands will have different constants for both laws.

Skills: • Applying Hooke’s Law • Relating graphs of experimental data to given equations • Understanding relationship between Hooke’s Law and Young’s modulus • Simple graphical analysis • Assigning errors and understanding error calculations

Materials/Equipment: • Three rubber bands of different sizes and thicknesses • Objects of given weight (granola bars, packaged foods, etc.) • Small metal hanger • Pushpin • Ruler (30cm) or flexible tape measure

Suggested assigned time: 2 weeks

Question to think about: • Why does Hooke’s law not apply for greater forces? • Why is Young’s modulus a more general descriptor of rubber band action than Hooke’s law?

Variations: • Try the experiment with something other than a rubber band. • Compare rubber band action with spring action. How do the graphs for Hooke’s law compare? • Combine multiple rubbers bands and analyze stretching action.

“ Do Rubber Bands Act Like Springs? ” article in Wired Magazine[note] Do Rubber Bands Act Like Springs? https://www.wired.com/2012/08/do-rubber-bands-act-like-springs /[2019-10-16].[/note] goes further and investigates the elastic hysteresis[note] Elastic Hysteresis, https://en.wikipedia.org/wiki/Hysteresis#Elastic_hysteresis [2019-10-16].[/note] of rubber bands.

Revised 2019-10-16

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• Young’s modulus is a measure of stress over strain.
• Hooke’s Law takes only applied force and change in length into account.
• Different rubber bands will have different constants for both laws.

Rubber Band Cannons: Harnessing Elastic Energy for Fun Projectile Experiments

Table of Contents

Rubber band cannons are a delightful blending of physics and fun, allowing you to explore the principles of elastic energy through hands-on experimentation. When you stretch a rubber band and let it snap, you’re releasing stored elastic energy in a way that’s analogous to how a real cannon fires a projectile. But instead of gunpowder, you’re using the potential energy stored in the stretched rubber band to propel your projectile forward.

Building a rubber band cannon is an exercise in ingenuity and understanding the mechanics behind elastic energy. The design and construction of your cannon will dictate its firing power and accuracy, as the elasticity of the rubber band interacts with the mass and shape of the projectile. Observing motion, load, and mass through your rubber band cannon, you can gain insight into the fundamentals of projectile motion and energy transfer in a safe and controlled environment.

Michelle Connolly, the founder of LearningMole and an educational consultant with a wealth of classroom experience, often says, “It’s through playful exploration that the most profound learning occurs, turning complicated physics into a tangible and joyous discovery.”

Key Takeaways

• Rubber band cannons utilise stored elastic energy to propel projectiles.
• Design variables like rubber band elasticity and projectile mass affect the cannon’s performance.
• Observational experiments with rubber band cannons can elucidate projectile motion principles.

The Science of Elastic Energy

Elastic energy plays an integral role in objects that stretch or compress, like rubber bands in cannons. This energy is crucial to understanding how these items are able to store and release energy.

Understanding Elastic Potential Energy

Elastic potential energy is the energy stored in an object when it is stretched or compressed. For instance, when you pull back a rubber band on a cannon, you are filling it with this type of energy. It’s the same kind of energy that allows a diving board to bend and then launch a diver into the air. In the context of a rubber band cannon, the stretched rubber band has the potential to do work when it’s released, propelling the projectile.

Properties of Elastic Potential Energy :

• Directly proportional to the stretch or compression.
• Depend on the material’s elasticity.

Conservation of Energy in Elastic Systems

The conservation of energy principle states that energy within a closed system is constant; it can neither be created nor destroyed, only transformed from one form to another. In elastic systems like rubber band cannons, the elastic potential energy is converted into kinetic energy—the energy of motion—as the rubber band returns to its normal shape and propels the projectile forward.

Key Points :

• Total energy is conserved when potential is converted to kinetic.
• Efficiency of energy transfer depends on material properties.

As Michelle Connolly, founder of LearningMole and an educational consultant with significant teaching experience, aptly puts it, “Energy transformation in a rubber band cannon is a tangible example for students learning the physics of elastic potential energy and conservation of energy.” The simplicity of rubber band cannons can teach you complex principles of physics in an interactive and engaging way.

Rubber Band Mechanics

In this exploration of rubber band mechanics, you will discover how stretching, various variables, and the forces involved result in the deformation of rubber bands. Understanding these mechanisms can improve the performance of rubber band cannons.

Stretching Rubber Bands

When you stretch a rubber band, you’re storing elastic energy within it. This stored energy, when released, allows the rubber band to perform work, such as propelling a projectile. The extent to which the rubber band is stretched plays a critical role in determining the amount of energy stored.

Variables Affecting Rubber Band Elasticity

Several variables influence how a rubber band deforms and returns to its original shape. The material’s temperature and the rate at which it is stretched can all impact elasticity. The age and the previous amount of use can also affect a rubber band’s elasticity, making it more prone to breakage or less able to hold its shape.

Force and Deformation

The relationship between the force applied and a rubber band’s deformation is non-linear. As you apply more force, the rubber band stretches correspondingly until it reaches its limit of elasticity. Michelle Connolly, an educational consultant, explains, “The fascinating part of rubber band mechanics is observing how they deform and eventually reach a point where they can’t return to their original shape. That’s a hands-on demonstration of material limits and elasticity.”

Each section of your understanding of rubber bands as mechanical devices helps make your homemade rubber band cannon more effective, by considering the energy stored from stretching a band to the variables that affect its performance.

Designing a Rubber Band Cannon

Designing an effective rubber band cannon requires careful consideration of the materials used, the underlying mechanical principles, and the launch mechanism preparation. When done correctly, you can transform simple household items into a fascinating exploration of physics and mechanics.

Material Selection

For constructing a rubber band cannon , it’s imperative to choose materials that are both sturdy and lightweight. A combination of plywood for the frame and rubber bands for the launching mechanism creates a balanced dynamic for projectile launching. Select a rubber band that is thick enough to withstand the tension without breaking, but elastic enough to store sufficient potential energy.

Mechanical System Principles

Understanding the mechanical system at play is crucial. Your cannon operates on the principle of elastic potential energy —as the rubber band stretches, it stores energy. When released, this energy is converted into kinetic energy, propelling the projectile. The tension and elasticity of the rubber band must be balanced to maximize the energy conversion.

Preparing the Launch Mechanism

Preparation of the launch mechanism involves securing the rubber band to the cannon while ensuring it has a smooth pathway for release. Cut notches in the frame to hold the rubber band in place, and use a trigger mechanism to control the release. Prepare your cannon by carefully stretching the rubber band to avoid premature snapping and ensure consistent performance.

“By encouraging children to build their own rubber band cannons, we’re not just teaching them about physics; we’re sparking an interest in the mechanics behind everyday objects,” shares Michelle Connolly, founder of LearningMole and an educational consultant with extensive classroom experience.

Projectiles and Motion

In this exploration of rubber band cannons, we will examine how elastic energy is converted into kinetic energy, propelling a projectile through the air. The principles of motion dictate the trajectory, and factors such as the angle of launch critically influence the path and velocity of the projectile.

Dynamics of Rubber Band Projectiles

When you release a stretched rubber band from a cannon, the stored elastic energy is suddenly converted into kinetic energy. The velocity at which the projectile, in this case, a rubber band, moves is directly influenced by the amount of elastic potential energy it had. The more you stretch the rubber band, the greater the kinetic energy will be upon release.

However, kinetic energy isn’t the only thing determining how far and fast your rubber band flies. Air resistance and gravity also play roles, slowing the rubber band down and pulling it towards the ground.

Angle of Launch and Its Effects

The angle of launch is critical to the motion and trajectory of your rubber band projectile. An angle of 45 degrees is often considered ideal for achieving maximum range, balancing both height and distance. Here’s how the angle you choose affects the motion:

• 0 degrees (horizontal launch) : The rubber band flies straight but quickly succumbs to gravity and falls to the ground.
• 45 degrees : Offers a blend of height and horizontal distance, often resulting in the greatest range.
• 90 degrees (vertical launch) : The rubber band shoots upwards, but it will not travel any horizontal distance.

The conditions of motion for your rubber band projectiles are a delicate dance between potential and kinetic energy, the angle of launch, and the inevitable forces of gravity and air resistance. By adjusting these variables, you can predict and alter the path your rubber band will take through the air.

The Mathematics Behind Rubber Band Cannons

Before launching into the complexities of rubber band cannons, it’s key to understand that it’s the elastic energy stored in the stretched rubber band that gets converted into kinetic energy. This translates into the cannonball’s motion . You’ll see how potential and kinetic energy calculations, spring constants, and linear regression can determine the distance a projectile will travel.

Calculating Potential and Kinetic Energy

When you pull back a rubber band on a rubber band cannon, you’re storing potential energy . Fundamentally, the potential energy (PE) of a stretched rubber band is calculated using the formula PE = 1/2 k x^2, where ‘k’ is the spring constant and ‘x’ is the displacement from its equilibrium position. Once released, this potential energy transforms into kinetic energy (KE), propelling the projectile. The kinetic energy can be found using the formula KE = 1/2 m v^2, where ‘m’ is the mass of the projectile and ‘v’ is its velocity.

Exploring the Spring Constant

The spring constant (k) is crucial in understanding a rubber band cannon’s power. It’s a measure of the elasticity of the spring—or in this case, the rubber band. Mathematically, it’s the ratio of the force exerted on the rubber band to the displacement (Force = k * displacement). A higher spring constant means a stiffer rubber band, requiring more force to stretch but potentially providing more energy to the projectile.

Linear Regression and Projectile Distance

To predict the distance a rubber band cannonball might travel, you can use linear regression . By plotting a graph of the distance travelled (dependent variable) against various levels of potential energy (independent variable), you can develop a linear equation that models the relationship. This equation can then be used to estimate distances for different potential energy levels. It’s a practical application of mathematics that brings predictability to the seemingly chaotic motion of projectiles.

Remember, each stretch of the rubber band is an experiment in physics , governed by theorems and equations. It’s not just about the thrill of seeing how far it’ll go but understanding the principles that make it happen. Michelle Connolly, founder of LearningMole and an educational consultant with 16 years of classroom experience, emphasises, “Playing with rubber band cannons provides a tangible way to connect children with the abstract concepts of energy and physics.”

Experimental Procedure and Observation

Before you begin experimenting with rubber band cannons, it’s crucial to understand the experimental procedure and the importance of meticulous observation. This will ensure that you can accurately measure the elastic energy and the movement of your projectile.

Setting up Experiments with Rubber Bands

To set up your experiments, you’ll need a rubber band cannon, a set of rubber bands, and a target area. Ensure that your cannon is securely mounted and that all variables, such as the angle of launch and the tension in the rubber bands, are consistently controlled. Stretch the rubber band to a measured distance before each shot, and launch several projectiles to test repeatability.

Recording Observations and Measurements

As you conduct your experiments, record all measurements precisely. Note down the stretch length of the rubber band and the distance each projectile travels. Observe the behaviour of the rubber band during launch: how it contracts and propels the projectile. The results you gather should reflect how changes in variables, like stretching the rubber band further, impact the distance travelled.

Michelle Connolly, founder of LearningMole, highlights that “Accurate recordings during experiments reinforce the learning process, offering practical insight into theoretical concepts.”

Remember, detailed observations are not only about what you expect to happen but also about any unusual occurrences. These unexpected results can be just as valuable for understanding the principles at play.

Analysing Results

In this section, we look at how you can interpret the elastic energy of rubber band cannons through the projectiles’ distance and speed, as well as the significance of graphical representations of such results.

Interpreting Distance and Speed Data

When you launch a rubber band from a cannon, measuring the distance it travels and the speed it maintains are critical for understanding the elastic energy conversion. By comparing distance values, you can infer the elasticity and potential energy of the rubber band. Furthermore, calculating the speed provides insight into energy efficiency and how much of that potential energy converts to kinetic energy.

“It’s astonishing to see how a simple experiment with a rubber band cannon can vividly demonstrate the principles of physics in action,” states Michelle Connolly, an expert with over 16 years of experience in the classroom.

Graphs and Their Significance

Graphs play a crucial role in analysing your results. A distance-time graph can show you the rubber band’s acceleration, which should peak as it leaves the cannon. You might also consider a speed-distance graph to visualise how speed alters in relation to the distance travelled. These visuals aid in identifying patterns and anomalies that might not be evident from raw data alone.

It’s vital to interpret these graphs with a critical eye, looking for consistency and repeatability in the results which echo the rubber band’s performance and the underlying physical laws.

Impact of Load and Mass

Understanding the impact of load and mass on the performance of rubber band cannons is crucial. How you manage these factors determines the energy stored and the velocity of the projectile once released.

Load Impact on Rubber Band Cannon Performance

Load refers to the force applied to the rubber band when stretching it to launch a projectile. Increasing the load by pulling the rubber band further converts more potential energy into kinetic energy once released. However, there’s a limit; exceed the elastic limit, and the rubber band may snap, failing to launch the projectile.

Mass and Speed Relationship

The mass of the projectile is a critical factor in determining its speed. A lighter projectile requires less energy to reach higher velocities, whereas heavier objects will generally travel at lower speeds for the same amount of stored energy. The relationship between the two is inversely proportional, meaning as the mass increases, the velocity will decrease, assuming all other variables remain constant.

Michelle Connolly, the founder of LearningMole and an educational consultant with extensive classroom experience, comments, “When teaching the principles of physics through engaging projects like rubber band cannons, observing the effects of mass and load on energy transformation not only cements the concept, but sparks curiosity.”

Real-World Applications

The incorporation of rubber band cannons in various contexts bridges the gap between engineering principles and hands-on educational experiences, equipping learners with a practical understanding of physics and design.

Engineering Principles of Rubber Band Cannons

Rubber band cannons serve as a prime example of elastic potential energy being converted into kinetic energy – a fundamental concept in mechanics. This transformation occurs when the tension within the stretched rubber band is released, propelling the projectile. It demonstrates how energy is stored and released , an essential principle in the design and functioning of real-world machinery and devices.

In the context of engineering, these cannons can be used to explore the effects of force, mass, and trajectory, which are pertinent when designing anything from automotive components to ballistic objects. The efficiency of energy transfer from the elastic band to the projectile underscores the concepts of energy conservation and material properties, elemental to an engineer’s skill set.

Educational Insights and School Projects

Rubber band cannons are a popular project in school physics classes . They offer a compelling demonstration of Newton’s laws of motion, where students can observe first-hand how forces act in the real world. Such projects also hone problem-solving and creativity as students iterate their designs for improved performance.

“ Rubber band cannons are marvellous tools for teaching, as they encapsulate energy, motion and forces in a single, tangible experiment ,” says Michelle Connolly, founder of LearningMole and an advocate for practical education with over 16 years of classroom experience. They provide an impactful way to engage students, by taking concepts out of textbooks and enabling them to ‘learn by doing’.

By constructing these simple devices, students delve into the iterative process of design-thinking and get a glimpse into how engineering solves real-life problems. This hands-on approach aligns with the mission of LearningMole, which aims to make learning interactive and accessible for every student, including those with special educational needs. Through such projects, educational principles are not merely taught but experienced, fostering a deeper comprehension of subjects like physics and design technology.

Remember, your cannon’s design can be simple or complex, but it’s how you apply the scientific method to test and refine your creation that truly enhances your learning journey.

Safe Use and Precautions

Rubber band cannons harness elastic energy and should always be handled with caution to ensure everyone’s safety. Specific safety guidelines and age-appropriate design considerations are crucial.

Safety Guidelines

• Always wear protective eyewear : When operating a rubber band cannon, it’s imperative to protect your eyes from potential mishaps.
• Never aim at people or animals : Use your rubber band cannon responsibly. Target inanimate objects in a controlled environment.
• Inspect before use : Check the integrity of the rubber bands and the structure of the cannon to prevent accidents.

“Ensuring the safe use of educational tools is vital in a school setting. By following clear guidelines, students can enjoy learning while minimising risk,” says Michelle Connolly, an education expert with extensive classroom experience.

Age-Appropriate Design and Use

• Appropriate sizing : Ensure the cannon’s size matches the age and handling ability of the user.
• Complexity of design : Younger children should use simpler designs to prevent confusion and frustration.

In school environments, always use rubber band cannons under the supervision of an educator who is trained in their safe operation and understands the design’s suitability for the age group involved.

Frequently Asked Questions

This section explores some of the most common inquiries regarding rubber band cannons, delving into the mechanics of elastic energy, physics principles at play, and experimental measurements involved in their operation.

How does a rubber band cannon use elastic energy to launch projectiles?

When you stretch a rubber band, you’re storing elastic potential energy within it. Releasing this stretched band in a rubber band cannon converts the potential energy into kinetic energy, propelling the projectile forward with a force that’s a result of the rubber band snapping back into its original shape.

What are the energy transformations involved when a rubber band is fired?

Initially, the rubber band holds potential energy; upon release, this energy transforms into kinetic energy of the projectile. “The beauty of physics is showcased in this simple transformation, where we see energy shifting forms right before our eyes,” explains Michelle Connolly, founder of LearningMole.

Can you explain the mechanism behind a rubber band gun?

A rubber band gun typically has a mechanism, such as a trigger or a notch, to hold the rubber band in place while it is stretched. When the trigger is released, the rubber band’s potential energy is swiftly converted into kinetic, launching the attached projectile.

What role does physics play in the operation of rubber band cannons?

Physics underpins the entire operation of a rubber band cannon. It involves concepts of elasticity, energy conservation, and projectile motion. Understanding these principles allows you to predict and control the motion and impact of the projectile.

In what ways can rubber band elasticity be measured during experiments?

You can measure the elasticity of a rubber band by recording the force applied to stretch it and the distance it stretches. This can help determine the potential energy stored, which is related to how the band will behave when released.

How can the principles of physics be demonstrated through a rubber band cannon lab?

A rubber band cannon lab offers a hands-on experience to demonstrate physics. By adjusting variables like the angle of launch and the stretch of the rubber band, you can observe the resulting changes in projectile motion. “It’s a fantastic way to bring physics to life and highlight the direct connection between theory and real-world application,” states Michelle Connolly.

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Shop Experiment Stretch It to the Limit – The Linear Force Relation for a Rubber Band Experiments​

Stretch it to the limit – the linear force relation for a rubber band.

Experiment #8 from Real-World Math with Vernier

Introduction

When a force is applied to a rubber band, it stretches a certain amount. Exactly how much it stretches depends on the applied force and the characteristics of the rubber band. In general, the more force that is applied, the more it stretches. For rubber bands that are not stretched too much, if you double the force applied, it turns out that the stretch doubles as well. Two quantities, x and y , that change in this way are said to be proportional . x and y are related by the constant K in the equation

In this activity you will use a Force Sensor and a Motion Detector to investigate the relationship between the force applied to a rubber band and the distance that the rubber band stretches. To measure how much a rubber band has stretched, we will use the stretched length of the band minus the relaxed length of the band.

• Record force versus stretch data for a rubber band.
• Model force versus stretch data with a proportional relationship.

Sensors and Equipment

This experiment features the following sensors and equipment. Additional equipment may be required.

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This experiment is #8 of Real-World Math with Vernier . The experiment in the book includes student instructions as well as instructor information for set up, helpful hints, and sample graphs and data.

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Entropy of a Rubber Band

Box of large rubber bands

Hand out rubber bands to the class. Ask them to stretch the rubber band, then place it on their upper lip. They will feel heat. Release the tension on the rubber band and touch it to their upper lip, the rubber band will feel cooler.

Entropy change (stretching and contracting at constant T):

Heat is produced in the rubber band as it is stretched. If we stretch slowly in air at room temperaure, we have a reversible, isothermal process with q< 0 (heat is lost to the surroundings). Then:

\( \ce{$\Delta S_{stretch} = \frac{q_{rev}}{T} < 0$} \)

in the stretching process. Since entropy is a state function:

\( \ce{$\Delta S_{contract} = \frac{q_{rev}}{T} > 0$} \)

for the reverse process of slowly allowing the rubber band to contract. The rubber band has lower entropy, (is more ordered) when stretched. Under tension, the molecules in a rubber band line up and the arrangement becomes much more ordered, lowering the entropy. The criterion for spontaneity for an isolated system is  \( \ce{\Delta S_{sys} > 0} \) .  Suppose the system is the rubber band and the air in a large room. Therefore, if a constraint keeping the rubber band stretched is removed, it will spontaneously contract, with ∆S sys , contract > 0

Enthalpy change (with heat source):

There is another "PV"-like term in the enthalpy, namely "-FD", where F is the force and D is the distance . The "-" sign is there because the force is taken to be positive (as is the pressure) but the force of the rubber band is in the opposite direction of the force on a piston, pulling in instead of pushing out. Thus:

H=E + PV - FD è q + w + PV - FD If we heat the rubber band with a weight attached, the force F is constant, but the band contracts. The work w is F∆D-P∆V, (the P∆V term is very small), and ∆H= q + F∆D-P∆V-(F∆D-P∆V) = q. Since we heated the band up, ∆H= q>0. This can be done reversibly, so that:

\( \ce{$\Delta S_{heat} = \frac{\Delta dq_{rev}}{T} > 0$} \)

This entropy change toward more disorder is perhaps not so surprising as in the isothermal case for contraction, since here it has been heated to a higher T.

LeChatelier : Heating the rubber band contracts it. Therefore, according to LeChatelier's principle, stretching the rubber band MUST increase it temperature, because by getting hotter it tends to contract, resisting the stress of stretching.

Bruce Robinson’s addition, thanks Bruce!

So here is my attempt to interpret the rubber band experiment.

The simplest way (to my mind) is to focus on the band as it is allowed to relax. So stretch it and hold it there for a bit, then let it relax (quickly) and feel whether it cooled or heated by touching the band to the upper lip.

The discussion of an enthalpic spring is that when it is stretched one did work to get it stretched, so that energy was put in it. Now when you relax it the energy must come out as heat. (No work is done relaxing the rubber band).

So this predicts that the energy must be in the rubber band as potential energy (it is exothermic in relaxation) and so the rubber band should be hotter as it is allowed to relax. If this is how a spring should work, and the comparison with the actual rubber band produced the opposite result, maybe our logic is faulty. We need a way to turn the temperature change totally around.

Now consider that a rubber band is composed of a bunch of polymer strands (looking like a bowl of cooked spaghetti). When stretched the polymer strands should be more aligned and straighten out along the direction of the stretching. When you relax it the strands go in all directions, or become more disordered.

So the entropy increases (the entropy change is positive) when the rubber band can relax. Entropy is related to heat as the amount of heat transferred (in a reversible fashion) at constant Temperature divided by the temperature:

\( \ce{$\Delta S = \frac{q_{rev}}{T} > 0$} \)

For this change the entropy increases, which means the heat is positive. So if the system (aka rubber band) heat is positive, heat must go into the strands of polymer. If the heat goes into the rubber band, where does it come from? The heat comes from the environment; so heat going into the rubber band comes from your lip, so it feels cold. The newly relaxed rubber band is poised to take heat from the room or your lip or whatever will provide the heat.

In summary: The rubber band is an entropic machine.

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Harris Chooses Walz

A guide to the career, politics and sudden stardom of gov. tim walz of minnesota, now vice president kamala harris’s running mate..

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Earlier this summer, few Democrats could have identified Gov. Tim Walz of Minnesota.

But, in a matter of weeks, Mr. Walz has garnered an enthusiastic following in his party, particularly among the liberals who cheer on his progressive policies. On Tuesday, Vice President Kamala Harris named him as her running mate. Ernesto Londoño, who reports for The Times from Minnesota, walks us through Mr. Walz’s career, politics and sudden stardom.

On today’s episode

Ernesto Londoño , a reporter for The Times based in Minnesota, covering news in the Midwest.

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An earlier version of this episode misstated the subject that Walz’s wife taught. She taught English, not Social Studies.

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Ernesto Londoño is a Times reporter based in Minnesota, covering news in the Midwest and drug use and counternarcotics policy. More about Ernesto Londoño

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