free fall and projectile motion experiment lab report

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Lab Experiment: Free Fall and Projectile Motion, Lab Report Example

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Introduction

The laboratory experiment was conducted in order to ascertain the qualities of bodies experiencing free fall and projectile motion. The movement in which a body is launched is designated as projectile motion. Free falling bodies only have the force of gravity exerted upon it. The interval of flight was determined for the vertical motion component of the projected bodies as y = y i + v i t -1/2gt 2 (Finocchiaro 21). In the case of the free falling bodies the equation y = 5.579x 2 – 0.2539x + 1.1108 was applied for the first free falling body.

The value of R 2 in the first equation was tabulated at 0.9999.  In the second trial the equation of y= 5.2039x 2 + 5.1837x – 0.0282 was applied. For the body starting with an initial velocity and falling afterward.  The value of R 2 that was applied in the second trial was one. In the third trial, a body with an initial horizontal speed was launched. The equation used in the third trial was y= 5.2338x 2 + 0.3808x + 1.0626. The value of R 2 that was applied in the first component of the third trial was one. The value of R2 that was used in the second component of trial three was R 2 = 0.9997. The second equation in the third trial that was applied had been y = 0.747x + 0.3954. In the fourth experiment the equation that was determined was y = 5.1174x 2 + 4.5126x – 0.0277. The R2 value that was used for the fourth trial was R 2 = 1.

The objective of the experiment was to confirm the theory proposed by Aristotle and Galileo with regards to bodies that are launched and free falling bodies (Finocchiaro 21).

The conventional procedure in each of the trials is identical.  A movie was filmed of the movement that was reviewed. In addition the position of the moving object had been measured in each of the movie frames. A graph was plotted in order to determine the manner that these positions changed as a function of the time passing. There had been two devices which were established for the creation of the movie. After the movie was filmed, a copy was sent to the group´s computer in order to evaluate the motion.

The lab experiment assisted in the comprehension of free falling and launched bodies. It had been demonstrated that with the effect of gravity, an object in free fall starts with an initial velocity and accelerates at a continuous pace toward the Earth. When an object is free falling, the unique force that is exerted is the force of the Earth´s gravity. The air resistance is not considered in the experiment due to its negligible contribution. The force exerted by the Earth´s gravity is almost constant as the body is free falling close to the Earth´s surface. As a result of this characteristic, the object is accelerated in a downward direction at a constant index. The acceleration index is represented by g. In this experiment, movies were filmed of the bodies which had been free falling and launched. The movies were transposed to the class computer and graphs had been depicted. The graphs demonstrated the equations and the slope of the object as it was in free fall or launched.

Works Cited

Finocchiaro, Maurice A. The Routledge Guidebook to Galileo´s Dialogue . New York, NY: Routledge, 2013. Print.

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Free Fall Motion: Explanation, Review, and Examples

• The Albert Team
• Last Updated On: February 16, 2023

Free fall and projectile motion describe objects that are moving through the air and acted on only by gravity. In this post, we will describe this type of motion using both graphs and kinematic equations. Since projectile motion involves two dimensions, these problems can be complex. We will explain many examples so you can see how to solve different types of projectile motion. 

What We Review

An object that is moving under only the influence of gravity is in free fall. In order for an object to be in free fall, wind and air resistance must be ignored. On Earth, all objects in free fall accelerate downward at the rate of gravity or 9.81\text{ m/s}^2 .

Applying Free Fall to Kinematic Equations

When analyzing free fall motion, we can apply the same kinematic equations as we did for motion on the ground. We can then use these equations to determine properties such as distance, time, and velocity. 

How to Find Distance Fallen for an Object in Free Fall

If an object is in free fall, we can use kinematic equations to find the distance it falls during a certain time. You will typically use the following kinematic equation to calculate the distance fallen:

In order to use this equation, you need to know the initial velocity of the object and the time of flight. Remember that the acceleration of a free falling object is always equal to the acceleration due to gravity, 9.81\text{ m/s}^2 . 

Many free fall physics problems will include scenarios where objects are dropped from rest. In this case, the initial velocity is zero and the first term of the kinematic equation above will cancel out. 

If the time is not known, another method for calculating the distance fallen is to use the following kinematic equation:

In this case, you must know the final velocity v_f of the object. Then, you can solve the equation for the distance d .

How to Find Time for an Object in Free Fall

The amount of time an object is in free fall will depend on its velocity and the distance it falls. Similar to distance, there are two equations you can use to find the time, depending on what you know. 

If you know the initial and final velocity of the object, then the simplest way to calculate time is using the kinematic equation:

This equation can be solved for time. Then, you’ll only need to substitute the values for the velocities and the acceleration due to gravity.

Another method to find time if you do not know the object’s final velocity is to use the equation:

Note that in this equation there are two terms that include the time t . Unless the initial velocity is zero, this can make it more challenging to solve this equation for time. If using this equation, you may need to use the quadratic formula to solve for time.

How to Find Final Velocity for an Object in Free Fall

The final velocity of an object in free fall depends on the amount of time it falls. Due to the acceleration of gravity, the velocity will increase every second by 9.81\text{ m/s} . The final velocity can be calculated using the equation:

If you do not know the amount of time the object is falling, another method for calculating the final velocity is using the kinematic equation: 

This equation requires that you instead know the distance that the object falls. If you are using this equation to find the final velocity, remember that the final velocity is squared in this equation. That means you will need to take a square root as your final step to solve for the final velocity. 

Examples of Free Fall

In this next section, we’ll apply the methods you just learned to solve some problems about free fall motion.

Example 1: How to Find the Distance for an Object Dropped from Rest

For example, an object is dropped from rest from the top of a tall building. It hits the ground 5\text{ s} after it is dropped. What is the height of the building? 

In this scenario, we know that the object’s initial velocity is zero because it was dropped from rest. We also know that the acceleration is 9.81\text{ m/s}^2 . This problem is asking us to find the distance the object falls. This will be equal to the height of the building.

Based on this information, we can use the following kinematic equation to find the distance:

Substituting the given values produces:

Therefore, the height of the building is about 123\text{ m} .

Example 2: How to Find the Final Velocity for an Object with Initial Velocity

In another example, an object in free fall has an initial, downward velocity of 2\text{ m/s} and falls a distance of 45\text{ m} . What is the object’s final velocity? 

In this scenario, we are given the object’s initial velocity, v_i and the distance d . We also know that the acceleration is 9.81\text{ m/s}^2 . Based on this information, we can use the following kinematic equation to find the final velocity:

Since the initial velocity is in the same direction as the acceleration (downward) we can use the same sign for both values.

Our last step is to eliminate the square by taking the square root:

Therefore, the final velocity of the object is about 30\text{ m/s} .

Motion Graphs for Objects in Free Fall

In addition to using physics equations, we can also represent free fall motion with motion graphs. Position-time graphs, velocity-time graphs, and acceleration-time graphs can tell us a lot about the object’s motion over time. Want a more in-depth review of motion graphs? Check out this blog post !

Position-Time Graph for an Object in Free Fall

In terms of position, many objects in free fall start at a high position, or height off the ground, and move downward. Objects in free fall accelerate due to gravity. Therefore, the position-time graph for free fall motion must be curved. This means that objects in free fall start with a slow velocity and gradually speed up which is represented by the steep downward curve of the graph. 

Velocity-Time Graph for an Object in Free Fall

As an object falls, its velocity increases due to the acceleration of gravity. This means that the velocity starts slow and steadily increases in the downward direction. The graph below shows the velocity-time for an object in free fall:

Note that the slope of this graph is constant and represents the acceleration due to gravity, or -9.81\text{ m/s}^2 .

Acceleration-Time Graph for an Object in Free Fall

Free fall acceleration is constant. Throughout the entire time that an object is falling, it is accelerating at a rate equal to the acceleration due to gravity, -9.81\text{ m/s}^2 . As shown in the graph below, the acceleration-time graph is a constant negative line. 

Projectile Motion

A projectile is an object that is launched or thrown into the air and then only influenced by gravity. Projectile motion has many similarities to free fall motion, however, projectiles may also travel a horizontal distance in addition to falling vertically down. 

Examples of Projectile Motion

The exact trajectory, or path, a projectile will take depends on how it is launched. However, all projectiles follow a curved trajectory such as in the image shown below:

If you play or watch sports, you likely have already observed projectile motion. Projectile motion describes the arc of a basketball in a free throw, a fly ball in baseball, or a volleyball bumped over the net. 

Horizontal Component of Velocity

To analyze projectile motion, we must separate the motion into horizontal and vertical components. The horizontal component of a projectile’s velocity is independent of the vertical component of velocity. Since gravity acts vertically, there are no horizontal forces acting on projectiles. This means that the horizontal component of a projectile’s velocity remains constant throughout the entire flight. 

Example: Finding the Horizontal Component

For example, a projectile is launched from the ground with an initial speed of 8\text{ m/s} at a 60^{\circ} angle. What is the horizontal component of the projectile’s velocity?

We will need to use trig identities to determine the components of the velocity. We can visualize the components as a triangle where the hypotenuse is the initial velocity and the sides represent the horizontal, v_{ix} , and vertical, v_{iy} , components of the velocity.

Cosine is defined as the adjacent side of the triangle divided by the hypotenuse. Since the horizontal component is adjacent to the angle, we can use cosine to find the horizontal component of velocity:

Therefore, the horizontal component of the initial velocity is 4\text{ m/s} .

Need to review your trig identities? Try out this resource from Khan Academy .

Vertical Component of Velocity

The vertical component of a projectile’s velocity will be influenced by gravity, which acts vertically on the object causing it to accelerate downward. Therefore, the vertical component of velocity will change throughout the projectile’s flight. We can calculate the vertical component of velocity at a particular time in a method similar to calculating the horizontal component. 

Example: Finding the Vertical Component

In the same example, a projectile is launched from the ground with an initial speed of 8\text{ m/s} at a 60^{\circ} angle. What is the vertical component of the projectile’s velocity?

As we visualize the velocity components, we are solving this time for the opposite side of the triangle. Sine is defined as the opposite side of the triangle divided by the hypotenuse. Therefore, the initial vertical velocity is:

Solving Projectile Motion Questions

Let’s apply what we’ve learned to some examples of projectile motion!

Example 1: Finding the Range of a Projectile

In this example, a projectile is fired horizontally with a speed of 5\text{ m/s} from a cliff with a height of 60\text{ m} . How far from the base of the cliff will the projectile land? 

In this scenario, we are given the initial horizontal velocity v_{ix}=5\text{ m/s} and the vertical change in position d_y=-60\text{ m} . Since the projectile is launched horizontally, the initial vertical velocity, v_{iy} , is zero. We also always know in projectile motion that the vertical acceleration is a_y=-9.81\text{ m/s}^2 and the horizontal acceleration, a_x , is zero.

This problem is asking us to find the horizontal displacement, or d_x . This is also referred to as the range . We can use the following kinematic equation to find the projectile’s final horizontal position:

Since the horizontal acceleration of a projectile is zero, this equation can be simplified to:

Before we can solve this equation, we must first determine the time of the projectile’s flight. We can actually use this same equation in the vertical direction to solve for time:

Since the initial vertical velocity is zero, this equation can be simplified to:

Solving for t :

Substituting the given values:

Now we can use this time to calculate the horizontal displacement of the projectile:

Therefore, the projectile will land about 17.5\text{ m} from the base of the cliff. 

Example 2: Finding the Maximum Height of a Projectile

As another example, a projectile is launched from the ground with an initial velocity of 25\text{ m/s} at an angle of 50^{\circ} . What is the projectile’s maximum height?

As a projectile travels upward, its vertical velocity becomes slower and slower due to the negative acceleration of gravity. At the maximum height of the trajectory, the projectile’s vertical velocity will momentarily be zero as the projectile stops and turns to move downward. Therefore, in this scenario, our final vertical velocity, v_{fy} , is zero.

We can use the following kinematic equation to solve for the maximum height, d_y :

Solving for d_y :

Before we can use this equation to calculate the height, we will need to use the sine trig identity to find the vertical component of the initial velocity:

Since the initial velocity is in the opposite direction as the acceleration, it’s really important to remember the sign here. If we define moving up as positive, then the initial velocity is positive and the acceleration is negative. Substituting this initial vertical velocity and the given values into the equation above gives:

Therefore, the projectile will reach a maximum height of about 18.7\text{ m} .

For more examples and an explanation of solving these types of projectile motion problems, check out this youtube video from Professor Dave . 

Understanding free fall and projectile motion allows you to solve some of the most complex problems you will encounter in introductory physics. All projectiles are acted on only by gravity, and the vertical and horizontal components of motion are independent of each other. This allows us to apply our kinematic equations to solve for a projectile’s time of flight, velocity, and displacement in each direction.  

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Free Fall And Projectile Motion Lab Report

Freefall and Projectile Motion Introduction and Objectives This lab experiment was done to determine the characteristics of free fall and projectile motion in Physics. The motion in which a body is thrown or projected is called Projectile motion while free fall is any motion of a body where gravity is the only force acting upon it, at least initially. In this experiment, a photogate, a chopper, and a Universal Lab Interface were used to determine the free fall motion of the chopper as it was released. A ball, carbon paper, and an L-shape projector were also used to determine the range of projectile motion of a ball being released from a horizontal yet slightly vertical slope. At the end of the experiment, one will know how velocity …show more content…

“The Photogate has a beam of infrared light that travels from one side to the other. It can detect whenever this beam is blocked.” A Picket Fence or a chopper, a piece of clear plastic with equally spread out black sections on it, was dropped. “As the Picket Fence passes through the Photogate, the computer will measure the time from the leading edge of one bar blocking the beam until the leading edge of the next bar blocks the beam.” This timing continues as all eight bars pass through the Photogate. From these measured times, the program will calculate the velocities and accelerations for this motion and graphs will be plotted. http://www.waukeshasouth.com/physics1/photo.html

Marble Launcher Results

Objective: Using a marble launcher, launch marbles from different angles with different forces to find the maximum height and the velocity as it leaves the launcher. Using different variables and results to determine how the different angles and amounts of force effect the variables. With this data show the effect the forces cause in 1-D and 2-D motion, as well as in the X and Y directions. This is done through kinematic equations and calculations.

Energy of a Tossed Ball

The purpose for the students of the Energy of a Tossed Ball Lab involved learning how to measure the change in kinetic and potential energies as a ball moves in free fall. Since there is no frictional forces working on the ball the total energy will remain constant and the students will see how the total energy of the ball changes during free fall.

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Resources Year 12 Physics

Year 12 Physics Practical Investigation | Projectile Motion Experiment

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Sample Physics Practical Assessment Task: Projectile Motion Experiment

Projectile motion experiment is used by most schools for their first Physics practical assessment task. This is because most Projectile Motion practical investigation is relatively easy to design and conduct by students.

A typical Projectile Motion practical assessment task used by schools is outlined below.

In this sample practical assessment task, we are required to investigate the relationship between the range s_x and the launch velocity of a projectile released from an elevated position.

Let’s apply the scientific method to design and conduct a practical investigation for the assessment task outlined above.

Sample Physics Practical Report

The simplest type of projectile motion is a ball being projected horizontally from an elevated position.

In this situation, the range of a projectile is dependent on the time of flight and the horizontal velocity. Hence this experiment is based on the equation s_x=u_xt .

To express the time of flight t in terms of the acceleration due to gravity, we analyse the vertical motion of the projectile

s_y=u_yt+\frac{1}{2}at^2

-h=0+\frac{1}{2}(-g)t^2

t^2=\frac{2h}{g}

t=\sqrt{\frac{2h}{g}}

Hence the range of a projectile can be expressed in terms of the horizontal velocity and the other control variables such as y and g by substituting t=\sqrt{\frac{2h}{g}} expression into s_x=u_xt :

s_x = u_x \times (\sqrt{\frac{2h}{g}})

\therefore s_x = (\sqrt{\frac{2h}{g}}) u_x

2. Variables

Before designing your investigation, all the variables need to be identified.

• Independent variable: Horizontal launch velocity u_x
• Dependent variable: Range \Delta x
• Control variables: Height of the table y , acceleration due to gravity g , the shape of the projectile

Keeping the control variables constant allows the experiment to be more valid.

To learn more about how to improve the validity of your experiment, read the Matrix blog on ‘ Validity, Reliability and Accuracy of Experiments ‘

To determine the relationship between the range of a projectile \Delta x  and its horizontal launch velocity  u_x and use the results to calculate the acceleration due to gravity  g .

• A smooth metal ball is placed at the top of the ramp, and the vertical distance from the ball to the table is measured.
• The ball is rolled down and timed along the 1 \ m horizontal length using a stopwatch. The time is recorded.
• The distance from the foot of the table to its landing point on the carbon paper is observed, measured and recorded.
• Steps 1-4 are then repeated at different heights up the ramp.

The results are given in the table below. Using the times taken for the ball to travel 1 metre. Data collected from the experiment is highlighted in blue.

6. Quantitative Analysis of Results: Graphs and calculations

Calculate the horizontal velocity of the ball as it leaves the table and hence complete the table.

Plot the range of the ball \Delta x against the launch velocity u_x and draw in the line of best fit. 

• The range of the ball is plotted against the horizontal launch velocity.

• A line of best fit is drawn.

Determine the relationship between the launch velocity u_x and the range of the ball \Delta x  and hence discuss its significance

• The relationship between the launch velocity and the range of the ball is linear.  The range of the ball is directly proportional to the horizontal launch velocity: s_x = u_x \times t
• The linear relationship implies that the horizontal launch velocity affects the range but not the time taken to fall from a fixed height. Therefore horizontal and vertical motions are independent of each other.
• This also validates the results expected from the equations of projectile motion.

Use the gradient to find the acceleration due to gravity

7. Qualitative Analysis: Evaluation of method and errors

Let’s investigate the errors, reliability and accuracy of this experiment.

Access our library of Physics Practical Investigations.

Written by DJ Kim

DJ is the founder of Learnable and has a passionate interest in education and technology. He is also the author of Physics resources on Learnable.

Learnable Education and www.learnable.education, 2019. Unauthorised use and/or duplications of this material without express and written permission from this site's author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Learnable Education and www.learnable.education with appropriate and specific direction to the original content.

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Search this blog, contoh lab report physics (free fall and projectile motion).

Untuk experiment 1 ada tak?

takde.. sorry

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nak exp. 4 please

ada experiment 10 tak

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