acceleration due to gravity experiment ball drop

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Acceleration Due to Gravity Lab

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Acceleration Due to Gravity: Vertical Drop Experiment Alianna Jones Partners: Sanjana, Deby, Lohita September 21, 2022 Lab Section: D

Lab Essay The experiment performed tested acceleration due to gravity using a free-falling ball. To perform the experiment a drop-stand and photogates were used to measure the time, in milliseconds, that it took for the ball to fall from the first photogate to the second photogate. Additionally, the distance from the drop point to the first photogate, D, and the distance from the drop point to the second photogate, d, were measured using a ruler in centimeters. The ball was placed on a magnetic release system to ensure no outside forces are affecting the drop rate of the ball.

Figure 1: Drop stand setup Five trials were performed in this experiment, and each time the photogates were moved to a different location. After each trial, the data collected was converted from centimeters to meters, and from millisecond to seconds. Then, using the equation, D, the values were substituted in to find the average acceleration due to gravity on the free-falling ball. The average acceleration value was then compared to the constant acceleration, g = 9/s 2.

Analysis The results of the experiment showed that the average acceleration due to gravity was 9. m/s 2. The accepted value for the average acceleration due to gravity is 9 m/s 2. After calculating the error there was a 3% error. Based on this result, the experiment was successful. The reason why the calculated value for the experiment was not the same as the accepted value could be caused by inaccurate readings given by the drop stand. Additionally, the method for measuring the distance was inaccurate and may have caused the data to deviate from the accepted value.

• Multiple Choice

Course : General Physics I/Lab (PHYS 2350)

University : nova southeastern university.

• Discover more from: General Physics I/Lab PHYS 2350 Nova Southeastern University 31   Documents Go to course
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Exercise 2: Ball Drop

For this experiment you will need the following items :

• A measuring device (ideally a measuring tape, but you can tape sheets of paper together and put markings on it as well).
• An object to drop (e.g. a marble, small ball, battery, a grape, or any similar object).
• A video recording device (a smartphone is ideal).
• QuickTime Player, Windows Media Player, Media Player classic, or any program that can view videos frame-by-frame (see the Frame-by-Frame analysis for help).

Think about it:

Would it matter if we set down as the positive direction? Further, does it matter if we set the origin as where we drop the object from?

You may find it useful to follow the video below where Sara marks positions on the wall and drops objects from a height of 1.0 m.

When you play back your video, you may find that the object moves too fast to make a clear position measurement and that the time it takes to fall is short. However, if you pause the video, you can observe a (possibly blurry) image of your object near one of your markings. Though the images may be blurry, comparing the location of your object to your markings will allow you to make adequate position measurements.

Videos are just a collection of still images taken in quick succession with a constant time between each image. The number of images your camera takes per second is known as the “frame rate” and is reported in frames-per-second (fps). In order to obtain the position of the object as a function of time, you will take advantage of the fact that most cameras record video at a constant frame rate to make your time measurements.

In order to make the measurements, you will need to be able to view the video frame-by-frame . This can be done in many ways, depending on the device you are using. See Frame-by-Frame Analysis for details on how to view and analyze videos. Additionally, you may use this guide to help determine the frame rate of your video for the analysis. Most smartphones will either display the frame rate before recording, or have the information accessible under the properties of the video.

Exercise 2.1 (2 marks)

Provide a picture of your experimental set-up that clearly shows the measuring device (i.e. measuring tape), dropped object, and the student card(s) of the participating member(s) in this lab. 

Secondly, provide an additional image of the student card(s) used in the previous photo. Here, the student name(s) and student number(s) must be legible. With your experimental set up in the background, you may take this image from a closer view to ensure the student card(s) is/are in full focus. Note: you do not need to be in the photo. If you are completing this lab with others virtually, you may provide a screenshot of your video call, with the student cards of all members visible. Your experimental set up must still be visible in the background.

Exercise 2.2 (3 marks)

Use your video to complete the table below (found in the same Excel sheet from Exercise 1). F rame # is the frame number starting at 0, t is the time since the drop in seconds (s) , τ is the time between frames and d is the position in meters (m) . Make sure to count your first frame as frame number zero. 

Helpful hints:

i) Be sure to report your answers in SI units.

ii) You can use the chart provided in Exercise 1, or you can make a new chart on any spreadsheet software you wish to use, or manually on paper, as long as it is clear in the image you submit.

iii) Since you will be recording data from d = 1.0 m until d = 0 m. Aim to have between 10-20 frames in your table in order to accurately see the trend. Depending on your frame rate, you may not need to record data on each consecutive frame (if you opt to record every other frame, ensure this is consistent for your entire analysis).

iv) When calculating your value of τ , reflect on its units and relationship to fps.

Ask yourself if the calculated time it took your object to fall makes sense. Does this roughly line up with the length of your video?

Exercise 2.3 (3 marks)

Use the data obtained in your chart to make the following two graphs (manually on graph paper or using any plotting/spreadsheet software of your choosing):

i) Graph position of the object, d , as a function of time, t

Have a careful look at Warm-up Exercise 3. In that exercise you used the kinematic equation:

Now think about how this applies to the graphs you made and which one is linear.

Draw or fit a best fit line to the linear graph (hint: only one of the two graphs you created should be linear) and submit this linear graph with the best fit line included . Only submit the linear graph. Please see the  Excel Help page and Helpful Graphing Tips found in the appendix as a guide.

Exercise 2.4 (3 marks)

Making sure to include proper units , calculate:

i) The slope of the best fit line to the linear graph

ii) The acceleration of your object during free-fall (acceleration is a vector!)

Hint: The most accurate way to calculate the acceleration is from your linear graph – how does the slope relate to acceleration? Keep in mind it is not equal but it is proportional.

iii) Finally, we know that objects in free-fall have an acceleration due to gravity of 9.8 m/s 2 [down]. Does the value you obtained agree with this? Why or why not?

Before you continue!

Before continuing, be sure you have completed Exercises 2.1 to 2.4 on Crowdmark for grading.

Physics 1A03 - Laboratory Experiments Copyright © by Physics 1A03 Team is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License , except where otherwise noted.

Gravity Drop

            The purpose of the laboratory today is to observe the motion of a ball in free fall.   We want to decide if it is in uniform acceleration, and if so, determine the value of the acceleration.   We expect that it is uniformly accelerated, of course, with the acceleration of gravity, 9.8 m/s 2 .   We will use two separate methods.   The first consists of a pair of photocells and lights (or “photogates”) which trigger when an object passes through.   These can measure the velocity of the ball at two points, as well as the time taken to travel between the photogates.   The second method will use a computer to analyze a video clip of the motion of the ball.

            The mathematical relationship which expresses the position of an object as a function of time is called the equation of motion.   The general form of this equation describes motion in three spatial dimensions (x, y, and z) as a function of time; proper incorporation of the initial values (i.e. at time t = 0) of position and velocity completely describes the motion of an object.   Three-dimensional motion is rather complicated to describe since three components of position and velocity must be considered.

            The simplest form of motion we can study is that of an object moving in a straight line (one-dimensional motion) under a constant acceleration.   Freefall of a mass over a short distance near the earth's surface (where the gravitational acceleration is almost a constant) is an example of such motion and the focus of this experiment.               There are three main equations which govern the basic motion of a freely falling object.   These relate the position, velocity, and acceleration of the object at any given moment to the force of gravity.   These equations are:

            We take the positive direction as downwards for our experiment.   The value g is the gravitational acceleration which all freely-falling objects experience (in the downward direction) near the earth's surface; the value of g is 9.8 m/s 2 .   For more complex motion, it is more typical to consider upwards to be the positive direction, so that the acceleration due to gravity is negative.

            The acceleration is the rate of change of the velocity.   This means that if the acceleration is 5 m/s 2 , (5 meters per second, per second), then every second the velocity changes by 5 meters per second.   Dividing the change in velocity by the time between measurements will give the average acceleration over that period of time.   If the acceleration is constant, then this should give you the same value for the acceleration regardless of how much time elapses between the two velocity measurements.   The change in the velocity will be different, but the ratio of this change to the amount of elapsed time will be the same.

            The timer can report three different values.   If just button “A” is pressed, this gives the time taken for the ball to pass through photogate “A”.   Similarly, if just button “B” is pressed, it gives the time taken to pass through gate “B”.   If both are pressed, the timer gives the time elapsed as the ball travels between the two gates.

            For our purposes, the amount of time taken to pass through a single gate is short enough that we can consider the velocity to be constant.   The velocity at this point can just be taken as the diameter of the ball divided by the time taken to pass through.   This means that it is very important that the diameter of the ball is measured carefully, and that the path takes it through the exact center of the gate.   If only the edge of the ball passes through, the photogate will be blocked for a shorter period of time, so the measured velocity will be too high.   By measuring the time at each gate separately, we can determine the velocity of the ball at each gate.

            For the video analysis, we’ll specify the position of the ball in each frame.   Then, we’ll measure an object in the field of view (the post used for dropping the ball would work well) to provide a conversion from pixels to an actual length.   Using the known number of frames per second, we can then determine the position, velocity, and acceleration of the ball at any point in its movement.   The VideoPoint software considers the positive y direction to be upwards, so the velocity and acceleration will be negative, since they are both directed downward.

Experimental Procedure, Photogates

1. First, measure the diameters of both the metal and plastic marbles with calipers, and weigh them.   Make your measurements in meters and kilograms.

Steel Ball                                                                     Plastic Ball

Mass:                                                                          Mass:                                                 

Diameter:                                                                   Diameter:                                          

2. Set up the post in a convenient place near the lab table.   Using a level, adjust the feet of the post until it is not tilted.

3. Select a position for the start photogate, and clamp it to the post, so that the path of the ball will pass through the photogate.

4. Select a position for the stop photogate, and clamp it to the post as well.

5. Use the plumb line to check whether the ball will fall through the center of the photogates, and adjust them if necessary.

6. Connect the timer box to the start and stop photogates with the cable.

7. Place the ball in the clamp at the top of the post.

8. Release the ball by opening the clamp.   It should land in the receptacle at the bottom, but be prepared to catch it if it bounces or rolls out!

9. Practice releasing the ball a few times and notice that the times displayed are rather consistent.

10. Record the values for D t a , D t b , and D t ab . at least three times with the photogates in the present configuration, filling in this table with the times.   Note that it is not necessary to drop the ball three times to get this measurement.   Dropping the ball once gives all three, and you can then read each one, depending on whether button “A” is pushed, button “B” is pushed, or both are pushed.   You can choose to either enter the data in the tables below, or you can use an Excel spreadsheet to record your data and make calculations.   The file “GravityDrop.xls” has been set up with these same tables for data entry.

11. Using the average value for each position, compute the velocity at each of the two photogates by dividing the diameter of the ball by the time taken to travel through each gate separately.   Divide the change in velocity by the time to travel between the two gates to find the acceleration.

12. Repeat steps 10 and 11 using the plastic ball instead.

Experimental Procedure, VideoPoint

1. Open the VideoPoint software.

2. Click to dismiss the opening splash screen, then choose “Open Movie”.

3. Select “Gravity Drop Steel Ball.mov”.

4. Specify that you will be locating a single object.

5. The first frame of the movie will appear, and the mouse pointer will be a target.   Click on the steel ball to mark its position in this frame.   The movie will advance to the next frame; continue marking the ball’s position in each frame.   You can use the frame advance and back buttons to move one frame at a time to help spot the ball in frames where it is difficult to see.

6. Do not set the position in the frames after the ball bounces at the bottom (and you may also want to ignore the first point before the ball actually starts moving).   It will be harder to use the automatic graph fitting capabilities of VideoPoint if you have the extra data points.

7. To provide a scale factor, measure the post (the clamp to hold the ball is in the top hole and the receptacle to catch it is in the bottom hole).

8. Click on the ruler icon in VideoPoint (or choose Scale from the Create menu).   Enter the length you measured.

9. As directed by the program, click on one end of your measured distance, then click on the other end.   This will automatically change the scale of the movie.

10. Choosing New Graph from the View menu will allow you to look at various views of the data.   First, leave the horizontal axis as time, and set the vertical axis to display the y -component and choose “Position”.   This will show a chart of the object’s motion as time passes.

11. Try viewing a graph of the y -component of velocity and acceleration.

12. You can use the Model or Fit capabilities of VideoPoint to determine the acceleration from the position graph, the velocity graph, or the acceleration graph.   Model (clicking the “M” next to the graph or choosing Add/Edit Model from the Graph menu) allows you to enter parameters for a line yourself to try to manually match the data, while Fit (clicking the “F” or choosing Add/Edit Fit) will automatically fit a line to the existing data.   Use Fit for the following exercises.

13. Fit a curve (use polynomial of degree 2 as the type) to the position graph.   The curve will have an equation of the form A t 2 + B t + C, where A, B, and C are constant values.   Since position depends on t 2 , we want the value of the first constant, A.   Looking at the above equations of motion, we see that g should be equal to twice this value.

14. Fit a line (use linear as the type) to the velocity graph.   The line will have an equation of the form A t + B, where A and B are constants.   Again, looking at the equations governing the motion, the velocty depends directly on t , so the slope of the line (the value of A) will give you the acceleration.

15. Fit a line to the acceleration graph.   The intercept of this line (the value of B) will give you the acceleration (the slope should be zero if acceleration is in fact constant).   The line may not be quite flat due to experimental error, so instead of taking the intercept, you may want to determine the value of the fitted line for some value of t near the middle of the fall.

Steel Ball Acceleration

From Position Graph:                                             

From Velocity Graph:                                            

From Acceleration Graph:                                     

16. Save your video analysis.

17. Repeat this procedure using “Gravity Drop Plastic Ball.mov”.

Plastic Ball Acceleration

18. VideoPoint can show other values as well, such as the kinetic or potential energy.   We’ll use these in later labs, but feel free to experiment with them now.   For these values to be correct, you’ll need to include the mass of the ball.   Choose Edit Selected Series from the Edit menu to enter the mass.

Is the acceleration in fact constant?

Is it the same for the metal ball and the plastic ball?

If your value does not exactly coincide with the expected value, what effects might have caused this?

If the values calculated by the two different methods are not the same, what differences are there in the measurement techniques that might cause this?

How accurately do you think that you measured the force of gravity?

To Measure Acceleration due to Gravity 'g' using a Free Fall apparatus.

In this experiment a ball is dropped from an electromagnet or other mechanism onto a trapdoor. When the ball is released a timer is started. When the ball hits the trapdoor the timer is stopped. If the distance from the ball to the trapdoor is measured the acceleration due to gravity (g) can be calculated. Use the formula; s = ut + ½at² and note that u = 0 and a = g.

• Click "Get Ruler". Measure and record the distance from the trapdoor to the bottom of the ball (s)
• Click "Drop Ball" to release the ball and start the timer. Record the time (t) for the ball to fall the measured distance. In the physics lab. the ball should be allowed to fall at least three times and the shortest time recorded. Not necessary here.
• Click "Reset".
• Click "Lower Ball". The release mechanism falls by a random amount thus changing the distance through which the ball will fall the next time
• Repeat steps 1 to 4 until at least six sets of results are collected
• Calculate g for each s value and its corresponding t value using the formula given above.
• Plot a graph of s (y-axis) against t². Draw a "best fit" straight line and measure its slope. Since s = ½gt², the value of g is calculated by g = 2 × slope.
• Record the shortest time of fall for each height
• Place a piece of paper between the ball and the electromagnet to ensure that the ball falls immediately when the switch is flicked
• Use large distances as much as possible so that measurement errors (distance and time) are relatively small.