PHYS 2425 – Engineering Physics I

Free Fall Motion

Leader: ___________________ Recorder: __________________________

Skeptic: ___________________ Encourager: ________________________

Materials

Laptop

Mini DV Camera with IEEE 1394 cable

Golf ball

High Contrast meter stick

Black cloth

Tripod

Introduction

In this lab we will examine free fall from several different experimental points of view. One particular goal is to study the graph of position vs. time for uniformly accelerated motion for several different initial velocities. Free fall is an excellent example of uniformly accelerated motion in one-dimension. It is a type of motion which we encounter all the time, and thus we have a lot of experience with it. Consequently, the study of free fall gives us a good opportunity to test our understanding of uniformly accelerated motion.

Part I – Graphs of Uniformly Accelerated Motion

Procedure

In this procedure we will record the motion of a golf ball in free fall. We will record the motion with a mini DV camera storing the data directly in the computer.

In the first case, you will release a golf ball from rest.

P1) If we take up as the positive direction, sketch in the space below what you think the graph of the y-position of the ball vs. time will look like.

P2) Sketch what you think the corresponding graph of velocity vs. time will look like.

P3) Sketch what you think the corresponding graph of acceleration vs. time will look like.

1. Set-up

Place the camera on the tripod and make sure that it is oriented straight up and down in all directions. Follow section I in the Quick Start Guide to Acquiring and Analyzing Video Data with LoggerPro to set up the camera and start the software.

2. Data Acquisition

In the first part we will drop the ball form rest. Follow section II in the the Quick Start Guide to Acquiring and Analyzing Video Data with LoggerPro to obtain the data. Hold the ball next to the high contrast meter stick. You may want to place a black cloth in the background. Start recording data just before you release the ball and stop recording as soon as the ball hits the ground. Use the slider or the single frame advance to move find the point in the video where you can clearly tell the ball is falling. Click on the location of the ball for each frame as described in section III of the Quick start guide. Once you have clicked on the position of the ball for each frame, follow the procedure for setting the distance scale given in section IV of Quick Start Guide. You are now ready to examine graphs of your data.

Data Analysis

1. LoggerPro will automatically display graphs of the x and y positions of the ball vs. time. Click on the label for the vertical axis and a box will appear. Choose y from this box to display the y position vs. time.

Q4) What is the shape of the graph of distance versus time?

Q5) What about the shape of the graph tells you that the motion is accelerated? Hint: What would the graph look like if you moved at constant velocity or stood still?

Q6) Does the shape of the graph agree with your prediction P1)? Explain.

2. We will now use LoggerPro to fit the data. Click on the curve fit button . From the box that appears click on the radial button for quadratic, and then click on the Try Fit button. Click OK to accept the fit. Print and attach the graph.

Q7) How can you use the information given to you by the fit to determine the acceleration due to gravity?

Q8) What values of acceleration and initial velocity are given by your graph? Don’t forget units.

Q9) Explain why the initial velocity might not be 0.

3. Click on the label for the vertical axis and this time choose y-velocity.

Q10) What is the shape of the graph of velocity versus time?

Q11) Does this agree with your prediction P2)? Explain.

Q12) What about the shape of the graph tells you that the motion is accelerated? Hint: What would the graph look like if you moved at constant velocity or stood still?

Q13) What about the shape of the graph of y-velocity vs. time tells you that the acceleration was constant? Explain.

4. Click on the linear fit button . This will fit a best fit line to the data. Print and attach the graph.

Q14) What physical quantities about the ball’s motion do the slope and y-intercept give you?

Q15) List the value for the acceleration of gravity given by the fit. Include units.

Q16) What would you expect to be the acceleration of the ball? Explain.

Q17) How well does the slope compare to the expected value? Compute the percent difference between your slope and the expected value. For this case you can define the percent difference as .

Part II - Free Fall with Upward Initial Velocity

In this part we will look at the motion of a ball that is initially tossed upwards.

P18) Once the ball has left your hand, and is traveling upwards, what will be the direction and magnitude of the acceleration?

P19) Once the ball has reached the highest point in its motion, what will be the magnitude and direction of its acceleration?

P20) Once the ball has started to fall, what will be the magnitude and direction of its acceleration?

P21) Sketch a graph of acceleration vs. time covering all parts of the motion of the ball in the air.

Procedure

1. Data Acquisition

Practicing tossing the ball straight up starting next to, but at the bottom of the meter stick so that it stays in the screen of the camera. Once you can toss the ball straight up and keep it in the screen, record the motion as before.

2. Analyze the motion as before.

3. LoggerPro doesn’t automatically determine the acceleration when we perform video analysis so we will calculate it using LoggerPro. Click on the Data menu and choose New Calculated Column… A window like the following will appear.

Rename the column acceleration with short name a and give it units of m/s².

Click in the box under Equation: and then click on Functions>. From the box that appears click on Calculus and then click on Second Derivative. Now click on Variables(Columns)> and choose Y, then click on Done. You have just made a new column which contains the second derivative of Y or a_y.

Delete the video window, and add two new graph windows by clicking on Insert then graph twice. Click on Page and choose Auto Arrange so that all three graphs show nicely. Make the top one show Y vs. t, the middle show v_y vs. t, and the bottom show a vs. t. Print and attach your graphs.

Q22) Describe the shape of the acceleration graph.

Q23) Does the graph you produced match your prediction in P21)? Explain.

D24) Label on the all three graphs where the ball is going up, is at the top, and is coming down.

Q25) Does the acceleration depend on the direction the ball travels? Explain.