Conservation Laws (Collisions) Phys101 Lab - 04

1.Objectives

The objectives of this experiment are to experimentally test the validity of the laws of conservation of momentum and kinetic energy in elastic collisions.

2. Theory

2.1 Conservation of Linear Momentum

For a system of particles, the forces that these particles exert upon each other are termed internal forces, while the forces exerted on the system by agents outside the system are termed external forces. If there are no external forces exerted on the system, the system is called an isolated system. Consider an isolated system comprised of just two particles, or objects, of mass m1 and m2 that are allowed to collide with each other. The free body diagrams of the two particles are shown here.

According to Newton's Third Law F 12=− F 21 , so the net force on the system is zero. This can be combined with Newton's Second Law. Combining Newton's Third Law with Newton's Second Law

leads to: F 12 F21=d pdt

=0 , where p= p1 p2 is the total linear momentum of the system.

Therefore, when two particles collide, with no net external; forces applied. The total linear momentum of the particles is conserved. Or, equivalently stated, the net momentum of the two particles prior to the collision is equal to the net momentum of the two particles after the collision.

2.2 Conservation of Kinetic Energy

For all collisions where the net external forces are equal to zero, momentum is conserved. Total Kinetic Energy of a system is not necessarily conserved, even if the net external force on the particles is zero. If the Total Kinetic Energy ( the sum of the kinetic energy of all the particles ) of a system is conserved, then we call that system Perfectly Elastic. In most realistic situations collisions are neither perfectly elastic or perfectly inelastic. In this lab, you will minimize any losses due to frictional forces by floating the pucks over a cushion of air and attempt to simulate a nearly perfectly elastic collision. The success of your attempt can be experimentally verified by measuring the kinetic energy of the system before and after the collision.

Name: ______________________ Sec./Group _____________ Date: ________________

Prelab:

1.) Consider a 0.52 g puck that moves as shown in the graph above. Consider each point to be a picture of the puck and consider that 60 pictures were taken each second. Plot the x position versus time and the y position versus time and use a linear trend line to find the x component of the velocity and the y component of the velocity. Attach you graphs.

a.) What are the x component of the velocity and the y component of the velocity?

b.) Write the velocity of the puck in i and j notation and in magnitude and angle notation.

c.) What is the momentum of the puck? (Write it both in I and j notation and as a magnitude and an angle.)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.10.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

Y Position vs X position

x(cm)

y(cm

)

2.) Consider the collision of a m1 = 0.52 g puck moving as shown in the graph, which collides with a m2 = 0.32 g puck initially at rest. Only the track of the m1 = 0.52 g puck, which is initially moving, is shown in the graph. Consider each point to be a picture of the puck and consider that 60 pictures were taken each second.

a.) What is the initial momentum of the m1 puck? (Write in both I and j format and as a magnitude and an angle.)

a.) What is the final momentum of the m1 puck? (Write in both I and j format and as a magnitude and an angle.)

c.) What is the final momentum of the m2 puck? (Write in both I and j format and as a magnitude and an angle.)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

-1.75

-1.50

-1.25

-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

0.75

1.00

Y Position vs X position

x(cm)

y(cm

)

Procedure:In this experiment you will take video of collisions of “pucks” on a frictionless table. The table is made frictionless much like an air hockey table is made frictionless, with the exception that instead of forcing air up through the table, air is by pumped down through and under the pucks. You will use these videos to analyze the collisions.

Figure 3.1 The VideoPoint Icons

This will involve two pieces of software. As the name suggests, VideoPoint Capture is the software for controlling the video camera and capturing the video. VideoPoint Physics Fundamentals is the software that will be used to analyze the data. The analysis that the software provides is a list of x and y coordinates as a function of time. This position versus time data will be exported to a spreadsheet, where the velocity as a function of time will be computed.

In this lab, you will verify if total linear momentum and total kinetic energy of a system are conserved during collisions. The collisions you will observe will be between two pucks ( masses ) on an air table. You will consider two collisions in this lab. The first collision will consist of one puck at rest and a second puck collides with a glancing blow ( Figure 3.2 ). The second collision will consists of two pucks, both pucks initially in motion, colliding together( Figure 3.3 ).

Figure 3.2 Collision Number One – One Puck Initially at Rest.

Figure 3.3 Collision Number Two – Both Pucks Initially in Motion.

( a ) ( b )

( c ) ( d )

( e )

Figure 3.4 Air Table, Compressor Pump, and “Pucks”.

To eliminate friction an air table is used. The air table, air compressor, and pucks are shown in Figure 3.4. The table must be level, and this is accomplished by adjusting the height of the legs shown in Figure 3.4e. The air compressor shown in Figure 3.4b pumps air through tubes and through the center of the pucks ( Figure 3.4c and 3.4d ). The pucks have two different masses. Your TA will tell you the masses or they will be written on the pucks. The masses are probably 0.21 kg and 0.52 kg. The compressor is turned on by plugging it in. Do not turn on the compressor until you are ready to take data.

Part One: Two Puck Collission, One Puck Initially at Rest

Capturing the Video Clip:

1. Open the VideoPoint Capture Software by clicking on the icon on the desktop. The icons are shown in Figure 3.1. The opening screen should resemble Figure 3.5.

Figure 3.5 VideoPoint Capture Opening Screen2. Next, turn on the camera. 3. Click on the Capture Button. This should bring up a screen which resembles Figure 3.6. You

should the video input from the camera. If you do not see any video input but instead see a black screen, click on the settings button. A pop-up window will appear ( Figure 3.7 ) with a drop down menu will appear which lists the cameras attached to the computer along with other camera settings. Choose the proper camera and press the OK button. ( If you still do not see any video, make sure the camera is on and press record, then press stop, and then press the back arrow. )

Figure 3.6 VideoPoint Capture Normal Operation Figure 3.7 Selecting the camera and settings.

4. Data can now be collected by capturing a video. The camera is mounted over the table. Recording the data is started by hitting the Record button. When recording, the Record button is “grayed out”. Keep the large mass at rest and fire the smaller mass to provide a glancing blow ( Figure 3.8 and Figure 3.9 ). The film may now be edited with the VideoPoint Capture Software.

Figure 3.8 Before the Collision. Collision of two masses where one mass is initially at rest.

Figure 3.9 After the collision. Collision of two masses where one mass is initially at rest.

Figure 3.10 VideoPoint Capture collecting data. Notice that the Record button is grayed out.

5. Once the Stop button is pressed, editing may begin. Save the video clip as a .mov movie file using the File drop down menu at the top of the screen.

Editing the Video Clip:

6. Data analysis will be easier if the length of the video is cropped to include only the frames of interest. After the stop button, the editing screen will appear. The editing screen contains a set of controls much like the set of controls on any dvd player. There are buttons for play, fast forward, fast rewind, step forward, and step backward. When the play button is pressed, the video will begin to play, and the button is transformed into a stop button. These controls are shown in Figure 3.8. There is also a slidebar with a black diamond on the top. Sliding this black diamond along the slide bar advances/recedes the video clip. Use these controls to review the film clip to decide where to crop the video clip. There are also two white triangles. These triangles are to mark the start and end of the frames that are to be analyzed.

Figure 3.11 VideoPoint Capture Editing Screen

7. After reviewing the video clip, use the white triangles to mark the start and finish of the frames that will be analyzed. Make sure that the start is marked after the puck has cleared the hand of the person shooting the puck. Deleting approximately five frames after the puck is released is recommended. Once you have chosen the start and finish, clip on the Confirm Edit button. This will crop the video clip to the chosen length. ( See Figure 3.12 )

8. After checking that the film clip has the needed frames, save the film clip.

Figure 3.12 VideoPoint Capture Editing Screen

Black Diamond

White Triangle - Start

White Triangle - Finish

Analyzing the Video Clip:

9. Open the VideoPoint Physics Fundamentals Software. Using the File drop down menu, load the video clip movie file saved in step 8.

Figure 3.13 VideoPoint Physics Fundamentals Preview Screen

10. The first screen can be used to view the video clip. This screen is labeled as the Preview Screen in the tabs which run along the top of the screen. These tabs may be used to navigate through the program. As each screen progresses, a hint will appear in a pop up window. These hints can be closed using the X button in the upper, right hand corner of the pop up window. Once the clip has been viewed, advance to the next screen using the forward arrow button.

11. This screen is the calibrate screen. Here a yellow calibration tool can be found. Move one end of the calibration tool to meet with one end of the meter street ( or some other known standard ) and move the other end of the yellow calibration tool to meet with the other end of the meter stick. Enter the length of the object between the jaws of the calibration tool, one meter if the meter stick is used. Advance to the next screen.

Figure 3.14 VideoPoint Physics Fundamentals Calibration Screen

12. This is the Set Up Analysis frame. Set the origin using Move Origin x and y position boxes. The axis may also be rotated and the t = 0.0 seconds frame may also be set. Go to the next frame.

Figure 3.15 VideoPoint Physics Fundamentals Set Up Analysis Screen

13. This is the Collect Data screen. Here the mouse can be used to select data points on the screen while in the Data Collection Mode. As the data point is selected, the video clip advances to the next frame. The set of data points may be completely deleted by selecting the data set name ( ex. Points S1 ) and pressing the Delete button. A new set may be started with the Add New Points drop down menu and hitting the OK button. Point locations may be moved while in the Point Editing Mode. When in the Point Editing Mode, the mouse can grab the point and drag it to a new position. Once the points have been collected for the one puck a window will appear that allows you to set up a second set of points ( Figure 3.17 ). Select “Track another point ( New Series )” and select “OK”.

Figure 3.16 VideoPoint Physics Fundamentals Collect Data Screen

14. Export the data set into a spreadsheet using the file drop down menu.

Figure 3.17 VideoPoint Physics Fundamentals Collect Data Screen

Data Collection ModePoint Editing Mode

Figure 3.18 VideoPoint Physics Fundamentals Collect Data Screen

Figure 3.19 VideoPoint Physics Fundamentals Export Data Menu

Analyzing the Data Collected:

15. Open the spreadsheet containing the data collected. 16. Plot the y position versus the x position.17. Calculate the x and y components of the initial and final velocities of each of the pucks by using

the linear trendlines of position versus time plots.

Part One: Two Puck Collission, Both Pucks Initially in Motion

18. Repeat steps 1 through 17, this time colliding two pucks initially in motion.

Figure 3.20 Collisions of Two Puck, Both Pucks Initially in Motion.

Figure 3.21 Collisions of Two Puck, Both Pucks Initially in Motion.

Data Analysis:

Part One: Two Puck Collision, One Puck Initially at Rest

m1=_________________ kgm2=_________________ kgv1xi

=_________________m/ sv1yi=_________________m/ sv1x f

=_________________m/ sv1y f=_________________m/ sv 2x f

=_________________m/ sv 2y f

=_________________m/ s

p1x i=_________________ kg m/ sp1yi=_________________ kg m/ sp1x f

=_________________ kg m/ sp1y f

=_________________ kg m/ sp2x f

=_________________ kg m/ sp2y f

=_________________ kg m/ s

px i=_________________ kg m/ sp yi=_________________ kg m / sp x f=_________________ kg m /sp y f=_________________ kg m /s

K i=_________________ JK f=_________________ J

a.) Was momentum conserved?

b.) Find the percent difference between the initial momentum and the final momentum.

% diff x=∣px i− px f∣px i

∗100% , % diff y=∣py i− py f∣p yi

∗100% ( Note: If the y component of the initial

momentum is equal to zero, use the final value of the y component momentum for the puck initially in motion.)

c.) Was kinetic energy conserved?

d.) Find the percent difference between the initial kinetic energy and the final kinetic energy.

Part Two: Two Puck Collision, Two Pucks Initially in Motionm1=_________________ kgm2=_________________ kgv1xi

=_________________m/ sv1yi=_________________m/ sv2xi=_________________m /sv2yi=_________________m /sv1x f

=_________________m/ sv1y f=_________________m/ sv 2x f

=_________________m/ sv 2y f

=_________________m/ s

p1x i=_________________ kg m/ sp1yi=_________________ kg m/ sp2x i=_________________ kg m/ sp2yi

=_________________ kg m/ sp1x f

=_________________ kg m/ sp1y f

=_________________ kg m/ sp2x f

=_________________ kg m/ sp2y f=_________________ kg m/ s

px i=_________________ kg m/ sp yi=_________________ kg m / sp x f=_________________ kg m /sp y f=_________________ kg m /s

K i=_________________ JK f=_________________ J

a.) Was momentum conserved?

b.) Find the percent difference between the initial momentum and the final momentum.

% diff x=∣px i− px f∣px i

∗100% , % diff y=∣py i− py f∣p yi

∗100 %

c.) Was kinetic energy conserved?

d.) Find the percent difference between the initial kinetic energy and the final kinetic energy.