Report Sheet for Lab M04: Center of Mass Velocity of an Isolated System

Report Sheet for Lab M04: Center of Mass Velocity of an Isolated System (Windows NT/2000 version) Jan 2, 2006 Experiment 1: One Glider on an Air Track In this experiment, you will send a glider along the air track and use photogates to measure its center- of-mass velocity at two different times (we will call these the “initial” and “final” times).

1. Which Gate is Which? Your first job is to experimentally determine which timing data goes with which gate. Click the Collect button and block a photogate with your hand. Now block the other photogate instead. Pay attention to the values appearing in the table so that you can identify which time data corresponds with which photogate--this is VERY IMPORTANT. You can switch which photogate is plugged into which port or switch the positions of the photogates along the track if you need to for convenience—no switching once you have started doing actual trials. 2. Measure and record the flag width on the glider you will use. Measure to the nearest 0.1cm. Make sure that the flag is properly oriented (not crooked). Record your result below. Adjust the height of the photogate and/or the flag so that the glider with flag can pass unobstructed through the photogate and so that the flag blocks the photogate when the glider passes through.

Flag width = ______cm

3. Before giving your glider a push along the air track, predict what you think will happen (increase ? decrease ? stay constant ?) to the glider’s center-of-mass velocity after you have pushed it. Explain your answer:

4. Now perform the experiment. Make sure that you are not pushing the glider at any time while it is passing through the photogate ! Use your data to determine the initial and final center-of-mass velocities of the glider. Show all calculations below (starting with a symbol followed by = sign and a formula, then subbing in numbers with units). Assign the positive direction to be in the direction of the glider’s motion.

5. If your air track were tilted so (instead of level), so that your glider went “downhill”, how would that affect each of the measured gate times? Be specific and give a complete answer.

6. If your air track had a lot of friction, how would that affect the measured gate times? Be specific and give a complete answer. 7. Friction, gravity and your hand’s push are examples of outside influences (“forces”) that can change the center-of-mass velocity of a system. Based on the results of Experiment 1, do you think that friction and/or gravity significantly affected the glider’s velocity ? Explain why or why not. If you answered “yes,” take steps now to minimize the effects of friction and gravity in the remainder of this lab (ask for help if you’re not sure how to do this).

Experiment 2: Sticky collisions between an initially stationary object and a moving object

In these collisions you will use gold, red and blue gliders (whose masses are 150g, 300g and 450 g). One of the gliders will be at rest before the collision and the other glider will initially be moving. After the collision, the gliders will be stuck together by velcro located on the ends of the gliders. You will need to use the photogates to ultimately determine the velocities of each glider before AND after the collision. You will then calculate the initial and final center-of-mass velocities of the two-glider system using the formula MCMVCM = M1V1 + M2V2

(We hope this formula reminds you of a similar formula we have used for center of mass position)

Make sure that the flags on both gliders have the same width and are properly oriented. Then perform a sticky collision. We suggest that you try two equal-mass gliders for your first experiment. Make sure that all gliders have completely cleared all photogates whenever the gliders are in contact with each other ! Use the diagrams at the end of the report sheet to indicate the locations of each glider BEFORE any glider has passed through a photogate and AFTER the gliders have collided and then passed through a photogate. Also indicate clearly the mass and the direction of motion of each glider on both diagrams. Finally, record the initial and final velocities of each glider. Be really sure you have the correct velocity associated with the correct glider ! Continue to choose the positive direction in the direction of motion of the gliders.

Calculate the center-of-mass velocity of your system before and after your collision. Show example calculations (before and after) for your first collision below (first using symbols, then subbing in numbers with units).

When you’ve finished your first experiment, call an instructor over to check your work. If everything looks good, finish Experiment 2 by completing two more collisions using different combinations of gliders. Experiment 3: Sticky collisions between two moving objects In these collisions, both gliders will initially be moving. After the collision, the gliders will be stuck together by velcro located on the ends of the gliders. You will need to think carefully about how to arrange the gliders so that you can measure each glider’s initial and final velocity ! Note that there are two possible types of collisions here (“head-on” and “overtaking”). If you have trouble getting the gliders to stick, keep trying… (hint: it sometimes helps if the initial speeds are not too high)

Repeat the steps you followed for Experiment 2, for three different collisions. Continue to record all data on the diagrams at the end of the report sheet. When recording velocities in your data table, take special care to include the correct signs !

Experiment 4: Bouncy collisions between an initially stationary object and a moving object This experiment is similar to Experiment 2, except that both gliders will have steel bumpers that should bounce instead of sticking to each other. Repeat the steps you followed for Experiments 2 and 3, for three different collisions. When recording velocities in your data table, take special care to include the correct signs !

We hope you noticed some trends in the direction of the final velocity of the initially moving glider. Describe below how you could predict whether the initially moving glider will continue moving in the same direction after the collision, or will reverse direction. Then test your prediction by doing two new collisions (involving combinations of gliders that you haven’t already tried).

Experiment 5: Bouncy collisions between two moving objects This experiment is similar to Experiment 4, except that both gliders are initially moving. Repeat the steps you followed for Experiments 2, 3 and 4, for three different collisions. When recording velocities in your data table, take special care to include the correct signs !

CLASS ANALYSIS PH302 LAB M4 CENTER OF MASS VELOCITY OF AN ISOLATED SYSTEM

1) What are the axes on the class data graph? (I.e., what is being graphed?) Sketch the class graph, including all labels.

2) What is the shape of the graph? What type of mathematical fit is appropriate?

3) Once the appropriate fit is made to the graph, record the equation of fit.

4) What does the result of the graph fit MEAN?

5) Now examine your data table before and after the collisions. Are there any quantities (other than total mass) that seem to be conserved (i.e., they stay constant)? Which (if any)?

7) Should the velocity of one of the carts remain constant during a collision experiment ? Why or why not ?

8) Create the velocity versus time graphs for both gliders on the same set of axes for a bouncy collision of red on blue. Assume that the blue glider was initially stationary and the red glider was moving for 2 seconds before encountering the blue one. Also assume that the gliders traveled for 2 seconds after the collision. Ignore friction.