# Extra Credit ProjecT: The Office Chair Radar Gun

This project may be done by teams of 1-2 individuals.

Your job in this assignment is to use an ordinary office chair (or any piece of furniture with wheels) to measure the speed at which objects are thrown. One might even try to measure the speed with which you can throw a baseball in this fashion -- hence the name "Office Chair Radar Gun." I suspect it won't work very well with projectiles as light as baseballs, though.

Be sure to draw a picture of your setup. Include the names of all people who participate. Describe carefully each piece of equipment you use (chair, measuring tape, thrown items, etc.).

You need to carry out several steps:

• measure the chair's coefficient of rolling friction
• throw objects so that they strike and stick to the chair, and measure the distance by which the chair recoils
• calculate the initial recoil velocity of the chair
• calculate the incoming velocity of the projectile

You'll need to devise some way of causing objects thrown into the chair to be "caught", so that they stay in the chair as it rolls backwards. Perhaps the solution is as simple as a cardboard box placed in the chair .... perhaps not. I'll refer to the mechanism for catching objects as the "catcher."

First, you must determine the coefficient of rolling friction of the chair. Place the catcher into the chair. Impart some known velocity to the catcher+chair system. It may take a little ingenuity and practice before you can figure out a method to give the catcher+chair a reasonably accurate velocity. Tell me exactly how you managed to do it. Then measure the distance it takes the catcher+chair system to slide to a halt, due to friction. Be sure to make several trials. Once you know the starting velocity, the mass of the catcher+chair, and the distance travelled, you can calculate the coefficient of rolling friction.

Next, the fun part: place the catcher in the chair, facing you. Mark the position of the chair carefully, and make sure that there is plenty of room for the chair to slide backwards. Choose some object (even better, choose several objects, and do this for each) and measure its mass. You will achieve the best results with massive objects, at least 5 or 10 kg. Then throw the object at the catcher. When the object reaches the catcher, its momentum will move the catcher+chair+object system backwards. Measure the distance the chair moves. Perform several trials for each object, being careful to throw it with the same speed each time.

Third, you must calculate the speed of the catcher+chair+object system immediately after the catch, for each trial. Because you know the mass of the system, and the coefficient of rolling friction, you can figure out the initial speed when the system started to move.

Finally, calculate the speed with which the object was moving just before it reached the catcher. How similar are the speeds for each trial with the same object? Is there some way to figure out the portion of the variation due to changes in throwing speed?

What are the largest sources of error in this experiment? How could you improve it? Would this really make a good "radar gun" with which to measure the speed of baseballs? If not, why?