Eric Murray, Spring 2006
Questions these experiments will enable you to answer: How does the kinetic energy of a system change in an elastic collision? How does the kinetic energy of a system change in a perfectly inelastic collision?
Features: The system is two carts on a track (a one-dimensional space). Automated measurements are made with devices that are interfaced to a computer. The velocity as a function of time is measured at short time intervals by motion sensors (see Technical Note 1) and recorded (and displayed in graphs) by the computer.
Preliminaries: Level the track. This can be done by gently rolling one of the carts in each direction, and seeing if the motion is the same each way. Check that each motion sensor is at an end of the track and is pointing down it. Make sure the left motion sensor is plugged in to channels 1 (yellow plug) and 2 (black plug) of the interface unit, and the right motion sensor is plugged in to channels 3 (yellow plug) and 4 (black plug). (There is, of course, nothing magic about the left sensor going into channels 1 and 2, but these experiments are written with that assumption.) Open the data template. You'll find a graph for velocity of carts as a function of time. The motion sensor has been set to record data at 25 Hz, beginning when the left cart reaches 1.0 cm/s and continuing for 3.5 s.
Find the mass of each cart and block. Be sure to place the carts upside down on the balance, do they don't roll off. These masses aren't going to change, so if a line has formed for the balance, you may measure the masses later.
Experiment 1: Record the mass of the cart you have chosen as the right
cart, and the total mass of the cart and block that you have chosen as the left
cart. Record your expectation for the fractional change in kinetic energy, ΔK/Ki, calculated from theory. Place the carts near the center of the track about 40–50 cm apart. If you have a pair of silver carts, only one end has magnets, so orient the carts so the magnets in them will repel. If you have a pair of red carts, both ends have magnets, but if you push the cart gently, the magnets will repel before the velcro grabs. Click Record
, and give the left cart a push toward the right cart (and let go). Do not let the right cart hit the motion sensor.
Find the velocity of the left cart at a time as close as possible to the beginning of the collision, while being unambiguously before the collision. Calculate the kinetic energy before the collision. Find the velocity of both the left and right carts at a time as close as possible to the end of the collision, while being unambiguously after the collision. (The minimum velocity of the right cart is displayed on the graph as a suggestion, but you should examine the curve to see if it is reasonable.) Calculate the total kinetic energy after the collision. Find the change in kinetic energy from before to after the collision, and the fractional change. (Your results may fit into the table better if you express K in mJ, and ΔK as a percent.)
You'll probably find a fractional change in kinetic energy that is inconsistent with your expectation. As you can see from the downward slope of the left cart's velocity graph before the collision takes place, friction is doing work on the left cart, changing its kinetic energy. In this situation, it is not surprising that your fractional change in kinetic energy is inconsistent with your expectation.
Experiment 2: Repeat Experiment 1. Once again, find the velocity of both the left and right carts at a time as close as possible to the end of the collision, while being unambiguously after the collision . Record the two times at which these velocities occurred. Fit a line to the left cart velocity data before the collision. The slope and intercept yield the equation of a line representing the velocity of the left cart as a function of time. Use the average of the two times recorded after the collision to calculate the velocity the left cart would have had at that time, had the collision not taken place. Calculate the total kinetic energy the system would have had at that time as the Before
kinetic energy. Calculate the total kinetic energy after the collision. Find the change in kinetic energy from before to after the collision, and the fractional change.
Experiment 3: If you have a pair of silver carts, only one end has magnets, so orient the carts so the magnets in them will not repel and the carts will stick together (a perfectly inelastic collision). If you have a pair of red carts, both ends have magnets, but if you push the cart more vigorously than in experiments 1 and 2, the velcro will grab before the magnets can repel. Repeat Experiment 2 (one block on the left cart, and none on the right).
Summary: Review your worksheet. Think about the goals of these experiments, your results, and the expectations from theory while writing your discussion.