Investigating momentum during collisions

Demonstration

A moving glider on a linear air track collides with a stationary glider, thus giving it some momentum. This datalogging experiment explores the relationship between the momentum of the initially moving glider, and the momentum of both gliders after the collision.

Apparatus and Materials

• Light gates, interface and computer, 2
• Linear air track with two gliders, each fitted with a black card
• Glider accessories: magnetic buffers, pin and Plasticine
• Clamps for light gates, 2
• Electronic balance

Health & Safety and Technical Notes

The most significant hazard is that of setting up the linear air track on the bench, especially if it is stored on a high shelf. Two people may be needed to achieve this safely.

Read our standard health & safety guidance

Photograph courtesy of Mike Vetterlein

Set up the linear air track in the usual manner, taking care to adjust it to be perfectly horizontal. A stationary glider should not drift in either direction when placed on the track.

Select two air track gliders of equal mass. Attach to each a magnetic buffer at one end, and a black card in the middle.

Prepare each card accurately to a width of 5.0 cm, and enter this value into the software.

The mass of the gliders must also be measured and entered into the software to prepare for the calculations (see below). If magnets are not available, crossed rubber band catapults are an acceptable alternative.

Connect the light gates via an interface to a computer running data-logging software.

The program should be configured to obtain measurements of momentum, derived from the interruptions of the light beams by the cards.

The internal calculation within the program uses the interruption times from each light gate to obtain two velocities. These are multiplied by the appropriate glider masses to give two values of momentum, one before the collision, and one after. This assumes that the measurements for the width of the card and the masses of the gliders have been entered into the program correctly.

For the elastic collision (first part), the momentum measured at A depends upon the mass of the moving glider only. The momentum measured at B depends upon the mass of the initially stationary glider only.

For the inelastic collision (second part), the momentum measured at A depends upon the mass of the moving glider, whereas the momentum measured at B depends upon the combined mass of both gliders.

Students accumulate a series of results in a table with two columns, showing the momentum before and after each collision. It is informative to display successive measurements on a simple bar chart.

Procedure

Data collection

Part 1: Elastic Collisions
1. Position the light gates A and B either side of the midpoint of the track as shown.
2. Place one glider at the left hand end of the track, and the second between the light gates, with the magnetic buffers facing. The second glider should remain stationary.
3. Give the first glider a short push so that it passes through light gate A. It then collides with the stationary glider. This then moves and passes through light gate B. If necessary, adjust the positions of the light gates to make sure that the sequence is correct. (As the magnetic buffers approach each other they repel so that there is no real contact between the two gliders. This creates the condition for 'elastic' collisions.)
4. Return the gliders to their starting positions, set the software to record data, and repeat the sequence. Observe the measurements of momentum before and after the collision. Repeat this whole process several times to obtain measurements for a series of collisions.
Part 2: Inelastic collisions
5. Replace the magnetic buffers with a pin on one glider and a lump of Plasticine on the other. (This will cause the gliders to stick together after the collision, making it an 'inelastic' collision.) The black card may be removed from the initially stationary glider.
6. Reset the program so that the measurements at B use the combined mass of both gliders.
7. Use the same procedure as for Part 1 to obtain measurements for a series of inelastic collisions.
Analysis
8. Depending upon the software, the results may be displayed on a bar chart as the experiment proceeds. Note the very similar values for momentum before and after each collision of either type.
9. The results can be displayed as a graph of 'momentum before collision' against 'momentum after collision'. A straight line graph would demonstrate that the relationship does not depend upon the magnitude of the initial momentum. If the graph is at 45°, this confirms the conservation of momentum.

Teaching Notes

• This is a computer-assisted version of the classic experiment, using light gates and electronic timers. The great advantage of this version is the instant presentation of momentum values using the software. This avoids preoccupation with the calculation process and allows attention to focus on the results.
• It is unusual for the measured values of momentum before and after each collision to be identical. It is wise to limit the number of decimal places displayed, so that the discrepancy does not appear exaggerated. Note how small the discrepancy is, compared with the magnitude of each value. A bar chart display makes this comparison very plain to see. Thus it can be argued that momentum is conserved in each case.
• A discussion of the measurement errors must consider the residual friction affecting the motion of the gliders. Errors may be kept to a minimum by strategically placing the light gates so that they capture the motion as close as possible to before and after a collision.

This experiment was safety-tested in June 2007