Two dimensional momentum interchanges with pucks

Demonstration

Multiflash photographs of momentum interchanges with pucks.

Apparatus and Materials

• Co₂ pucks kit

• CO2 cylinder (syphon type)

• Dry ice attachment
• Camera
• Motor-driven stroboscope
• Gantry for CO2 pucks kit
• Bright lamps, 2

Health & Safety and Technical Notes

When using CO₂ and dry ice it is essential to have good ventilation to the room.

Remember to wear heat-insulating gloves when handling dry ice.

Avoid flash frequencies between 15-20 Hz and avoid red flickering light which makes some people feel unwell. Rarely, some people can experience photosensitive epilepsy.

Read our standard health & safety guidance

In all of the following experiments, the magnetic pucks should be pushed gently to avoid their being chipped and thereby damaged.

The glass plate must be very carefully cleaned with ethanol and carefully levelled using the wedges supplied with it. The CO₂ pucks are themselves the best ‘spirit level’ when adjusting the wedges.

About two or three cm ³ of solid CO₂ are placed underneath the puck, which will float on a layer of gas as the solid CO₂ evaporates.

To avoid troublesome condensation of water vapour on the glass plate, it is advisable to work with the laboratory windows open.

The camera is attached to the supporting frame set up over the glass plate. The motor-driven stroboscope is put in front of the camera.

Alternatively, a camera gantry can be improvised using laboratory stools and a trolley runway.

Two bright lamps (up to 500 W) are used to illuminate the pucks at a glancing angle from the floor. They should not cast a reflection from the glass plate through the strobe disc into the camera.

An alternative way of illuminating the pucks is to place a small flashing light on the top of the puck. The home-made flashing light used to take the photograph has a 'lop-sided' mark space ratio so that the time for which the light is off can be marked accurately. The time intervals for the light off period can be calculated from the electronics or measured using a xenon strobe. For most measurements it is enough to know that the time intervals are constant before and after the collision and so the number of light offs is proportional to the time taken.

A metre rule needs to be visible in the photograph if measurements are to be taken, however, the distances moved are proportional to the length of the light streaks and so actual measurements are not really necessary.

The pucks can be either:

• ring magnets, of the kind used in TV sets, with a white lid fixed to them and solid carbon dioxide placed in the hole underneath them so that the magnet glides on a cushion of carbon dioxide. The motion is practically frictionless. Too much humidity (breathing students!) causes condensation on the cold plate, which then freezes the puck to the glass plate.
• motorized pucks which pump an air cushion underneath themselves so that the puck rides on the air.

Procedure

1. Obtain a multiflash photograph of a single magnetic puck moving freely across the plate. The photograph should show constant velocity.
2. Photograph a magnetic ring making a head-on collision with another ring of the same mass, originally at rest.

3. Repeat step 2 with the second puck twice the mass of the moving one. This is realized by putting one of the brass rings on top of the magnetic ring as all the rings provided have the same mass. A number of variants of these head-on collisions can be tried by varying the masses of both the pucks.
4. Photograph some collisions that are not head-on, so the colliding puck and the stationary puck afterward move off in different directions. Try to show a collision between two equal masses (one stationary) so that after the collision the pucks move off at a 90 ° angle.
5. Photograph collisions between two pucks which are already moving. This is more difficult but rewarding.

Teaching Notes

• In studying linear collisions with the CO₂ pucks, it is helpful to put magnetic strips across the glass plate, as illustrated, in order to confine the motion to one dimension. The repulsion between the strip and the pucks keeps the pucks’ motion linear.
• Demonstrations 4 and 5 involve velocities and therefore momenta in two dimensions. Momentum is a vector quantity which must be added by the parallelogram rule. The diagram shows the result of pucks colliding and moving off after the collision at an angle. These collisions may also show a 90-degree angle between the tracks after collision.

• Multiflash photographs can be analyzed by projecting a photograph onto a screen and separating the screen from the projector so that an actual puck just covers the image of the puck on the screen. In this way scaling factors are avoided.
• Knowing the time intervals and the distances travelled by a puck (centre to centre), the velocities can be calculated, the momentum of the pucks calculated and the angles between the colliding pucks measured. Taking account of the vector nature of the movement, then the momentum before collision can be compared with the momentum after collision.
• A scale drawing can also be used to analyze the motion before and after the collision. This will eliminate difficult mathematics. Use a photo of a puck colliding with another puck of the same mass producing a right angle collision (see below).
• Place an acetate sheet over the photograph. Draw lines through the centres of the pucks and mark the centres of the pucks on the lines. This can then be scanned and projected on a whiteboard.
• Line A is the incoming puck which strikes a stationary puck that bounces off along line C, while the incoming puck travels on along line B. If you are lucky enough to get a right angle, then linear momentum is conserved. If it is not a right angle and the masses are really equal, then some momentum will have been carried off by the pucks gaining angular momentum.
• Resolving along the two sides of the right angle for convenience and simplicity, then only track A has to be resolved along lines D and E. The distances travelled in equal time intervals along lines B and D are equal, representing equal momenta before and after the collision. The analysis is similar along lines C and E.
• The other photos (see below) can be analyzed in a similar way but there is no convenience of a right angle for resolving the momenta. In this case resolve along and perpendicular to the incoming puck. Remember that the masses are different when calculating the momentum before and after collision.