# Inelastic collision of trolleys

##### Class practical

Collisions when objects 'stick together'.

#### Apparatus and materials

Per student pair

Dynamics trolleys, 2

Runway, friction-compensated

Ticker-tape vibrator

Cork

Needle or large pin

#### Health & Safety and Technical notes

The runways are heavy and long. They need to be handled with care to avoid damage to students or nearby equipment. Runways are best lifted into position by 2 people. Place a barrier to ensure the trolleys do not roll off the end of the bench.

The method by which the cork and pins are attached to the trolley will depend on the particular make used. With most, it is easy to wedge a pin so that it sticks out from the trolley. It may be easier to fix a pin on both trolleys and stick a cork on one of them rather than to fix the cork directly on the trolley.

Another way to get the trolleys to stick together after collision is to fix a block of Plasticine onto one trolley with strong insulating tape at the edges. For the other trolley, another piece of Plasticine can be used or a series of drawing pins can be poked through a strip of insulating tape, before that too is attached to the trolley.

Yet another method is to attach double sided adhesive pads to the trolleys.

#### Procedure

a Fix a needle on the front of the moving trolley and a cork on the back of the second trolley, so that the trolleys stick together on collision. They will then move on as one unit after collision.

b Use a single ticker-tape attached to the back of the first trolley and pulled through a ticker-tape vibrator, to record the motion before and after collision.

c Make a moving trolley collide with an identical trolley at rest.

d Make a moving trolley collide with a trolley double the mass (one trolley stacked on top of another).

e Analyze the tapes to see if momentum is conserved.

#### Teaching notes

1 In these experiments the colliding bodies have constant speeds before collision and constant speeds (of different size) after collision. Make it clear beforehand that the students are to measure speeds, not accelerations, before and after impact. They then calculate momentum. A lot of kinetic energy will be lost in this inelastic collision, up to 50%, but hopefully it will demonstrate that momentum is conserved.

2 You could say:

'Elastic' has a special meaning in science. A spring is termed 'elastic' if, when stretched and released the spring goes back in exactly the same way and to exactly the same length as it was originally. It shows no sign of fatigue or of permanent stretch. Springs of good, hardened steel are elastic over a large range of stretches. Rubber cords are not perfectly elastic. They show a little fatigue and after-effects so it is unfortunate that we call them 'elastic'.

In a collision, the objects approach each other, losing kinetic energy, come to rest momentarily then move apart. If they end up with the same total kinetic energy as they started with, then we say that the collision has been 'perfectly elastic'.

3 The collision is inelastic if the total kinetic energy is much less after collision than before. Some of the original energy has been transferred elsewhere; often to warm up the colliders. If two lumps of sticky clay are thrown at each other so that they stick together then the collision is completely inelastic. If the two masses were equal and the velocities were equal, the combined lump would be at rest. All the kinetic energy will have been transferred, probably to thermal energy. However, momentum is a vector quantity (energy is not) and the two equal and opposite lots of momentum before the collision add up to zero before and after the collision. Conservation of momentum always holds.