# Momentum interchanges with other objects

##### Demonstration

Collision between long pendulums.

#### Apparatus and materials

Steel ball with hook, 2.5 cm diameter

Steel balls with hooks, 5 cm diameter, 2

1 steel ball with hook, 1.25 cm diameter

Plasticine

#### Health & Safety and Technical notes

If multi flash photography is used, avoid flash frequencies between 15-20 Hz and avoid red flickering lights, which makes some people feel unwell. Rarely, some people experience photosensitive epilepsy.

For this experiment to be effective, it is necessary to suspend the steel balls from a rigid support in the ceiling so that they form really long pendulums.

Multiflash photographs of these events could be taken, but the experiments are better shown directly. Photographs can be taken by illuminating the spheres strongly and positioning the camera and strobe disc in a direction at right angles to the direction of collision.

#### Procedure

Demonstrate collisions in this order:

a Head-on collisions between two equal masses (large balls).

b Head-on collisions between the medium size and large mass.

c Oblique collision between a moving mass and an equal mass at rest (large balls). Try and show that the angle between the paths after collision is 90 degrees.

d Collisions between a very small ball and a large heavy one.

#### Teaching notes

1 These collisions are more obviously friction-free than the collisions of trolleys and pucks.

In step c, make the link between the colliding steel balls of equal mass and the collision between alpha particles and helium nuclei in a cloud chamber.

In step d, the small ball colliding with a large ball shows the small ball bouncing off the large one at almost the same velocity as its incoming velocity and little recoil from the large one. When the large ball strikes the small one then the small one bounces off the large one at a speed greater (up to twice the speed) than the large ball was moving towards it. The large one continues its motion with little change in velocity.

2 The collisions described are almost perfectly elastic. Inelastic collisions can be produced by putting wax or Plasticine on the ball at rest in such a way that the balls stick together on collision. Although such inelastic collisions are very important this particular demonstration is not one that students understand clearly and easily.

3 You could invoke the principle of Galilean relativity, though students may just take it for granted. Newton's laws of motion and the events that they describe are independent of uniform motion of the observer or apparatus. The same laws of motion will be observed in a steadily moving train as in a laboratory test.

Using the concepts learnt when the large and small pendula collided try this story, a thought experiment: An elephant on roller skates.

Consider a collision between a table tennis ball and an elephant on roller skates. Throw the ball at the stationary elephant’s head at 5 m/s. The elastic ball will bounce back at almost 5 m/s and the elephant will recoil backwards very slowly, barely noticeably.

Now hang the ball at rest by an imaginary thread in mid-air and let the elephant rush towards it at 5 m/s. When the elephant hits the table tennis ball what motion will the ball take?

It seems quite difficult to answer this until we try the following trick. Imagine the elephant surrounded by fog so that the rider on his shoulders has no idea that he is moving along the road. Likewise the elephant is moving smoothly on his roller skates and the rider knows nothing at all of his motion. Then in the fog the rider sees a table tennis ball ahead. What will the rider think that the ball is doing? He will think that the ball is moving towards him at 5 m/s. He still does not know that the elephant is sliding along through the fog. Seeing the ball rushing towards him at 5 m/s to hit the elephant’s head, he knows what it will do. It will bounce away at 5 m/s from the head of the elephant.

Now instead, suppose there is no fog and an observer standing on the ground watches what is happening. The outside observer sees the ball bounce away from the elephant’s head at 5 m/s relative to the elephant but he also sees that the elephant is moving at 5 m/s so the ball moves at 10 m/s relative to the ground.

This result has applications in sport and, for example, the kinetic theory of gases. Whenever a massive bat hits a stationary ball of much smaller mass, making an elastic collision, the ball moves away at double the speed of the bat. When gas molecules hit a stationary piston head-on they rebound, on average, with an equal speed in the opposite direction. However when they are hit by a moving piston that is approaching them they rebound with a gain in speed which is twice that of the moving piston. Bicycle pumps get hot.