# Two-dimensional collisions with ball bearings

##### Demonstration

Another interesting study of momentum conservation.

#### Apparatus and materials

Collisions in two dimensions kit, with steel balls and marbles of 1.5 cm diameter

G-clamps

Sheet of carbon paper (or use coloured paper with the balls covered in chalk dust)

Large sheet of white drawing-paper

Marbles, 2 identical

Marbles of different mass, ball bearing (OPTIONAL)

#### Health & Safety and Technical notes

Set up the ramp at the edge of a bench, fixed with a G-clamp.

#### Procedure

a Place a large sheet of white drawing-paper on the floor and cover it with carbon paper (carbon side downwards). The point of impact will be marked on the white paper by the carbon paper.

b Release a marble so that it is projected horizontally off the edge of the table onto the floor.

c Find the point on the drawing-paper vertically below the point of projection with a plumb line or a falling marble, and mark it on the paper. The distance between this point and the point of impact is proportional to the horizontal velocity of the ball on projection.

d Balance a second marble on the support, which is attached to the bottom of the ramp using a small piece of Plasticine. Arrange it so that the ball is exactly opposite the end of the ramp.

e Release a marble so that a collision occurs at the bottom of the ramp and both balls hit the paper. Investigate whether momentum is conserved in the collision.

f Offset the support to show oblique impacts use two spheres of the same mass.

#### Teaching notes

1 The velocities are estimated by measuring the horizontal distance travelled by each ball in the time of vertical fall. It is essential to measure from the projection point found in step c. As a measure of reliability, repeat each reading a few times.

Note that, at the moment of collision, the difference in position of the two balls equals the sum of their radii.

2 The projected marble takes the same time to reach the floor as a marble falling vertically.
The horizontal motion of the projected marble is not affected by its vertical motion and so the horizontal component of its velocity is constant. The horizontal distance the projected particle moves is proportional to the time for which it is falling and the horizontal component of its velocity.

In step e, the first marble collides with the one at the end of the ramp. The first marble stops and just topples off the ramp to fall vertically. The one which is originally stationary is projected outwards.

If the collision is elastic then it should be projected outwards as far as the marble in step a. Momentum is conserved in the collision. The masses are the same and so the horizontal speed of the first marble before the collision is the same as the horizontal speed of the second one after collision.

3 You can also try collisions between marbles of different masses, or a marble and a steel ball bearing.

4 Both marbles are projected outwards. Allow for the diameter of the spheres. The positions where they both reach the floor are joined to the position just below the starting point for the projection. A line representing the marble falling down the ramp can be drawn from step C. A scale drawing will show momentum is conserved.

5 Compare the paths of the oblique collisions with cloud chamber photographs.