During collisions involving two bodies, equal and opposite forces are set up between them. These impact forces influence the subsequent motion of the bodies. Momentum of the system (consisting of both bodies) is preserved if both bodies are free to move in space. This is because there is no external forces act on the system.

The forces acting between the bodies during the small interval of time when they are in contact cause changes in the velocities of each separate body. An exact determination of these forces is not practical but the presence of the forces can be allowed for by using a property known as the coefficient of restitution. The coefficient of restitution is the ratio of speeds of a falling object, from when it hits a given surface to when it leaves the surface. In laymen's terms, the coefficient of restitution is a measure of bounciness. It basically is a property of collisions and depends upon the materials that are colliding.

In this experiment, the coefficient of restitution between two balls, (a glass marble and a steel ball bearing) and the apparatus it is colliding with will be determined.

AIMS

To determine the coefficient of restitution between two balls, (a glass marble and a steel ball bearing) and the apparatus it is colliding with.

THEORY

When two bodies collide, equal and opposite forces act on each body and will cause a motion. If there is no external force exerted to the system, then momentum will be conserved. Momentum is defined as (kg.m/s) and is a vector in the direction of v.

(Newton’s Second Law) … equation (1)

Impulse is defined I =F dt as which has useful applications in solving problems for forces when very short times are involved, such as during collisions.

By taking the equation (1) for an integration, it shows that the impulse due to a force over a given time period is equal to the change in momentum as shown in equation (2).

….. equation (2)

Figure 1

Consider the collision of the bodies in figure 1, there are equal and opposite forces (Newton’s Third Law) acting on each body for the same amount of time during the collision. This condition can be represented mathematically as in equation (3).

…. Equation (3)

Conservation of momentum tells that G1 + G2 = 0 during a collision. But, this is unlikely to happen in real case because there is always some energy loss, whether through deformation, heat or sound. The coefficient of restitution is used to described this loss. This coefficient is constant and depends only on the materials from which the bodies are made, provided that the relative velocity of the bodies coming into contact is not too low,. The coefficient of restitution, e, is defined as

After carrying out a simple substitution and simplification, the coefficient of restitution can be given by:

e=|v'Bn-v'An|vAn-vBn

For a perfectly elastic collision, the coefficient of restitution is 1.0 where all the kinetic energy is conserved. For a perfect plastic collision, the coefficient of restitution is 0 in which the loss in kinetic energy is a maximum. All collisions lie somewhere between these extremes. ( 0 < e < 1)

APPARATUS

Marble, steel ball, white paper, carbon paper, cylindrical pipe and ruler.

PROCEDURE

Figure 2

1. The apparatus is set up as shown above in Figure 2.

2. An inclined steel block is set to 35 ̊, a white paper is placed on the board and covered with carbon paper.

3. The height of the steel pipe from the point of impact is measured by using a ruler.

4. Drop the marble through the pipe and record the distance to the point of first impact.

5. Repeat step 4 at least three times.

6. Repeat steps 4 and 5 for the steel ball.

7. Set the steel block to 10 degrees and repeat steps 4-6.

8. Set the steel block to 22.5 degrees and repeat steps 4-6

DATA PROCESSING

Sample Calculations

The...