Worked Examples

• Example 4.5
• Example 4.6

In the last section the bodies were assumed to stay together after impact. An elastic body is one which tends to return to its original shape after impact. When two elastic bodies collide, they rebound after collision. An example is the collision of two snooker balls.

If the bodies are travelling along the same straight line before impact, then the collision is called a direct collision. This is the only type of collision considered here.
 
 

Consider the two elastic spheres as shown in Figure 4.4. By the principle of conservation of linear momentum

When the spheres are inelastic v₁ and v₂ are equal as we saw in the last section. For elastic bodies v₁ and v₂ depend on the elastic properties of the bodies. A measure of the elasticity is the coefficient of restitution e, For direct collision this is defined as

The values of e in practice vary from between 0 and 1. For inelastic bodies e = 0, for completely elastic e = 1. in this latter case no energy is lost in the collision.
 
 

Worked Example 4.5

A body of mass 2kg moving with speed 5m/s collides directly with another of mass 3 kg moving in the same direction. The coefficient of restitution is 2/3. Find the velocities after collision.
 
 

Solution

[1]

By Equation 4.5

[2]

Adding [1] and [2] gives

and by [1]

Worked Example 4.6

A railway wagon has mass 15 tonnes and is moving at 1.0 m/s. It collides with a second wagon of mass 20 tonnes moving in the opposite direction at 0.5m/s. After the collision the second wagon has changed its speed to 0.4m/s in the opposite direction as before the collision.

Find:

The negative sign means it has change direction of travel.
 
 

b)

Coefficient of restitution is given by Equation 4.5

c)