1.1. A popular demonstration of the conservation of momentum and conservation of energy is the  Newton’s cradle. 

It features several identical polished steel balls hung in a straight line in contact with each other. 

If one ball is pulled back and allowed to strike the line, one ball is released from the other end whilst the rest are stationary. If two are pulled out, two are released on the other end and so forth as shown in Figure 1. 

Figure 1

Explain, with energy and momentum considerations, why swinging one ball from the left will not release two balls on the right. 

Assume the Newton’s cradle is in a vacuum.

1.2. The speed of an air rifle pellet is measured by firing it into a wooden block suspended from a rigid support. 

The wooden block can swing freely at the end of a light inextensible string of length 2.0 m measured from the pivot to the centre of the block, as shown in Figure 2 below. 

Figure 2

A pellet of mass 2.81 g strikes a stationary wooden block and is completely embedded in it. The centre of mass of the block rises by h at an angle of 35º to the vertical. The wooden block has a mass of 520 g. 

Determine the speed of the pellet when it strikes the wooden block.

1.3. The wooden block is replaced by a steel block of the same mass. The experiment is repeated with the steel block and an identical pellet. The pellet rebounds after striking the block. 

A student makes an assumption that the angle that the steel block makes with the vertical will be greater than 35º because the block doesn’t have the additional mass of the pellet embedded within it. 

Discuss the validity of the student’s assumption.