Question

A block of mass m is pressed against a light spring by a distance d and is kept at rest (Fig. 1). The spring, of elastic constant k, is released and the block is thrown on a horizontal surface without friction. The smooth surface curves upward and the block rises. Calculate your speed when you have climbed a height h. (Express v as a function of k, m, d, h and g). 

Answer 1

Solution:

The mass m compresses the spring by a distance d. The spring constant is k. Then the elastic potential energy of the spring is given by,

   ........(1)

Let the mass have a velocity v when released. The kinetic energy of the mass when released is given by,

..........(2)

Elastic potential energy of the spring is equal to kinetic energy of the mass when released. Thus, we have

Let the mass rises to a height h. At height h, let it have a velocity v'. Thus the total energy of the mass at height h is the sum of kinetic energy and potential energy . That is,.

............(3)

Thus By the law of conservation of energy,

we have,

   ...........(4)

So,

Therefore,