How much work is done on the block between its release at height h and its ascent to its next maximum height?

Question

A block is released from rest, at a height h, and allowed to slide down an inclined plane. There is friction on the plane. At the bottom of the plane, there is a spring that the block will compress. After compressing the spring, the block will slide up the plane to some maxi-mum height, hA, after which it will again slide

back down.

How much work is done on the block between its release at height h and its ascent to

its next maximum height?

1. None of these

2. 2µ mA g hA

3. mA g (h − hA)

4. More information is needed.

5. 0

Answer 1

There are three forces involved:

gravity, friction, and the force of the spring.

And there are two kinds of energy involved: potential energy and heat energy.

There is no change in kinetic energy, therefore we do not need to consider it.

By definition of potential gravitational energy,

the loss of potential gravitational energy equals the work of gravity.

Therefore the work of gravity is mA g (h - hA).

I am assuming no loss of energy in the spring, because none is mentioned.

Under this assumption, by definition of potential spring energy,

the loss of potential spring energy equals the work of the spring.

As the spring energy remains unchanged, the force of the spring performs work of 0.

(During compression the spring performs negative work, and during the

subsequent expansion it performs positive work of equal magnitude.)

Friction performs work equal to the amount of heat energy generated (in absolute value).

By the law of conservation of energy, the heat energy must equal the loss of

potential gravitational energy.

Please note that the work of friction is always negative, and is the

negative of the heat energy generated.

So the conclusion is that

- Gravity performs work equal mA g (h - hA)

- The spring performs work of 0

- Friction performs work of mA g (hA - h)

- The sum of the work performed by the three forces is 0.

I am sorry, but the given question is too ambiguous to choose one of the answers.