Question

A 100 kg block is started with a speed of $2.0m{s}^{-1}$ on a long, rough belt kept fixed in a horizontal position. The coefficient of kinetic friction between the block and the belt is 0.20. 3. Consider the situation from a frame of reference moving at $2.0m{s}^{-1}$ along the initial velocity of the block. As seen from this frame, the block is gently put on a moving belt and in due time the block starts moving with the belt at $2.0m{s}^{-1}$

Calculate the increase in the kinetic energy of the block as it stops slipping past the belt.Find the work done in this frame by the external force holding the belt.

• A. 200 J
• B. 0 J
• C. 100 J
• D. 400 J

Answer 1

The correct option is C

100 J

According to this frame of reference the block initially had zero velocity.
As the friction between the block and belt decreases the velocity of the block in an initial frame, the velocity of the block in the opposite direction increases.
When the block completely stops moving with respect to the belt, it velocity in this new frame would be -2m/s.

Therefore final kinetic energy is 200 J. Initial kinetic energy is zero. Therefore total change in kinetic energy is also 200 J.