Work Energy and Power

Shi Qi 20 Feb 2018

Question

A wire that obeys Hooke’s Law of length x1 when it is in equilibrium under tension T1. It’s length becomes x2 when the tension is increased to T2. What is the extra energy stored in the wire as a result of this process?

A) 1/4 ( T2 + T1 ) ( x2 - x1 )

B) 1/4 ( T2 + T1 ) ( x2 + x1 )

C) 1/2 ( T2 + T1 ) ( x2 - x1 )

D) 1/2 ( T2 + T1 ) ( x2 + x1 )

E) ( T2 - T1 ) ( x2 - x1 )

Answer

The extra energy is stored as elastic potential energy.

The graph of tension against total length is shown below. The extra elastic potential  energy is given by the shaded area.

Graph01.jpg
Working01.jpg

Answer is C.

David 07 May 2016 - 3

Question

12. A pendulum bob is released from rest at position X which is at a height h above its lowest position Y and then passes through position Z. Position Z is 0.4h above Y. Assuming air resistance is negligible, find the ratio of the speed of the bob at position Y to that at position Z.

Answer

By Principle of conservation of energy, the energy at points X, Y and Z are all the same. This means that we can express the speeds at Y and Z in terms of the gravitational field strength, g, and h.

Now, we can find the ratio of the speed at Y to the speed at Z.

Hence, the ratio is 1.29 : 1.

David 07 May 2016 - 2

Question

11. A block of mass 2.0 kg is released from rest at point P as shown in the figure below. It is found that the block finally comes to rest at point Q.

The length of the track PQ is 2.5 m What us the average value of frictional force acting on the block when it is moving from P to Q?

Answer

All the initial energy of the block was lost to work done against friction.

The average frictional force is 4.0 N.