Question

A block of mass 1kg when placed on an inclined plane does not slip down. Now it is taken from A to B and then B to A very slowly such that pulling force is always along the direction of motion of block. If work done by friction in the round trip is 15J, then find maximum value of h (in m).
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Answer 1

Given:

A block of mass 1kg when placed on an inclined plane does not slip down. Now it is taken from A to B and then B to A very slowly such that pulling force is always along the direction of motion of block.

To find:

Maximum height of incline ?

Calculation:

Work done by friction in round trip is 15 Joules, hence the work done by friction while the block is pulled from top to bottom will be 15/2 = 7.5 Joule.

Now, we shall apply WORK-ENERGY THEOREM, which states that :

• The net work done by all the forces on an object will be equal to the change in kinetic energy of the object.

• Since the block is pulled slowly, we can assume that the initial and the final velocity of the block is zero.

$\therefore \: W_{gravity} + W_{friction} = \Delta KE$

$\implies\: W_{gravity} + W_{friction} = 0 - 0$

$\implies\: W_{gravity} + W_{friction} = 0$

$\implies\: W_{gravity} +( - 7.5)= 0$

$\implies\: W_{gravity} - 7.5= 0$

$\implies\: W_{gravity} = 7.5$

$\implies\: mgh = 7.5$

$\implies\: 1 \times 10 \times h = 7.5$

$\implies\: h = 0.75 \: metres$

So, max height of inclined plane is 0.75 metres.