Question

1. Luna wants to put her books on a shelf in her room. Does the work Luna does depend on how fast she puts the books on the shelf? Does the power Luna uses depend on how fast she puts her books on the shelf? Explain.

Answer 1

Work done dW by Luna when she applies the force F to the books to displace them by distance dS is given by;

dW = F.dS ......eqn1

where '.' denotes the dot product

Since, in  eqn 1, expression for work does not contain speed. Hence, work done by Luna does not depend on how fast she puts the books on the shelf.

Also, Power, P = Workdone(W)/Time .........eqn 2

i.e Power is defined as the ability to do the work dW in a gven time dt and its magnitude is given by eqn 2

Now, using equation 1 in equation 2; we get

P = F.dS/dt

Since, change in displacement with change in time gives rise to velocity, i.e dS/dt = v

hence P = F.v .....eqn 3

Eqn 3 indicates that power depends on the velocity v .

Hence, power used by Luna to put her books on the shelf is dependent of velocity.

Yes, power Luna uses depend on how fast she puts the books in shelf .