CBSE Class 11-science Answered

During calculation of acceleration due to gravity above the surface of earth if we assume that there is an external force opposite to that of Earth's gravity then the cos angle will be 180 between the two forces which is negative(-1), if we put the value in the equation of dw = F.dx then the final value of potential energy is positive which is not possible.how and why??

Asked by anushkaverma.25707 | 24 Aug, 2023, 07:35: PM

Expert Answer

Let us assume , a block of mass m is on earth's surface . Let this block is lifted above earth surface to a height y

by external force F in the direction opposite to the gravitational force and the block is coming to rest at a height y.

workdon W = ( net Force ) × distance

workdone W =

begin mathsize 14px style left parenthesis space F with rightwards arrow space on top minus m g with rightwards arrow on top right parenthesis space times space y with rightwards arrow on top end style

.......................(1)

In the above process, work is to be done so that given external lifting force F equals to gravitational pulling force mg at each vertical displacement dy .

Other wise , if F < (mg ) , then block can not be lifted . If F > mg , then block moves with acceleration and move beyond the height y

and it will not come to rest at y .

Hence , in order to lift the block to a height y and make it to come to rest after vertical displacement of y , applied external force F

should be equal in magnitude to gravitatioal force mg . Hence net force in eqn.(1) is zero while lifting the block and net workdone is zero.

Hence we get ,

begin mathsize 14px style F with rightwards arrow on top times space y with rightwards arrow on top space equals space m g with rightwards arrow on top times space y with rightwards arrow on top space end style

......................(1)

i.e. workdone by external force equals workdone by gravitational force .

Equal work is done by external force against the workdone by gravitational force and the workdone by external force is stored as potential energy in the block.

Hence potential energy is