Question

50 J of work is done against the force of gravity in lifting a stone to a certain height. What will be the potential energy of the stone at that height

Answer 1

Dear student,

According to the law of conservation of energy, the total energy of a system remains conserved That means change in kinetic energy= change in potential energy
And according to work energy theorem, we know, the net work done of the object by a force is equal to the change in kinetic energy.
So, combining these two laws, we can write;

$$\begin{gathered} from,conservationofenergy, \\ ∆(K.E.)=∆(P.E) \\ andfromworkenergytheorem, \\ Workdone\left(W\right)=∆(K.E.) \\ combiningthesetwolaw, \\ Workdone\left(W\right)=∆(P.E) \\ W=50Joule\left(given\right) \\ andinitialP.E.={(P.E.)}_i=0 \\ [asP.E.=mgh;consideringtheinitialpositionoftheobjecttobeground,h=0] \\ hence,finalPotentialenergyatthecertainheight=workdone=50Joule \end{gathered}$$

Regards,