Question

Why is change in potential negative of the work done by conservative forces

Answer 1

Work energy theorem states,
Work Done, W= Change in Kinetic Energy
= K.E. (final) - K.E. (initial)
= Change in K.E .................................................(1)
Now, by Law of conservation of energy,
Kinetic Energy + Potential Energy = Constant,
=>Change in K.E. + Change in P.E.=0
=> Change in K.E = - (Change in P.E.)
From Equation (1),
W = - (Change in P.E.)
=> Change in P.E. = - W
Hence, change in potential energy =-work done.