Why work done is negative of potential energy.

Consider an example,  A mass hanging from the ceiling will have a kinetic energy equal to zero. If the cord breaks, the mass will rapidly increase its kinetic energy. This kinetic energy was somehow stored in the mass when it was hanging from the ceiling: the energy was hidden, but has the potential to reappear as kinetic energy. The stored energy is called potential energy. Conservation of energy tells us that the total energy of the system is conserved, and in this case, the sum of kinetic and potential energy must be constant. This means that every change in the kinetic energy of a system must be accompanied by an equal but opposite change in the potential energy.

 

U represents potential energy and K represent Kinetic energy.

 

So,  Delta(U) + Delta(K) = 0

and

 

 

E = U + K = constant

According to work-energy theorem , amount of work done is equal to change in kinetic energy of the system.

W = [Delta]K

The change in the potential energy of the system can now be related to the amount of work done on the system

[Delta]U = - [Delta]K = - W

 So work done is negaitive of potential energy.