# What is the work energy theorem?

Dec 19, 2014

The work-energy theorem relates the net work done by all the forces acting on an object to its change in kinetic energy. This theorem is applicable even when the forces acting on the object are not conservative.

The work-energy theorem says that the net work done by all the forces on an object is equal to the change in the kinetic energy of the object .

${W}_{\text{ne} t} = \setminus \Delta K = {K}_{f} - {K}_{i}$

• ${W}_{\text{ne} t} > 0 \setminus \quad \implies \setminus \Delta K > 0 \setminus \quad \implies {K}_{f} > {K}_{i} :$
So the kinetic energy of the object increases when the net work done on the object is positive. Energy is imparted into the object.

• ${W}_{\text{ne} t} = 0 \setminus \quad \implies \setminus \Delta K = 0 \setminus \quad \implies {K}_{f} = {K}_{i} :$
So the kinetic energy of the object does not change when the net work done on the object is zero. Energy is neither imparted into the object nor is it taken off of it.

• ${W}_{\text{ne} t} < 0 \setminus \quad \implies \setminus \Delta K < 0 \setminus \quad \implies {K}_{f} < {K}_{i} :$
So the kinetic energy of the object decreases when the net work done on the object is negative. Energy is taken off of the object.