Can something have energy without having momentum? Explain. Can something have momentum without having energy?

Ex 7.7 Can something have energy without having momentum? Explain. Can something have momentum without having energy? Defend your answer.

 

Answer

An object at rest has no momentum; its velocity is zero. But it can still have potential energy -- PE -- because of work we have done on it. We can lift an object and give it gravitational PE = m g h. It has PE because it can do work on something else as it falls -- or it can increase its own KE. Lifting the object, to give it PE, requires that work be done on it. If we compress a spring, we must do work on it. That work is then stored in the compressed spring and is available to do work on something else. That means there is PE stored in a compressed spring. If we bend a bow we must do work on it. That work is then stored in the bent bow and is available to do work on something else. That means there is PE stored in a bent bow. In all these cases, on object can have energy -- potential energy -- even though it is at rest; an object at rest has no momentum.