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What type of quantity—scalar or vector—is energy? How does this follow from the definition of work...

What type of quantity—scalar or vector—is energy? How does this follow from the definition of work done by a force?

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Answer #1

Energy is a scalar quantity.

The work is defined as a product of two vector quantities: force and displacement.

We know that a dot product of two vectors is a scalar quantity. Therefore, the work done is a scalar quantity.

Work is directly related to the energy. For example, work done by gravitational force on an object is stored as gravitational potential energy of the object. Likewise, the work done by an electric force on a charge is stored as electric potential energy of the charge. Work done is related to the kinetic energy of an object by work energy theorem which says that the net work done on an object is equal to the change in kinetic energy of the object.

The work is directly related to the energy and work being a dot product of two vectors is a scalar quantity. Therefore, we conclude that energy is also a scalar quantity.

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