7.3 Work and Kinetic energy

To calculate the work done on an object by a constant force during a horizontal displacement along a frictionless surface, we use only the force component along the object's displacement. The force component perpendicular to the displacement does zero work.

The expression for work is:

We note that the right hand side of this equation is equivalent to the scalar product (chapter 3.7), we can also write

The work done is either positive (if  is < 90°) or negative (if  is > 90°).

If several forces are involved in the problem, we can proceed in two ways to compute the net work. Either add all the forces and then determine the work done by the net force or compute the work done by each force and then add them (including the correct sign).

The net work is also related to the change in the kinetic energy of the object as:

This is called the work - kinetic energy theorem.

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