Section 6
Work, energy and power
Parallel case
The work of a constant force is the scalar product of the force and the displacement.
In one dimension
The work of a variable force is the integral of the force along the path.
Energy associated with motion, equal to half the product of mass and the square of the speed.
Change
Gravitational potential energy near the surface, proportional to height.
- approximately constant.
Potential energy of an ideal spring, proportional to the square of the deformation.
The work of a conservative force is minus the change in potential energy.
The net work done on a body equals the change in its kinetic energy.
In three dimensions
The conservative force is minus the gradient of the potential energy.
Mechanical energy is the sum of kinetic and potential energies.
In a conservative system, the initial mechanical energy equals the final mechanical energy.
- only conservative forces do work.
Equivalently
The work of non-conservative forces equals the change in mechanical energy.
For motion on a flat surface with constant friction
The work of kinetic friction is minus the product of the friction force and the distance traveled.
Ratio of the work done to the elapsed time interval.
Derivative of work with respect to time, equal to the scalar product of force and velocity.
or
Ratio of useful energy or power to input energy or power.