Work is not totally done by only conservative forces. There is a mixture of conservative and nonconservative forces. The work done by nonconservative forces acting on parts of a system equals the change in mechanical energy of the system.
W (done by nonconservative forces) = (KE final + PE final) – (KE initial + PE initial)
Work and energy are interrelated. In general, energy is the capacity to do work or cause change. There are several kinds of energy which can be converted to each other.
1. Potential energy (EP) energy of position; stored energy
- Gravitational potential energy (GPE) energy due to height above or below some reference level (GPE = mgh)
- Elastic potential energy (EPE) energy acquired when stretched or compressed out of rest position (F = kd where k = spring constant; EP = 1/2 kd2)
- Chemical potential energy (CPE)
2. Kinetic energy (EK or K) energy of motion (EK = 1/2mv2)
3. Mechanical energy total amount of EK and EP in a system
4. Thermal energy total amount of EK and EP of the particles in a substance
5. Internal energy (U) the energy associated with the microscopic components of a system
When the work done on an object is done by gravity and is a change in the objects position:
W g = PE (initial) – PE (final)
Notice that its initial minus final , not vice versa.
If you consider the elastic PE of springs, you get another value introduced; the spring constant. The force applied to a spring (to stretch or compress it) is proportional to the spring constant and the distance it is stretched/compressed.
Fs = – kx
Sir Robert Hooke discovered the relationship between the force exerted on the spring and the distance stretched/compressed. (Hooke’s Law)
You should realize now that there are 3 ways to store energy in a system kinetic energy , potential energy , and internal energy .
The way you get energy out of a system is work, transfer of heat, and mechanical waves (i.e., sound waves, water waves, seismic waves).