Work
When a force is applied to an object over a displacement, work is done to the object. Work is transfer of energy.
W = F * d * cos Ɵ
Work is measured in joule and is a scalar, 1 joule = 1 Newton meter
Energy
Energy is a measurement of the ability of something to do work.
W = ΔE
Energy is measured in joule and is a scalar, 1 joule = 1 Newton meter
Power
When work is done over some amount of time, we can measure the power, or the rate at which the work is performed.
P = W/t
Power is measured in watt and is a scalar. 1 watt = 1 joule/second
When a constant force is applied to an object moving at constant velocity, power p = F * v
Kinetic Energy
Kinetic energy is the energy of motion. KE = 1/2 * m v2, where m is mass and v is velocity.
Work energy theorem
Wtotal = ΔKE
Total work done = change in kinetic energy.
Conservative forces & potential energy
Conservative force is a force with the property that the total work done in moving an object between two points is independent of the path taken.
If a force is conservative, it is possible to assign a numerical value for the potential at any point. When an object is moved by the force from one location to another, the force changes the potential energy of the object by an amount that does not depend on the path taken. If the force is not conservative, then defining a scalar potential is not possible, because taking different paths would lead to conflicting potential differences between the start and end points.
Gravitational force is an example of a conservative force, while frictional force is an example of a non-conservative force.
Other examples of conservative forces are: force in elastic spring, electrostatic force between two electric charges, magnetic force between two magnetic poles.
Conservation of energy
If only conservative forces are present, the initial mechanical energy (kinetic energy + potential energy) = final mechanical energy (kinetic energy + potential energy)
If non conservative forces are present, then you must account for the work done by the non conservative forces:
The initial mechanical energy (kinetic energy + potential energy) + Work done by non conservative forces = final mechanical energy (kinetic energy + potential energy)