Kinetic energy is the energy associated with the motion of an object. Kinetic energy (Ek) can be calculated from mass and speed:
Ek = 0.5 m v2
This means that, for a constant speed, Ek is directly proportional to mass. For a given mass, Ek is directly proportional to the square of the objects speed.
We need to know how to derive this:
Take an object that initially starts at rest (u = 0). We can determine it's velocity at a certain distance using v2 = u2 + 2as:
s = (v2-u2)/2a = v2/2a
This means that the work done by the force moving the object is entirely transferred to Ek:
Work done = Ek = F x = F s
F = ma
Ek = ma s = ma (v2/2a)
Ek = mv2/2 = 0.5 m v2
Gravitational potential energy
Gravitational potential energy os the capacity for doing work as a result of an object's position in a gravitational field. You can calculate change in GPE from it's mass and height:
Ep = m g h
This one is a lot simpler to derive: When you lift something through a height h at a constant speed (no change in Ek) you have applied a force that equates to mg. The work done is transferred into Ep (GPE)
Ep = W = force x distance moved in the direction of the force
Ep = (mg) h
Ep = m g h
Also (when we cover gravitational fields):
The gravitational potential energy 'E' of any object with the mass m within a gravitational field is defined as the work done to move the mass from infinity to a point in a gravitational field:
E = m Vg
In a uniform gravitational field, in order to change the gravitational potential energy of an object its height above the surface must be changed as this results in a change in gravitational potential.In a radial field (remember Vg = -GM/r) the gravitational potential energy can be written as:
E = m Vg = -GMm/r
Energy exchanges
Often, kinetic energy and gravitational energy will be exchanged. For example, if you drop a book it's gravitational energy will decrease whilst its terminal velocity increases:
0.5 m v2 = m g h
0.5 v2 = g h
v2 = 2 g h
v = √(2 g h)
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