Sunday 13 May 2018

3.3.2 Kinetic and potential energies

Kinetic energy
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 v= 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 v= m g h

0.5 v= g h

v= 2 g h

v = √(2 g h)

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