Kinetic Energy and Gravitational Potential Energy

Kinetic Energy

Kinetic energy is the energy an object has due to its motion. In other words it is the amount of work the object can do due to its motion.

Kinetic energy (E_k) can be calculated using the following equation:

Where m is the mass of a body measured in kilograms (kg) and v is the velocity of the body measured in meters per second (ms^-1).

Gravitational Potential Energy

Gravitational potential energy is the energy an object has (the amount of work it can do) due to its position in a gravitational field.

As an object is raised it gains gravitational potential energy and as it is lowered it loses gravitational potential energy.

Gravitational Potential energy (E_g) can be calculated using the following equation:

Where m is the mass of a body measured in kilograms (kg), g is the acceleration of the body due to gravity measured in meters per second squared (ms^-2)  and h is the height of the object above a chosen reference point measured in meters (m).

Conservation of Energy

If an object is lifted it has gravitational potential energy. If the object is dropped it begins to lose this potential energy, but as it loses gravitational potential energy it gains kinetic energy.

Due to the principle of the conservation of energy, the amount of gravitational potential energy lost by the object must be equal to the amount of kinetic energy gained by the object.

Therefore, the kinetic energy just before the object hits the ground is equal to the gravitational potential energy of the object just before it is dropped. This can be stated as:

E_g (initial) = E_k (final)

Worked Examples

Example 1

A car is travelling at 17ms^-1 and its kinetic energy is 220,000J. Calculate the mass of the car.

Example 2

A ball of mass 12.7kg is dropped from the top of a cliff. Before it is dropped it has a gravitational potential energy of 3430J. Calculate the height of the cliff given that g = 9.81ms^-2.

Example 3

An apple, of mass 0.1kg, is hanging from the branch of a tree 2.1m above the ground before a gust of wind knocks it off and it falls to the ground. Calculate the gravitational potential energy of the apple before it falls, and its velocity just before it hits the ground. Use g = 9.81ms^-2.

This question requires knowledge of the Conservation of Energy.

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