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Gravitational Potential Energy.

Gravitational Potential Energy is energy stored within an object due to its height above the

surface of the earth.

In order for an object to be lifted vertically upward, work done must against the downward

pull of gravity.

The amount of energy used to lift the object against is then stored as gravitational potiential

energy.

The general form of the gravitational potential energy is:

Where G is the gravitational constant which is equal to 6.67428 X 10-11 m3 kg-1 s-2. Or 6.67428

X 10-11

N(m/kg)2

. M is the mass of the attracting body, and r is the distance between theircenters.

This equation is actually the derivation from the equation . This equation only

valid when the particle is near the Earths surface where the gravitational force is constant.

The gravitational force between two particles varies as 1/ r2 so, more general potential energy

function which is either one of that particles is valid without any restriction of having to be

near the Earths surface. Then it will differentiate from

The change in the gravitational potential energy due to the displacement of the system is the

negative work done which is:

The Gravitational potential energy function can be evaluate from the equation above. Assumethat a particle of mass m, is moving between the point A and B above the Earths surface.

The particle is the subject of gravitational force by the law of gravitational :

The negative sign above shows that the force is attractive. By substituting the equation above

into the equation of the change of gravitational potential energy. So we can calculate the

change of the gravitational potential energy function for the particle Earth system is equal to

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With the choice of the zero value for the initial potential energy at infinite initial

distance, where the force approaches to zero, the gravitational potential energy is actually the

work done that bring the object from infinity to radius .

If so, we can get the gravitational potential energy is:-

For any pair of particles varies as where the force between them varies as . From the

equation above, the gravitational potential energy is negative because of the attractive force

and the potential energy is zero when the separation between them is at infinite.

A

Fg

ri

Fg B

rf

A

particle of mass,m move

From A to B above the earth

Surface.

RE

ME

m

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Example:

The mass of a planet is 5.0 x 1024 kg and its radius is 6.0 x 108 m. What is the energy required

to bring a mass of 2.0 kg from the surface of the planet to outer surface?

( r for the surface of the planet to the outer surface is 400 km)

Solution:

Where G = 6.67 X10-11N(m/kg)2

r = 400 x10

3

+ 6.0x 10

8

m

= 6-004 x 108m

ME = 5.0 x1024 kg

m = 2 kg

(negative sign is ignore during calculated its because negative sign stand for attractive force)

Reference:

From book

John W. Jewett and Raymond A. Serway (2008). Physics for Scientists and Engineers,

Seventh Edition, united kingdom: International Student Edition

Poh Liong Yong and S. Nagappan (2007). Physics for Matriculation, Second Edition,

Selangor: Penerbitan Oxford Fajar Bakti Sdn. Bhd.