# Work Done By Gravity Formula

## Work Done By Gravity

Gravity is defined as the force that attracts a body towards the earth or towards any other physical body having mass.

If a particular object is falling, the particle is bound to point in the direction of gravity. The magnitude of the falling body depends on the mass, gravitational constant and height from which it is falling.

The work done by gravity is given by the formula,

Wg = -mg(∆ h)

Where,

m = mass,

g = gravity,

h= height

The negative sign shows that the particle is dropping from a height Δ h vertically in the direction of gravity.

If θ is the angle made when the body falls, the work done by gravity is given by,

W = m g h cosθ

Where the theta is the angle made when the body falls.

### Solved Examples

Example 1

A 15 kg box falls at angle 25 from a height of 10 m. Determine the work done by gravity.

Solution:

Given:

Mass m = 10 kg,

angle =

The work done by gravity formula is given by,

W = mgh cos θ

W = 15 × 9.8 × 10× $cos 25^{0}$

=15  × 9.8 × 10×0.9063

=   1332 J

Therefore, the work done by gravity is 1332 J.

Example 2

A boy drags a 10 kg box across the friction-less surface. He applies a force of 30 N at an angle of $30^{0}$ to the horizontal for 6m. Determine the work done by gravity.

Solution:

Given:

Mass m = 10 kg,

Force F = 30 N,

angle θ$30^{0}$

Displacement s = 6m

The work done by gravity formula is,

W = mgh cos θ

W = 10 x 9.8 x 6 × cos $30^{0}$

W = 10 x 9.8 x 6 × 0.866

The work done by gravity is 509.208 J

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