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×
=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 to the horizontal for 6m. Determine the work done by gravity.
Solution:
Given:
Mass m = 10 kg,
Force F = 30 N,
angle θ =
Displacement s = 6m
The work done by gravity formula is,
W = mgh cos θ
W = 10 x 9.8 x 6 × cos
W = 10 x 9.8 x 6 × 0.866
The work done by gravity is 509.208 J
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