A shot-putter puts a shot (weight =
71.1 N) that leaves his hand at a distance of 1.52 m above the ground. Find the work done by the gravitational force when the shot has risen to a height of 2.13 m above the ground and determine the change in the gravitational potential energy of the shot.
To find the work done by the gravitational force, we can use the formula:
Work = change in gravitational potential energy
The work done by gravity can be calculated by the formula:
W = -mgh
where:
W = work done by gravity
m = mass of the shot (m = 71.1 N / 9.81 m/s^2 ≈ 7.25 kg)
g = acceleration due to gravity (g = 9.81 m/s^2)
h = change in height (2.13 m - 1.52 m = 0.61 m)
Plugging in the values, we get:
W = -7.25 kg * 9.81 m/s^2 * 0.61 m
W = -43.03 Joules
Therefore, the work done by the gravitational force when the shot has risen to a height of 2.13 m above the ground is -43.03 Joules.
To determine the change in gravitational potential energy of the shot, we use the formula:
Change in potential energy = mgh
The change in potential energy can be calculated by:
ΔPE = 7.25 kg * 9.81 m/s^2 * (2.13 m - 1.52 m)
ΔPE = 7.25 kg * 9.81 m/s^2 * 0.61 m
ΔPE = 43.03 Joules
Therefore, the change in gravitational potential energy of the shot is 43.03 Joules.