A 2.1 kg ball is attached to a ceiling by a string. The distance from the ceiling to the center of the ball is 1.20 m, and the height of the room is 3.00 m.
(a) What is the gravitational potential energy associated with the ball relative to the ceiling?
(b) What is the gravitational potential energy associated with the ball relative to the floor?
(c) What is the gravitational potential energy associated with the ball relative to a point at the same elevation as the ball?
To calculate the gravitational potential energy associated with the ball in each scenario, we need to consider the formula for gravitational potential energy:
Gravitational potential energy (PE) = m * g * h
Where:
m = mass of the object (in kg)
g = acceleration due to gravity (approximately 9.8 m/s^2 on Earth)
h = height or distance relative to a reference point (in meters)
(a) Gravitational potential energy relative to the ceiling:
In this case, the ball is attached to the ceiling, and we want to find the potential energy relative to the ceiling. The distance from the ceiling to the center of the ball is given as 1.20 m.
Using the formula, we have:
m = 2.1 kg (mass of the ball)
g = 9.8 m/s^2 (acceleration due to gravity)
h = 1.20 m (height relative to the ceiling)
Plugging these values into the formula:
PE = 2.1 kg * 9.8 m/s^2 * 1.20 m = 24.192 J
Therefore, the gravitational potential energy associated with the ball relative to the ceiling is 24.192 Joules.
(b) Gravitational potential energy relative to the floor:
In this case, we want to find the potential energy relative to the floor, which means we need to consider the height of the room as well. The height of the room is given as 3.00 m.
Using the formula again, but this time with the height relative to the floor:
h = 1.20 m + 3.00 m = 4.20 m (height relative to the floor)
Plugging the new height value into the formula:
PE = 2.1 kg * 9.8 m/s^2 * 4.20 m = 87.948 J
Therefore, the gravitational potential energy associated with the ball relative to the floor is 87.948 Joules.
(c) Gravitational potential energy relative to a point at the same elevation as the ball:
In this case, we want to find the potential energy relative to a reference point at the same elevation as the ball, which means the height relative to this point is zero.
Using the formula once again, but now with a height of zero:
h = 0 m (height relative to the reference point)
Plugging this value into the formula:
PE = 2.1 kg * 9.8 m/s^2 * 0 m = 0 J
Therefore, the gravitational potential energy associated with the ball relative to a point at the same elevation as the ball is 0 Joules.