A 1.70 kg ball is attached to a ceiling by a 1.50 m long string. The height of the room is 3.36 m.

The acceleration of gravity is 9.81 m/s2 .
What is the gravitational potential energy associated with the ball relative to
a) the ceiling? Answer in units of J
b) the floor?
Answer in units of J
c) a point at the same elevation as the ball? Answer in units of J

a. it has mg(1.50) PE less that at the ceiling

b. it has mg(3.36-1.50) PE more than at floorlevel.
c. at the same mpoint it has the same PE

To calculate the gravitational potential energy associated with the ball, we can use the formula:

Gravitational Potential Energy = mass * gravity * height

a) To find the gravitational potential energy of the ball relative to the ceiling, we need to consider the height from the ceiling to the ball. In this case, the height is the length of the string, which is 1.50 m.

So, using the formula:
Potential Energy = 1.70 kg * 9.81 m/s^2 * 1.50 m
Potential Energy = 24.3775 J

Therefore, the gravitational potential energy associated with the ball relative to the ceiling is 24.3775 Joules (J).

b) To find the gravitational potential energy of the ball relative to the floor, we need to consider the total height from the floor to the ball. This would be the height of the room minus the length of the string.

So, the total height from the floor to the ball is:
3.36 m - 1.50 m = 1.86 m

Using the formula:
Potential Energy = 1.70 kg * 9.81 m/s^2 * 1.86 m
Potential Energy = 29.3172 J

Therefore, the gravitational potential energy associated with the ball relative to the floor is 29.3172 Joules (J).

c) To find the gravitational potential energy of the ball relative to a point at the same elevation as the ball, we consider that the height is zero because the ball is at the same level.

Using the formula:
Potential Energy = 1.70 kg * 9.81 m/s^2 * 0 m
Potential Energy = 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 (J).