a 1.67kg ball is atached to a ceiling by a 1.29m long string. the height of the room is 3.08m. the acceleration of gravity is 9.81 m/s^2. what is the gravitational potential energy associated with the ball relative to the ceiling?
gpe= mgh= mg*(-1.29)
-1.67*9.81*1.29 joules
The height of the room does not matter. Note the minus sign, because the potential energy is being refered to a higher elevationm (the ceiling).
To calculate the gravitational potential energy of the ball relative to the ceiling, we can use the formula:
Gravitational potential energy = mass x gravity x height
1. First, let's calculate the mass of the ball. We are given that the mass is 1.67 kg.
2. Next, we need to calculate the height of the ball relative to the ceiling. The total height of the room is 3.08 m, and the length of the string is 1.29 m. Since the ball is attached to the ceiling, the height is the difference between the two:
Height = Total height - Length of the string
Height = 3.08 m - 1.29 m
3. Now that we have the mass and the height, we can substitute these values into the formula:
Gravitational potential energy = 1.67 kg x 9.81 m/s^2 x (3.08 m - 1.29 m)
4. Calculate the values inside the parentheses:
Gravitational potential energy = 1.67 kg x 9.81 m/s^2 x 1.79 m
5. Calculate the final result:
Gravitational potential energy ≈ 29.67 Joules
Therefore, the gravitational potential energy associated with the ball relative to the ceiling is approximately 29.67 Joules.