A 2.94 kg ball is attached to a ceiling by a
1.88 m long string. The height of the room is
5.05 m .
The acceleration of gravity is 9.8 m/s2 .
What is the gravitational potential energy
associated with the ball relative to the ceiling?
Answer in units of J
What is its gravitational potential energy rel-
ative to the floor?
Answer in units of J
What is its gravitational potential energy rel-
ative to a point at the same elevation as the
ball?
Answer in units of J
To find the gravitational potential energy associated with the ball relative to the ceiling, we can use the formula:
Gravitational Potential Energy = mass * gravity * height
Given:
mass = 2.94 kg
gravity = 9.8 m/s^2
height (distance from the ceiling) = 5.05 m
Substituting the values into the formula:
Gravitational Potential Energy = 2.94 kg * 9.8 m/s^2 * 5.05 m
Now, let's calculate the answer:
Gravitational Potential Energy = 145.7634 J (rounded to four decimal places)
Therefore, the gravitational potential energy associated with the ball relative to the ceiling is approximately 145.7634 J.
To find the gravitational potential energy relative to the floor, we need to consider the total height the ball is off the ground. Since the height of the room is given as 5.05 m, the distance from the floor to the ceiling is twice this value.
Total height = 2 * 5.05 m = 10.1 m
Using the same formula as before with the updated height, we can calculate the answer:
Gravitational Potential Energy = 2.94 kg * 9.8 m/s^2 * 10.1 m
Calculating this:
Gravitational Potential Energy = 287.394 J (rounded to three decimal places)
Therefore, the gravitational potential energy associated with the ball relative to the floor is approximately 287.394 J.
Finally, to find the gravitational potential energy relative to a point at the same elevation as the ball, we can simply use the height from the formula without any adjustments.
Gravitational Potential Energy = 2.94 kg * 9.8 m/s^2 * 5.05 m
Calculating this:
Gravitational Potential Energy = 145.7634 J (rounded to four decimal places)
Therefore, the gravitational potential energy associated with the ball relative to a point at the same elevation as the ball is approximately 145.7634 J.