A 2.00 kg ball is attached to a ceiling by a 1.40 m long string. The height of the room is 3 m. What is the gravitational potential energy of the ball relative to the ceiling?
What is the gravitational potential energy of the ball relative to the floor?
(c) What is the gravitational potential energy of the ball relative to a point at the same elevation as the ball?
For each of your questions, the gravitational P.E. is M g times the distance of the ball above the reference plane. "g" is the acceleration of gravity.
That distance is zero for part (c).
Now you calculate the others. One answer will be negative, if done correctly.
The answers should be in Joules.
Oh, the potential energy of the ball is ready to make an entrance! Let's calculate it step by step.
To find the gravitational potential energy of the ball relative to the ceiling, we need to use the formula U = mgh, where U is the potential energy, m is the mass, g is the acceleration due to gravity, and h is the height.
So, for the ball attached to the ceiling, the mass is 2.00 kg and the height is 3.00 m. Since the ball is hanging from the ceiling, the potential energy relative to the ceiling is U = (2.00 kg)(9.81 m/s²)(3.00 m). Crunching the numbers gives us the answer!
For the gravitational potential energy of the ball relative to the floor, we can use the same formula as before. The only difference is that the height in this case is the distance from the floor to the ball, which is the height of the room minus the length of the string. So, the potential energy relative to the floor is U = (2.00 kg)(9.81 m/s²)(3.00 m - 1.40 m).
Finally, for the gravitational potential energy of the ball relative to a point at the same elevation as the ball, we can use the same formula again. This time, the height is just the length of the string, since the point is at the same elevation as the ball. So, the potential energy relative to the same elevation point is U = (2.00 kg)(9.81 m/s²)(1.40 m).
Now, it's time for some serious number crunching! I'll wait here while you calculate the answers.
To calculate the gravitational potential energy of the ball relative to the ceiling, you can use the formula:
Gravitational Potential Energy = mass x gravity x height
Given:
mass of the ball (m) = 2.00 kg
height from the ceiling to the ball (h) = 1.40 m
acceleration due to gravity (g) = 9.8 m/s^2
Gravitational Potential Energy relative to the ceiling = 2.00 kg x 9.8 m/s^2 x 1.40 m
= 27.44 J
To calculate the gravitational potential energy of the ball relative to the floor, you need to consider the total height from the floor to the ball:
Total height = height from ceiling to ball + height of the room
Given:
height from the ceiling to the ball (h) = 1.40 m
height of the room (H) = 3 m
Total height from the floor to the ball = 1.40 m + 3 m
= 4.40 m
Gravitational Potential Energy relative to the floor = 2.00 kg x 9.8 m/s^2 x 4.40 m
= 85.12 J
To calculate the gravitational potential energy of the ball relative to a point at the same elevation as the ball, you need to consider the height of the ball from that reference point.
Given:
height from the reference point to the ball (h) = 1.40 m
Gravitational Potential Energy relative to the reference point = 2.00 kg x 9.8 m/s^2 x 1.40 m
= 27.44 J
To calculate the gravitational potential energy, we need to use the formula:
Gravitational Potential Energy = mass * acceleration due to gravity * height
First, let's calculate the gravitational potential energy of the ball relative to the ceiling:
1. Determine the height between the ball and the ceiling. In this case, it is the distance at which the string is attached, which is 1.40 m.
2. Determine the mass of the ball. In this case, it is given as 2.00 kg.
3. Determine the acceleration due to gravity. The standard value for this is 9.8 m/s^2.
4. Plug in the values into the formula:
Gravitational Potential Energy = 2.00 kg * 9.8 m/s^2 * 1.40 m
Gravitational Potential Energy = 27.44 J
Now, let's calculate the gravitational potential energy of the ball relative to the floor:
1. Determine the height between the ball and the floor. In this case, it is the total height of the room, which is 3 m.
2. Plug in the values into the formula:
Gravitational Potential Energy = 2.00 kg * 9.8 m/s^2 * 3 m
Gravitational Potential Energy = 58.8 J
Lastly, let's calculate the gravitational potential energy of the ball relative to a point at the same elevation as the ball:
1. Determine the height between the ball and the reference point. In this case, it is at the same elevation as the ball, so the height is 0 m.
2. Plug in the values into the formula:
Gravitational Potential Energy = 2.00 kg * 9.8 m/s^2 * 0 m
Gravitational Potential Energy = 0 J
Therefore, the gravitational potential energy relative to the ceiling is 27.44 J, relative to the floor is 58.8 J, and relative to a point at the same elevation as the ball is 0 J.