A 2.41 kg ball is attached to a ceiling by a
1.86 m long string. The height of the room is
3.38 m.
The acceleration of gravity is 9.81 m/s
2
.
What is the gravitational potential energy
associated with the ball relative to
a) the ceiling?
Answer in units of J
b) the floor
c)a point at the same elevation as the car
35.935992
(not right)
To find the gravitational potential energy associated with the ball relative to different points, we can use the formula:
Gravitational Potential Energy (PE) = mass (m) * acceleration due to gravity (g) * height (h)
a) Relative to the ceiling:
In this case, the height at which the ball is attached to the ceiling is given as 1.86 m. Therefore, we can calculate the gravitational potential energy as follows:
PE = m * g * h = 2.41 kg * 9.81 m/s^2 * 1.86 m = 44.4406 J
Therefore, the gravitational potential energy associated with the ball relative to the ceiling is 44.4406 J.
b) Relative to the floor:
To find the gravitational potential energy relative to the floor, we need to consider the total height of the room, which is given as 3.38 m. In this case, the height would be the sum of the string length (1.86 m) and the distance from the end of the string to the floor (3.38 m - 1.86 m).
Height (h) = 3.38 m - 1.86 m = 1.52 m
PE = m * g * h = 2.41 kg * 9.81 m/s^2 * 1.52 m = 35.4808 J
Therefore, the gravitational potential energy associated with the ball relative to the floor is 35.4808 J.
c) Relative to a point at the same elevation as the car:
Since the height at the same elevation as the car is not given, we cannot determine the gravitational potential energy value in this case. We need the specific height to calculate the potential energy relative to that point.