Question

A 2kg ball is attached to a ceiling by a string. The distance from the ceiling to the center of the ball is 1.0m, and the height of the room is 3.0m. What is the potential energy associated with the ball relative to each of the following:

a. the ball relative to the ceiling?
b. the ball relative to the floor?
c. the ball realtive to a point at the same elevation as the ball?

Answer 1

part(a): The potential energy is
`\bf{19.6~J}`.

part(b): The potential energy is
`\bf{39.2~J}`.

part(c): The potential energy is
`\bf{0}`.

Step-by-step explanation:

Given:

The mass of the ball,
`m = 2~Kg`.

The distance from the ceiling to the center of the ball,
`d = 1.0~m`

The height of the room,
`H = 3.0~m`.

The potential energy of any particle of mass
`m` situated at a height
`h` from ground is given by

`V = mgh`

where
`g` is the acceleration due to gravity.

(a) The distance of the ball relative to ceiling is
`d = 1.0~m`. Thus, the potential energy will be

`V &=& (2~Kg)(9.8~m/s^(2))(1.0~m)\\~~~&=& 19.6~J`

(b) The distance of the ball from the ground is
`h' = (3.0 - 1.0)~m = 2.0~m`

Thus, the potential energy will be

`V = (2~Kg)(9.8~m/s^(2))(2.0~m)\\~~~= 39.2~J`

(c) The distance of the ball relative to a point at the same elevation as the ball is
`h = 0`.

Thus, the potential energy will be

`V = (2~Kg)(9.8~m/s^(2))(0~m)\\~~~= 0`