Question

A 38.0 kg child is in a swing that is attached to ropes 1.50 m long. The acceleration of gravity is 9.81 m/s^2 . Find the gravitational potential energy associated with the child relative to the child's lowest position under the following conditions: A) when the ropes are horizontal. b) when the ropes make 34.0 degree angle with the vertical.

Answer 1

Answer on Question#37803 – Physics – Mechanics

Question:

A 38.0 kg child is in a swing that is attached to ropes 1.50 m long. The acceleration of gravity is 9.81 m/s^2. Find the gravitational potential energy associated with the child relative to the child's lowest position under the following conditions:

a) when the ropes are horizontal.

b) when the ropes make 34.0 degree angle with the vertical.

Answer:

a) Change of potential energy equals:

$$\Delta U = m g \Delta h$$

where $\Delta h$ is change of height.

When the ropes are horizontal change of height equals length of the ropes:

$$\Delta h = l$$

Therefore:

$$U = m g l = 559 J$$

Answer: 559 J

b) Change of potential energy equals:

$$\Delta U = m g \Delta h$$$$\Delta h = l - l \cos 3 4 = l (1 - \cos 3 4)$$

Therefore, gravitational potential energy of child equals:

$$W = m g l (1 - \cos 3 4) = 9 5. 6 J$$

Answer: 95.6 J