A190 n child is in a swing that is attached to ropes 2.10 m long. find the gravitational potential energy of the child-earth system relative to the child's lowest position at the following times.
(a) when the ropes are horizontal the correct answer is not zero.
(b) when the ropes make a 34.0° angle with the vertical.
(c) when the child is at the bottom of the circular arc

a) Gravitational potential energy = 399 J

b) Gravitational potential energy = 66.5 J

c) Gravitational potential energy = 0 J

Explanation:

Hi there!

Please, see the attached figure for a better understanding of the problem.

a) When the ropes are horizontal, the height of the child, relative to the child's lowest position, is 2.10 m (see figure).

The gravitational potential energy is calculated as follows:

PE = mgh

Where:

PE = potential energy.

mg = weight of the child

h = height.

Then when the ropes are horizontal, the potential energy will be:

PE = 190 N · 2.10 m = 399 J

b) When the ropes make a 34.0° with the vertical, the height of the child is 2.10 m minus x (see figure). To find x, we can use trigonometry of right triangles:

cos angle = adjacent side / hypotenuse

cos 34.0° = x / 2.10 m

x = 2.10 m · cos 34.0° = 1.75 m

Then, the height of the child relative to the lowest position is

(2.10 m - 1.75 m) = 0.35 m

Therefore, the gravitational potential energy will be:

PE = 190 N · 0.35 m

PE = 66.5 J

c) When the child is at the bottom of the circular arc the height is zero (the child is at the lowest position), then, the gravitational potential energy will be zero.

b.

explanation:

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