# Potential Energy of a child on a swing

## Homework Statement

a 40.0 kg child is in a swing hat is attached to ropes 2.00 m long. 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 a 30.0 degree angle with the vertical
c. at the bottom of the circular arc

## Homework Equations

so i used the gravitational potential energy formula which is mass x free-fall acceleration x height
i used 9.81 as the acceleration and that i thought wait if for a it is horizontal

## The Attempt at a Solution

for my answer i kept on getting 1200 but in the text book part a is 785 J for part b it is 105 J and for part c it is 0.00 J. i figured out Part A but i cannot figure out part b or c please help i need someone to just help walk me through it since i am stuck i am a high school student doing physics one honors

## Answers and Replies

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How are you calculating the height? Since you have the acceleration and the mass, that seems to be the place you might be tripped up. You'll need to do some trig for part b.

What's a swing hat?

LowlyPion
Homework Helper
Draw a picture.

When the swing is horizontal apparently you figured out it's at 2m * 40 kg * 9.81m/s2 = 785N

For b though when the swing is at 30° with the vertical what is the distance from the top that the child is?
Think the length of the swing ropes and a trig function of 30°.

If you know the distance from the top, then you can subtract that from the length of the ropes and that's your height.

For c) when it's at the bottom how much higher than the bottom is it?

The first question you should consider is what is the "lowest position" that the child will attain during his swing? In the context of this problem you should label this position as the point at which the child has exactly zero potential energy. Part (c) should become clear immediately after choosing this point.

In order to find the child's potential energy relative to this point you should find the height difference (ie. the difference in vertical position) between the point you want to examine and your reference point. You should use some trigonometry to do this in part (b).

Draw a right triangle with the swing's rope (the length of which you know) as the hypotenuse and the angle mentioned in the problem labeled. Then use sin and cosine functions as needed to find the length of the vertical edge of this triangle. From here it should be clear how to proceed.

thank you very much for the help i figured it out thanks to your hints and suggestions and got the problem right thank you once again.

Wait, what is a swing hat?

It's a typo, it should say "swing that"..