Gravitational Potential Energy of a swing

AI Thread Summary
To find the gravitational potential energy of a child in a swing at a 30° angle, the vertical displacement (y) must be calculated correctly. The child’s height above the lowest point is determined by the difference between the swing's full length and the vertical component at the angle, specifically y = 1.8 - 1.8cos(30). The gravitational potential energy (U) is then calculated using U = mgy, where m is the child's weight, g is gravitational acceleration, and y is the correct height. The initial calculation did not account for the correct vertical displacement, leading to confusion. Understanding the geometry of the swing is crucial for accurate energy calculations.
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A 395 N child is in a swing that is attached to ropes 1.8 m long. Find the gravitational potential energy of the child+Earth system relative to the child's lowest position when the ropes make a 30° angle with the vertical.

What I did with this problem is I drew a diagram and then figured that y would be 1.8cos30

U=mgy
U=395(1.8cos30)= 6.16e2 J

Is there anything that I did wrong with this problem it's confusing me with the angle. I feel like there's more to do than this but I'm not sure what.

Thanks for any help
 
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The 'y' in the formula is the vertical displacement measured from the lowest point on the swing.
 
That doesn't really help.
 
Draw the swing with the child just sitting there. Then draw the swing when it's pulled back 30o. The 'y' is how high the child has moved vertically.
 
The gravitational potential you calculated just now is at a height of 1.8\cos{30}m from the ground. However the guy is hanging down from a swing that's 1.8m long.
 
So it's the difference. Thanks for clarifying.
 
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