Calculating Gravitational Potential Energy of a Child on a Swing

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Homework Help Overview

The problem involves calculating the gravitational potential energy of a child on a swing, given the child's weight and the angle of the swing ropes with the vertical. The subject area pertains to gravitational potential energy and trigonometric applications in physics.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the formula for gravitational potential energy and the significance of height in relation to the angle of the swing. Some explore the relationship between the angle and height, while others question the assumptions made regarding the height at different angles.

Discussion Status

The discussion is ongoing, with various interpretations of how to calculate the height based on the angle of the swing. Some participants have offered insights into the relationship between the angle and gravitational potential energy, but no consensus has been reached on the correct approach.

Contextual Notes

Participants are working with the constraints of the problem, including the child's weight and the length of the swing ropes, while also grappling with the implications of different angles on the height calculation.

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A 30.3 N child is in a swing that is attached to ropes 2.14 m long. What is the gravitational potential energy when the ropes make a 30.9° angle with the vertical?

So far I've tried 6 different answers ranging between 0-64.8 J and no luck. Need a clue to get me on the right track. Thanks in advance.
 
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You know [itex]E_{gravitational potential}=mgh[/itex], where h is height off the ground and m is mass. I believe you must assume that when the ropes make an angle of 0 with the vertical h=0. Does that help?
 
Pretend that its like those incline questions.
 
I did assume that when the angle is zero E=0 and when the angle is 90 E=mgh=64.8, so I thought the answer would be (sin30.9)(mgh), but that answer was incorrect. I also tried (sin59.1)(mgh) which was also incorrect, I am not sure where to go from here.
 
Well I think when the kid swings up to make a [itex]30.9^\circ[/itex] with the vertical, his height above the ground is increased. By how much? The answer is

[tex]R \cos (30.9^\circ)[/tex]

So the kid's [itex]U=mg(R\cos (30.8^\circ))[/itex]
 

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