Finding Potential Energy of a Swing When the Ropes Are Horizontal?

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SUMMARY

The discussion focuses on calculating the gravitational potential energy of a child in a swing with ropes measuring 1.90 m when the ropes are horizontal. The correct height at this position is determined using the formula h = L(1 - cos(θ)), where θ is 90 degrees, resulting in a height of 1.90 m. The potential energy is calculated using PE = mgh, yielding a value of 793.05 J, not 1213.99 J as initially stated. The error arose from an incorrect height assumption and a calculator set to radians instead of degrees.

PREREQUISITES
  • Understanding of gravitational potential energy (PE = mgh)
  • Knowledge of pendulum height calculations (h = L(1 - cos(θ)))
  • Familiarity with trigonometric functions and their degrees/radians
  • Basic physics concepts related to swings and pendulums
NEXT STEPS
  • Review the concept of gravitational potential energy in physics
  • Learn about pendulum motion and its equations
  • Study the differences between degrees and radians in trigonometry
  • Practice similar problems involving potential energy calculations
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Students studying physics, particularly those focusing on mechanics and energy concepts, as well as educators looking for examples of potential energy calculations in real-world scenarios.

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Homework Statement



A 45.0 kg child is in a swing that is attached
to ropes 1.90 m long.
The acceleration of gravity is 9.81 m/s2 .
Find the gravitational potential energy as-
sociated with the child relative to the child’s
lowest position under the following condi-
tions:
a) when the ropes are horizontal.
Answer in units of J.

Homework Equations



Height of a pendulum:
h=L(1-cos(θ))

Potential Energy

PE=mgh

The Attempt at a Solution



So first I found the height of the swing at a horizontal position which I assumed is as at 90°.

h=L(1-cos(θ))
2.75m=1.9(1-cos(90))

Then I used that height and put it into the formula for potential energy

PE=mgh

1213.99 J? = (45)(9.81)(2.75)

but the online homework interface I have to use to input my answer tells me this isn't correct. I was wondering if maybe my answer isn't in Joules, do I need to convert something. Any help would be greatly appreciated.

I realized my problem, i had my calculator in radian's sorry for the stupid question, I'd delete the question if i can find out how
 
Last edited:
Physics news on Phys.org
The ropes are 1.9 m long while the height you used is 2.75 m. How exactly did you get 2.75 m using h = L(1-cosθ)?
 

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