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

AI Thread Summary
To find the gravitational potential energy of a child in a swing with ropes at a horizontal position, the height is calculated using the formula h = L(1 - cos(θ)). For θ at 90 degrees, the height is determined to be 1.9 m. The potential energy is then computed using PE = mgh, resulting in 1213.99 J. However, the user initially miscalculated the height as 2.75 m, leading to confusion about the correct answer. The issue was later identified as a calculator setting in radians, highlighting the importance of unit consistency in calculations.
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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:
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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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