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

In summary, the gravitational potential energy associated with a 45.0 kg child on a swing with ropes 1.90 m long and an acceleration of gravity of 9.81 m/s2 is 1213.99 J when the ropes are horizontal. This is calculated using the formula PE=mgh, with the height of the swing at a horizontal position being 2.75 m. However, this answer may not be correct as it is possible that the calculator was set to radians instead of degrees.
  • #1
falconpunch
1
0

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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  • #2
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)?
 

1. How is potential energy defined?

Potential energy is the energy possessed by an object due to its position or state. In the case of a swing, it is the energy that is stored when the swing is at its highest point.

2. What factors affect the potential energy of a swing?

The potential energy of a swing is affected by the mass of the swing, the height of the swing, and the strength of the ropes supporting the swing.

3. Can potential energy be measured?

Yes, potential energy can be measured using the formula PE = mgh, where m is the mass of the swing, g is the acceleration due to gravity, and h is the height of the swing.

4. Does the angle of the ropes affect the potential energy of a swing?

Yes, the angle of the ropes can affect the potential energy of a swing. When the ropes are horizontal, the potential energy is at its maximum. As the angle of the ropes decreases, the potential energy decreases as well.

5. How does potential energy change as the swing moves?

As the swing moves, potential energy is constantly being converted into kinetic energy and vice versa. When the swing reaches its highest point, the potential energy is at its maximum. As the swing moves downward, the potential energy decreases and the kinetic energy increases.

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