Gravitational Potential Energy child swing Problem

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Homework Help Overview

The problem involves calculating the gravitational potential energy of a child in a swing at different positions relative to the lowest point of the swing. The scenario includes a child weighing 140 N and a swing with ropes that are 2.00 m long, with specific angles being considered for potential energy calculations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss using the formula for gravitational potential energy (PE = mgy) and explore how to determine the height of the child above the ground using trigonometric relationships. There are attempts to clarify the correct height calculation at a 25° angle from the vertical.

Discussion Status

Some participants have provided guidance on using trigonometry to find the height, while others express confusion regarding their calculations and the expected results. There is an ongoing exploration of the correct interpretation of height in relation to the swing's position.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the amount of direct assistance they can receive. There is a focus on understanding the geometry involved in the problem and ensuring that the calculated height remains consistent with the physical setup of the swing.

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Homework Statement



A 140-N child is in a swing that is attached to ropes 2.00 m long. Find the gravitational potential energy associated with the child relative to her lowest position at the following times.

(a) when the ropes are horizontal

I get this one. I used PE=mgy; PE=(140-N)(2.00 m)= 280 J

However, I'm unsure how to approach part B, so if someone could just nudge me in the right direction I would really appreciate it (you certainly don't have to work it out--I'm not asking you to do my work).

(b) when the ropes make a 25.0° angle with the vertical
 
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Sketch the rope, the angle and the height. Use trigonometry to find the height. Then use mgy again.
 
Use trig to find the height of the child above the ground, using this number as variable "y" in the PE formula.

Think right triangles.
 
T.T i don't understand this at all.

I drew a whole lot of right triangles solving for a h and o using 90 degrees and 25 degrees and 65 degrees (basically everything I can think of) and get small numbers such as 2.21 and when I add that in that gives you a.. LOT of joules which is nonsensical.
 
Certainly the height has to be less than 2 meters!

Show the swing rope at an angle of 25 degrees from vertical.
Draw a vertical line down from where the ropes are held at the top.
Draw a horizontal line across from the bottom of the child to the vertical line.
Now you have a right triangle with a 25 degree angle in it. You know the length of one side. You should be able to find the height . . .
 
Even if I do 2.00m*cos25 degress it comes out as 1.81 m.

If I plug that into my 140 N * (1.81 m) = 153 which is far too large. It must be much less and that is what I'm failing to understand.
 
Oops - I forgot about something!
Your 1.81 m is the vertical distance from the top of the swing down to the child. The height above the ground will be 2 - 1.81.
 
*facepalm*

Thank you so much for your help.
 

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