How to Calculate Gravitational Potential Energy for a Swinging Toy?

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SUMMARY

The discussion focuses on calculating the gravitational potential energy (PE) of a 40 N toy in a swing with 2.0 m long ropes at various positions. The key equations used include PEg = mgy and Wg = -mg(yf - yi). The participants analyze the toy's potential energy when the ropes are horizontal, at a 30-degree angle with the vertical, and at the lowest point of the swing. The calculations involve determining the vertical displacement (y) based on the swing's position.

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  • Understanding of gravitational potential energy (PE) concepts
  • Familiarity with basic trigonometry, particularly sine and cosine functions
  • Knowledge of free body diagrams and their application in physics
  • Ability to manipulate equations involving energy and work
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  • Study the derivation of gravitational potential energy formulas
  • Learn how to apply trigonometric functions in physics problems
  • Explore the concept of energy conservation in mechanical systems
  • Practice solving problems involving pendulums and swings
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Students studying physics, particularly those focusing on mechanics and energy concepts, as well as educators looking for examples of gravitational potential energy calculations.

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1. Homework Statement

A 40 N toy is placed in a light swing that is attached to ropes 2.0m long. Find the gravitational potential energy associated with the toy relative to its lowest position when (a) the ropes are horizontal (b) the ropes make a 30 degrees angle with the vertical and (c) at the bottom of the circular arc.

2. Homework Equations

PEg = mgy (note: y is distance)
Wg = -mg(yf-yi)=mgyi-mgyf=PEi-PEf
Wg=-deltaPE

3. The Attempt at a Solution

I do not know what to start. Well, as my prop show a similar problem with (b) problem, I tried to draw free body diagram. like vertical = y-axis and horizontal = x axis. So the the rope and y-axis makes a sort of triangle. and the unknown length of the one side of triangle must be length of cord multiplied by cos30. And I cant' go further. Maybe I went down all wrong. Will you help?
If I am asked solve the length between the maximum point reached by toy or something like that, I think I can do it. However, about energy, I am confused.
 
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At the bottom PE = ...?
a) The rope is horizontal. So the displacement is L ( length of the rope). So PE = ...?
b) The displacement is (L - Lcasθ). So PE =...?
 

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