What is the Gravitational Potential Energy of a Toy in a Swing?

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SUMMARY

The gravitational potential energy (PE) of a 40 N toy in a swing can be calculated using the formula PE = mgy, where 'm' is the mass, 'g' is the acceleration due to gravity, and 'y' is the height relative to the lowest position. For the swing with ropes 2.0 m long, the potential energy at the horizontal position is 80 J, at a 30-degree angle with the vertical is approximately 69.28 J, and at the bottom of the arc, the potential energy is 0 J. Understanding these calculations requires knowledge of basic physics principles, particularly energy conservation and trigonometry.

PREREQUISITES
  • Understanding of gravitational potential energy (PE = mgy)
  • Basic knowledge of trigonometry (cosine function)
  • Familiarity with free body diagrams
  • Concept of energy conservation in physics
NEXT STEPS
  • Study the derivation of gravitational potential energy formulas
  • Learn about the conservation of mechanical energy in pendulum systems
  • Explore trigonometric applications in physics problems
  • Practice solving similar problems involving swings and pendulums
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Students studying physics, particularly those focusing on mechanics and energy concepts, as well as educators looking for practical examples of gravitational potential energy in action.

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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.

Homework Equations



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

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.
 
Last edited:
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As usual I'd begin by drawing a picture!:wink:

What is the minimum potential energy of the toy?
 

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