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

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In summary, the problem involves finding the gravitational potential energy of a 40 N toy attached to ropes 2.0m long in three different scenarios. The equations for gravitational potential energy and work are provided, but the student is unsure of how to proceed. They suggest using a free body diagram and trigonometry to find the length of the rope in one of the scenarios, but are unsure of how to apply the concept of energy.
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stanton
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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.
 
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  • #2
As usual I'd begin by drawing a picture!:wink:

What is the minimum potential energy of the toy?
 

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

What is gravitational potential energy?

Gravitational potential energy is the energy that an object has due to its position in a gravitational field. It is the potential to do work by virtue of the object's position.

How is gravitational potential energy calculated?

Gravitational potential energy is calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object relative to a reference point.

What factors affect the gravitational potential energy of an object?

The gravitational potential energy of an object is affected by its mass, the acceleration due to gravity, and its height above a reference point. The higher an object is and the more massive it is, the greater its gravitational potential energy.

Is gravitational potential energy a form of potential or kinetic energy?

Gravitational potential energy is a form of potential energy, meaning it is stored energy that can be converted into other forms of energy, such as kinetic energy, when the object is in motion.

How is gravitational potential energy related to gravitational force?

Gravitational potential energy is directly related to gravitational force. The greater the gravitational force acting on an object, the greater its potential energy. This is because the force of gravity is what gives the object its potential to do work.

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