Calculate the gravitational potential energy of the child-Earth system

[Chuck 86]

Homework Statement

A 32.2 N child is in a swing that is attached to ropes 1.65 m long. Calculate the gravitational potential energy of the child-Earth system relative to the child's lowest position when the ropes are horizontal

Homework Equations

GPI=mgy
Ke= 1/2 m v^2

The Attempt at a Solution

0+.5mv^2= mgy + 0
i think I am on the right track but i don't seem to get the right answer

 

[Delphi51]

Just use GPI=mgy where y = 1.65 m.

 

[tomcue]

.

Your attempt at a solution is on the right track, but there are a few things to clarify and adjust in order to get the correct answer.

First, the equations you listed are correct, but they are not all necessary to solve this problem. The gravitational potential energy equation (GPE = mgh) is sufficient for calculating the potential energy in this scenario.

Second, you will need to define all of the variables in your equations. In this case, m represents the mass of the child, g represents the acceleration due to gravity (approximately 9.8 m/s^2), and y represents the height of the child above the lowest position when the ropes are horizontal.

Third, make sure to convert all units to the correct form. In this case, the mass should be in kilograms, the acceleration due to gravity should be in meters per second squared, and the height should be in meters.

Finally, when plugging in the values into the equation, make sure to use the correct value for the height (y). Since the ropes are 1.65 m long, the height would be half of that, or 0.825 m.

Therefore, the correct equation and solution would be:

GPE = mgh
GPE = (32.2 N)(0.825 m)(9.8 m/s^2)
GPE = 264.87 J

So, the gravitational potential energy of the child-Earth system in this scenario is 264.87 Joules.