Find the gravitational potential energy

[mustang]

Given: g=9.81 m/s^2.
A 41.7 kg child is in a swing that is attached to robes 2.16 m long. Find the gravitational potiental energy associated with the child relative to the child's lowest position under the following conditions:
B. when the ropes make a 34.7 degree angle with the vertical.

What equation would I use?

 

[HallsofIvy]

Well, potential energy = mgh looks good!

You might also want to draw a picture and use a little trigonometry to determine exactly what h is when the swing makes an angle of 34.7 degrees with the vertical.

 

[M98Ranger]

To find the gravitational potential energy of the child in this scenario, you would use the equation PE = mgh, where m is the mass of the child, g is the acceleration due to gravity (given as 9.81 m/s^2), and h is the height of the child above their lowest position. In this case, h would be equal to the vertical component of the ropes, which can be found using trigonometry as h = 2.16sin(34.7) = 1.23 m.

Plugging in the values, we get PE = (41.7 kg)(9.81 m/s^2)(1.23 m) = 509.5 J. Therefore, the gravitational potential energy associated with the child in this scenario is 509.5 joules.