A 39.5 N child is in a swing that is attached to ropes 2.01 m long.
What is the gravitational potential energy when the child is at the bottom of the circular arc?
I thought that you would multiply the force given by 2.01 m, but the answer I calculated was incorrect.
GPE is relative to some point. Normally, that point would be the lowest point, so the kid is there, and GPE is zero.
To calculate the gravitational potential energy when the child is at the bottom of the circular arc, you need to use the formula:
Gravitational Potential Energy = m * g * h
Where:
m is the mass of the child,
g is the acceleration due to gravity (9.8 m/s²),
h is the height of the swing from the lowest point.
In the given problem, the force (39.5 N) is given instead of the mass. However, you can calculate the mass of the child using the formula:
Force = m * g
Rearranging the formula, we get:
m = Force / g
Substituting the given values:
m = 39.5 N / 9.8 m/s²
m ≈ 4.04 kg
Now that we have the mass of the child, we can calculate the gravitational potential energy by substituting the values into the formula:
Gravitational Potential Energy = 4.04 kg * 9.8 m/s² * h
The height (h) in this case is the length of the ropes (2.01 m), as the child is at the bottom of the circular arc.
Gravitational Potential Energy = 4.04 kg * 9.8 m/s² * 2.01 m
Gravitational Potential Energy ≈ 80.1648 J
So, the gravitational potential energy of the child when at the bottom of the circular arc is approximately 80.1648 Joules.