To find the gravitational potential energy, we can use the formula:
Gravitational potential energy (PE) = mgh
Where:
m = mass of the child
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height above the child's lowest position
(a) When the ropes are horizontal:
In this case, the height (h) is equal to the length of the ropes (1.80 m).
PE = mgh
PE = m * 9.8 * 1.80
PE = 17.64 m * g
(b) When the ropes make a 32.0° angle with the vertical:
To find the height, we can use the vertical component of the rope's length:
h = length of the ropes * sin(angle)
h = 1.80 * sin(32.0°)
PE = mgh
PE = m * 9.8 * h
PE = 9.8 * m * 1.80 * sin(32.0°)
(c) When the child is at the bottom of the circular arc:
In this case, the height (h) is zero since the child is at the lowest position. Therefore, the gravitational potential energy is also zero.
PE = 0
Note: To find the gravitational potential energy in terms of the child's mass (m), we need to know the mass of the child.
370-N child is in a swing that is attached to a pair of ropes 1.80 m long. Find the gravitational potential energy of the child-Earth system relative to the child's lowest position at the following times.
(a) when the ropes are horizontal
(b) when the ropes make a 32.0° angle with the vertical
(c) when the child is at the bottom of the circular arc
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