Question

A child with a weight of 220 N swings on a playground swing attached to 1.90-m-long chains. What is 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 25.0° angle with the vertical
(c) when the child is at the bottom of the circular arc

Answer 1

The gravitational potential energy of the child-Earth system can be calculated using the formula GPE = mgh, where m is the mass of the child, g is the acceleration due to gravity, and h is the height above the reference position. The GPE depends on the height of the child from the reference position in each scenario. At the bottom of the circular arc, the GPE is zero.

Step-by-step explanation:

Gravitational potential energy of the child-Earth system can be calculated using the formula: GPE = mgh, where m is the mass of the child (weight divided by acceleration due to gravity), g is the acceleration due to gravity, and h is the height above the reference position.

(a) When the ropes are horizontal, the child's height from the reference position is 1.90 m. Hence, the gravitational potential energy is given by GPE = (220 N/10 m/s²) * 10 m/s² * 1.90 m = 418 Nm (Unit: Nm).

(b) When the ropes make a 25.0° angle with the vertical, the height of the child from the reference position would be h = 1.90 m * sin(25°) = 0.79 m. Therefore, the gravitational potential energy is GPE = (220 N/10 m/s²) * 10 m/s² * 0.79 m = 171.6 Nm (Unit: Nm).

(c) When the child is at the bottom of the circular arc, the height from the reference position is zero. Hence, the gravitational potential energy is zero.