A child with a weight of 190 N swings on a playground swing attached to 2.20 m long chains. What is the gravitational potential energy (in J) of the child-earth system relative to the child's lowest position at the following times?(a)when the chains are horizontal J(b)when the chains make an angle of 26.0° with respect to the vertical J(c)when the child is at his lowest position J

The gravitational potential energy (PE) of an object is given by the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height above the reference point.

In this case, we are given the weight of the child, not the mass. The weight of an object is the force exerted on it due to gravity and is given by the formula W = mg. So, we can find the mass by rearranging this formula to m = W/g.

Given: Weight (W) = 190 N Length of chains (L) = 2.20 m Acceleration due to gravity (g) = 9.8 m/s²

(a) When the chains are horizontal, the child is at the maximum height. This height (h) is equal to the length of the chains. So, h = L = 2.20 m.

First, find the mass: m = W/g = 190 N / 9.8 m/s² = 19.39 kg

Then, find the potential energy: PE = mgh = 19.39 kg * 9.8 m/s² * 2.20 m = 419.5 J

(b) When the chains make an angle of 26.0° with the vertical, the height (h) is less than the length of the chains. We can find h using the cosine of the angle: h = L * cos(26.0°) = 2.20 m * cos(26.0°) = 1.96 m

Then, find the potential energy: PE = mgh = 19.39 kg * 9.8 m/s² * 1.96 m = 372.6 J

(c) When the child is at his lowest position, the height (h) is zero. So, the potential energy is also zero: PE = mgh = 19.39 kg * 9.8 m/s² * 0 = 0 J