Final answer:
The tension in the ropes of a swing when a 15.0-kg child is at the lowest point is the weight of the child, which calculates to 147 N.
Step-by-step explanation:
The question is asking to calculate the tension in the ropes of a swing when a child is at the lowest point. This is a physics problem that involves concepts of Newton's laws of motion and centripetal force. When the child is at the lowest point of the swing, the tension in the rope is the sum of the force due to gravity acting on the child and the force required to keep the child moving in a circular path (centripetal force).
Firstly, the force due to gravity (weight) is given by W = m × g, where m is the mass of the child and g is the acceleration due to gravity. For a 15.0-kg child, the weight W is 15.0 kg × 9.80 m/s² = 147 N. Secondly, when the child is at the lowest point, the centripetal force required for circular motion is provided by the vertical component of the tension in the ropes, which is equal to the weight of the child in this case because there is no vertical acceleration at the lowest point.
Thus, the total tension T in the ropes when the child is at the lowest point is simply the weight of the child, which is 147 N. Therefore, the tension in the ropes is 147 N.