A 35.0 kg child swings on a rope with a length of 6.50 m that is hanging from a tree. At the bottom of the swing the child is moving at a speed of 4.20 m/s. What is the tension in the rope?
A) 95.0 N
B) 438 N
C) 343 N
D) 366 N

Question

Quizplus · Accepted Answer

The tension in the rope can be calculated by considering the forces acting on the child at the bottom of the swing: the gravitational force (weight) and the centripetal force needed to keep the child moving in a circular path. The total tension is the sum of the weight of the child and the centripetal force. Weight $W = mg = 35.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 343 \, \text{N}$. The centripetal force $F_c = \frac{mv^2}{r} = \frac{35.0 \, \text{kg} \times (4.20 \, \text{m/s})^2}{6.50 \, \text{m}} = 95 \, \text{N}$. Therefore, the total tension $T = W + F_c = 343 \, \text{N} + 95 \, \text{N} = 438 \, \text{N}$.

A 350 Kg Child Swings on a Rope with a Length