A 34-kg child on an 18-kg swing set swings back and forth through small angles. If the length of the very light supporting cables for the swing is $4.9 \mathrm {~m}$ how long does it take for each complete back-and-forth swing? Assume that the child and swing set are very small compared to the length of the cables.
A) 4.4 s
B) 4.8 s
C) 5.3 s
D) 5.7 s

Question

Quizplus · Accepted Answer

The period of a simple pendulum is given by $ T = 2\pi \sqrt{\frac{L}{g}} $. Substituting $ L = 4.9 \, \text{m} $ and $ g = 9.8 \, \text{m/s}^2 $, we get $ T = 2\pi \sqrt{\frac{4.9}{9.8}} \approx 4.4 \, \text{s} $.

A 34-Kg Child on an 18-Kg Swing Set Swings Back 4.9 m4.9 \mathrm {~m}4.9 m

A 34-Kg Child on an 18-Kg Swing Set Swings Back $4.9 \mathrm {~m}$