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 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) 5.3 s
B) 5.7 s
C) 4.8 s
D) 4.4 s

Question

Quizplus · Accepted Answer

The period of a pendulum is given by $T = 2\pi\sqrt{\frac{L}{g}}$, where $L$ is the length of the pendulum and $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$). Plugging in the given length $L = 4.9 \, \text{m}$, we get $T = 2\pi\sqrt{\frac{4.9}{9.8}} = 2\pi\sqrt{0.5} = \pi$. Since $\pi \approx 3.14$, $T \approx 3.14 \times 1.4 = 4.4 \, \text{s}$. Note that the mass of the child and swing set does not affect the period of the swing, as the formula for the period of a pendulum does not include mass.

A 34-Kg Child on an 18-Kg Swing Set Swings Back