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 4.9m.
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

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 4.9m. 
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

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 of $4.9 \, \text{m}$ for $L$, we get $T = 2\pi\sqrt{\frac{4.9}{9.8}} = 2\pi\sqrt{0.5} = 2\pi\sqrt{\frac{1}{2}}$. This simplifies to $T = 2\pi\left(\frac{1}{\sqrt{2}}\right) = \pi\sqrt{2}$. Numerically, this evaluates to approximately $4.4$ seconds, making choice A correct. The mass of the child and swing set does not affect the period of a pendulum for small angles.

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