You do 116 J of work while pulling your sister back on a fritctionless swing, whose chain is $5.10 \mathrm {~m}$ long, until the swing makes an angle of 32.0° with the vertical. What is your sister's mass?
A) 15.3 kg
B) 13.0 kg
C) 17.6 kg
D) 19.0 kg

Question

Quizplus · Accepted Answer

The work done is equal to the change in potential energy of the system:$$W = \Delta U = mgh$$where $m$ is the mass of the sister, $g$ is the acceleration due to gravity, and $h$ is the change in height of the center of mass of the system.The change in height is:$$h = L - L\cos\theta = L(1 - \cos\theta)$$where $L$ is the length of the chain and $\theta$ is the angle the chain makes with the vertical.Substituting into the first equation, we get:$$W = m g L(1 - \cos\theta)$$Solving for $m$, we get:$$m = \frac{W}{g L(1 - \cos\theta)} = \frac{116 \mathrm{~J}}{(9.81 \mathrm{~m/s^2})(5.10 \mathrm{~m})(1 - \cos32.0^\circ)} = 15.3 \mathrm{~kg}$$Therefore, the correct answer is A.

You Do 116 J of Work While Pulling Your Sister 5.10 m5.10 \mathrm {~m}5.10 m

You Do 116 J of Work While Pulling Your Sister $5.10 \mathrm {~m}$