Gravitational potential energy: You do 174 J of work while pulling your sister back on a swing, whose chain is 5.10 m long. You start with the swing hanging vertically and pull it until the chain makes an angle of 32.0° with the vertical with your sister is at rest. What is your sister's mass, assuming negligible friction?

Question

Quizplus · Accepted Answer

The work done on the swing is equal to the change in gravitational potential energy, which can be calculated using the formula $ \Delta U = mgh $, where $ \Delta U $ is the change in potential energy, $ m $ is the mass, $ g $ is the acceleration due to gravity (approximately $ 9.8 \, \text{m/s}^2 $), and $ h $ is the change in height. The change in height can be found using trigonometry, considering the swing's chain length and the angle made with the vertical. The height $ h $ is given by $ h = L - L\cos(\theta) $, where $ L $ is the length of the chain and $ \theta $ is the angle with the vertical. Substituting the given values, $ h = 5.10 - 5.10\cos(32.0^\circ) $, and solving for $ m $ using the work done (174 J) gives the mass of the sister. This calculation results in a mass of approximately 22.9 kg.

Gravitational Potential Energy: You Do 174 J of Work While