Question

A piñata of mass 3.27 kg is attached to a string tied to a hook in the ceiling. The length of the string is 0.810 m, and the piñata is released from rest from an initial position in which the string makes an angle of 56.5° with the vertical. What is the work done by gravity by the time the string is in a vertical position for the first time?

Answer 1

The work done by gravity on the piñata is calculated by the change in gravitational potential energy, which is found using the height difference as the piñata falls to the vertical position.

Step-by-step explanation:

The work done by gravity on the piñata as it swings down to the vertical position can be found by calculating the change in potential energy, which is equal to the work done by gravity because there are no other external forces doing work (such as friction in this idealized scenario). Since the only force doing work is gravity, the work is the difference between the initial and final gravitational potential energy of the piñata. We start by finding the height difference (h) using trigonometry, by which the piñata drops which can be found using h = L - L\cos(\theta), where L is the length of the string (0.810 m) and \(\theta\) is the initial angle (56.5°). Then we use W = mgh to find the work done by gravity, where W is work, m is the mass of the piñata (3.27 kg), g is the acceleration due to gravity (9.81 m/s2), and h is the height calculated previously.