Serway & Jewett — Conservation of Energy: Problem 42

You are working in the distribution center of a large online shopping site. Efforts are being made to increase the number of packages per unit time that are being loaded onto a conveyor belt to be carried to waiting trucks. But the motor driving the conveyor belt is having difficulty keeping up with the increased demands. Your supervisor has asked you to determine the requirements for a new motor that can provide enough power to keep the conveyor belt moving smoothly under the increased loading rate. You are given the following information: The design goal is to have 50.0-kg packages loaded onto the belt at several locations at an average rate of 5.00 packages per second. The belt moves at a horizontal speed of 1.35 m/s. Humans at the various locations along the belt place the package on the belt so that it is initially at rest relative to the floor of the building just before being dropped from negligible height onto the belt. Your task is to determine the minimum power the driving motor must have to accelerate these packages and keep the belt moving at constant speed.