Question

Let us look at an inclined plane problem, involving two objects that are tied together by a cable. Blocks of granite, each with weight w1, are being hauled up a 30 ∘ slope out of a quarry. For environmental reasons, dirt is also being dumped into the quarry to fill up old holes. You have been asked to find a way to use this dirt to move the granite out more easily. You design a system that lets the dirt (weight w2, including the weight of the bucket) that drops vertically into the quarry pull out a granite block on a cart with steel wheels (total weight w1), rolling on steel rails. Ignoring the weight of the cable and friction in the pulley and wheels, determine how the weights w1 and w2 must be related for the system to move with constant speed.

The system you have designed could also be used to remove dirt from the quarry by letting the cart slide back down the incline. If the incline is changed from 15∘ to 30 ∘ and the cart slides back down the incline at a constant speed, determine the total normal force n that the tracks apply to the wheels of the granite cart, as a fraction of w1.

Answer 1

Part a

Part b

n=w₁cos15 = 0.97w₁