Question

w = ? 22.0° Crate Ramp 30.0°

A 2000-N crate is to be held in place on a ramp that rises at 30.0° above the horizontal (see figure). The massless rope attached to the crate makes a 22.0° angle above the surface of the ramp. The coefficients of friction between the crate and the surface of the ramp are μk​=0.450 and μs​=0.650. The pulley has no appreciable mass or friction.

A. What is the MAXIMUM weight w that can be used to hold this crate stationary on the ramp? Include free-body diagrams of the two masses.

B. Now assume that the weight w=3000N. What is the acceleration of the crate?

C. Find the speed of the masses after the weight w=3000N has dropped a distance of 1.6m after being released from rest. Find this speed two ways: using kinematics and the acceleration derived in the previous subquestion, and using energy considerations.

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