A winch is used to drag a 320 N crate up a ramp at a constant speed of 59.0 c m

Question

A winch is used to drag a 320N crate up a ramp at a constant speed of 59.0cm/s by means of a rope that pulls parallel to the surface of the ramp. The rope slopes upward at 35.0? above the horizontal, and the coefficient of kinetic friction between the ramp and the crate is 0.250.

What is the tension in the rope?

If the rope were suddenly to snap, what would be the acceleration of the crate immediately after the rope broke?

Explanation / Answer

since acceleration is 0, all the forces must equate to 0. T = mg*sin(theta) +uk*mg*cos(theta) => T = 320*sin35 + 0.25*320*cos35 = 249.08 N mass of crate = 320/g = 32.65 kg when the rope snaps, a = F/m = [mg*sin(theta)-uk*mg*cos(theta)]/m => a = [320*sin35 - 0.25*320*cos35]/32.65 = 3.614 m/s^2

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