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A box of mass 5 kg is on a ramp tilted 36.9o above the horizontal. It starts at the bottom with an upward velocity along the ramp of 15 m/s. A person applies a constant force of 20.0 N to the box, with direction parallel to the ramp and directed up the ramp. The coefficient of kinetic friction between the box and ramp is 0.3. Please show all work.

a) What is the magnitude of the friction force that the ramp exerts on the box?

b) What is the magnitude of the acceleration of the box along the ramp?

c) How far along the ramp does the box go before coming to rest?

d) What is the minimum static coefficient of friction needed to prevent the box from sliding back down the ramp?

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