physics

I am helping my friend move into his new apartment. During the move, we have to load boxes into the back of his truck. To make it easier to load them, we've set up a metal ramp so that we can slide the boxes up to the deck of the truck. The box shown in the figure has a mass of 42.8 kg. The ramp has coefficients of friction given by μs = 0.3 and μk = 0.15. The ramp forms an angle of 44.7 degrees with the ground.

a) What is the minimum amount of tension I must apply to the rope to keep the box from sliding down the ramp? (The rope is parallel to the ramp.)

b) What is the minimum amount of tension I must apply to the rope to get the box to move up the ramp?

c) Once the box is moving up the ramp, how much tension must I apply to the rope to keep the box moving at a constant speed up the ramp?

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  1. N= mgcosα
    F(fr)=μN
    (a) T₁= mgsinα -F(fr) =
    = mgsinα - μ(s)mgcosα
    (b) T₂=F(fr) +mgsinα=
    =μ(s)mgcosα +mgsinα
    (c) T₃=F(fr) +mgsinα=
    =μ(k)mgcosα +mgsinα

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