A box of mass?=21.0 kgm=21.0 kg is pulled up a ramp that is inclined at an angle?=21.0∘θ=21.0∘ angle with respect to the horizontal. The coefficient of kinetic friction between the box and the ramp is? k=0.285μk=0.285, and the rope pulling the box is parallel to the ramp. If the box accelerates up the ramp at a rate of?=2.09 m/s2a=2.09 m/s2, calculate the tension? TFT in the rope. Use?=9.81 m/s2g=9.81 m/s2 for the acceleration due to gravity.

Question

Physics

Camille Murray

1 July, 16:30

A box of mass?=21.0 kgm=21.0 kg is pulled up a ramp that is inclined at an angle?=21.0∘θ=21.0∘ angle with respect to the horizontal. The coefficient of kinetic friction between the box and the ramp is? k=0.285μk=0.285, and the rope pulling the box is parallel to the ramp. If the box accelerates up the ramp at a rate of?=2.09 m/s2a=2.09 m/s2, calculate the tension? TFT in the rope. Use?=9.81 m/s2g=9.81 m/s2 for the acceleration due to gravity.

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Gregory Perez · Answer 1

The tension of the rope is T = 172.52 N

Explanation:

m = 21 kg

α = 21º

μ = 0.285

a = 2.09 m/s²

g = 9.81 m/s²

W = m*g

W=206.01 N

Fr = μ*W*cos (α)

Fr = 54.81 N

Fx = W * sin (α)

Fx = 73.82 N

T-Fr-Fx = m*a

T = m*a + Fr + Fx

T = 172.52 N