A mover has to move a heavy sofa of mass 112 kg to the second floor of the house. He uses a rope to pull the sofa up a ramp from the first to the second floor. As he pulls the sofa he makes sure that the rope is parallel to the surface of the ramp which is at 30.0° to the horizontal. If friction between the sofa and the ramp is negligible, and the sofa has an acceleration of 0.700 m/s2, find the tension in the rope (in N).

Question

Physics

Yoselin Jennings

10 September, 11:10

A mover has to move a heavy sofa of mass 112 kg to the second floor of the house. He uses a rope to pull the sofa up a ramp from the first to the second floor. As he pulls the sofa he makes sure that the rope is parallel to the surface of the ramp which is at 30.0° to the horizontal. If friction between the sofa and the ramp is negligible, and the sofa has an acceleration of 0.700 m/s2, find the tension in the rope (in N).

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Tyler Mosley · Answer 1

663.2 N

Explanation:

mass of sofa, m = 112 kg

inclination, θ = 30°

acceleration, a = 0.7 m/s^2

Let T be the tension in the rope.

Component f weight acting downwards along the ramp = mg sinθ

= 112 x 9.8 x 0.5 = 548.8 N

So, by the Newton's second law

T - mgsinθ = ma

T - 548.8 = 112 x 0.7

T = 78.4 + 548.8

T = 663.2 N

Thus, the tension in the rope is 663.2 N.