Question

A mover has to move a heavy sofa of mass 47.0 kg to the second floor of the house. As he pulls on the rope tied to 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 the coefficient of kinetic friction between the sofa and the ramp is 0.420, and the sofa has an acceleration of 0.700 m/s2, find the tension in the rope.

Answer 1

Given Data

mass, m = 47 kg

Angle θ = 30.0°

coefficient of kinetic friction, μ = 0.420

acceleration a = 0.700 m/s2

Fg = m*g*sin θ

    = 47*9.8*sin 30

   = 230.3 N

Ff = m*g*cos θ *μ

    = 47*9.8*cos 30*0.420

   = 167.53 N

Fa = m*a

     = 47*0.7

     = 32.9 N

Total force F = Fg+Ff+Fa

                  = 230.3 N + 167.53 N + 32.9 N

                   = 430.73 N
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