A mover has to move a heavy sofa of mass 49.0 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 0.320, and the sofa has an acceleration of 0.800 m/s2, find the tension in the rope.

Question

-I made a free body diagram, but I just can't get the right answer.

Answer 1

Ws = M*g = 49 * 9.8 = 480 N. = Wt. of sofa.

Fp = 480*sin30 = 240 N. = Force parallel
to ramp.

Fn = Normal = 480*Cos30 = 416 N. = Force perpendicular to incline.

Fk = u*Fn = 0.320 * 416 = 133 N. = Force
of kinetic friction.

T-Fp-Fk = M*a.
T-240-133 = 49*0.80,
T-373 = 39.
T = 412 N.