Question

A mover has to move a heavy sofa of mass 63 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 0.410, and the sofa has an acceleration of 0.700 m/s2, find the tension in the rope in newtons.

Answer 1

Answer:572.02 N

Explanation:

Given

mass of sofa m =63 kg

inclination$=30 ^{\circ}$

$\mu _k=0.41$

acceleration $a=0.7 m/s^2$

Let T be the tension in the string

$T-mg\sin \theta -f_r=ma$

$f_r=\mu _kmg\cos \theta$

$f_r=0.41\times 63\times 9.8\times \cos (30)$

$f_r=219.22 N$

$T-63\times 9.8\times \sin (30)-219.22=63\times 0.7$

$T-308.7-219.22=44.1$

$T=527.92+44.1=572.02 N$