A block of mass 10 kg is pulled up a rough inclined plane of angle 37^ at a constant speed of 2 m s ⁻¹ . If the power delivered by the pulling force is 160 W , what is the coefficient of kinetic friction between the block and the incline? (Take g = 10 m s ⁻² , 37^ = 0.6 , 37^ = 0.8 )

Step-by-step solution

The power delivered by the pulling force is given by P = F_ pull v . 160 = F_ pull 2 F_ pull = 80 N Since the block moves up the incline at a constant speed, the net force on it is zero. The pulling force must balance both the component of gravity along the incline and the kinetic friction force ( f_k ). F_ pull = mg + f_k 80 = (10)(10)(0.6) + f_k 80 = 60 + f_k f_k = 20 N The normal force exerted by the incline on the block is: N = mg = (10)(10)(0.8) = 80 N The coefficient of kinetic friction is: _k = f_k N = 20 80