A block of mass 5 kg is placed on a rough inclined plane which makes an angle of 37^ with the horizontal. It is connected by a light string passing over a smooth pulley at the top of the incline to a hanging block of mass 10 kg . The coefficient of kinetic friction between the 5 kg block and the incline is 0.25 . Find the acceleration of the system when released from rest. (Take g = 10 m s ⁻² , 37^ = 0.6 , 37^ = 0.8

Step-by-step solution

Let the mass on the incline be m₁ = 5 kg and the hanging mass be m₂ = 10 kg . The driving force pulling the system is the weight of the hanging mass: W₂ = m₂ g = 10 10 = 100 N . The forces opposing the motion of the 5 kg block up the incline are the component of its weight parallel to the incline and the kinetic friction. Component of weight down the incline: m₁ g 37^ = 5 10 0.6 = 30 N . The normal force on the block is N = m₁ g 37^ = 5 10 0.8 = 40 N . The kinetic friction force is f_k = _k N = 0.25 40 = 10 N . The