A block of mass m1 rests on a rough plane inclined at an angle θ to the horizontal. It is connected by a light, inextensible string passing over a small frictionless pulley at the top of the incline to a hanging mass m2. The coefficient of kinetic friction between m1 and the plane is μ. Assume the string and pulley are ideal.
a. (i) Draw separate free-body diagrams for m1 and m2, taking the direction of potential motion of m2 downward.
b. (ii) Using the diagrams, derive expressions for the magnitude of the acceleration a of the system and the tension T in the string.
c. (iii) Show that the block m1 will start sliding up the plane if m2>m1(sinθ+μcosθ).