Question

Blocks 1 and 2 of masses m₁ and m₂,  respectively, are connected by a light string, as shown. These blocks are further connected to a block of mass M by another light string that passes over a pulley of negligible mass and friction. Blocks l and 2 move with a constant velocity v down the inclined plane, which makes an angle θ with the horizontal. The kinetic frictional force on block 1 is f and that on block 2 is 2f.

a. On the figure below, draw and label all the forces on block m₁.

Express your answers to each of the following in terms of m₁, m₂, g, θ, and f

b. Determine the coefficient of kinetic friction between the inclined plane and block 1.

c. Determine the value of the suspended mass M that allows blocks 1 and 2 to move with constant velocity down the plane.

d. The string between blocks 1 and 2 is now cut. Determine the acceleration of block 1 while it is on the inclined plane.

Answer 1

d. Applying Newton’s second law to block 1 gives ΣF = m₁g sinθ – f = m₁a which gives a = g sinθ – f/m₁