Evaluate the angle - block impends down the plane:
What should be value of the angle shown in the figure so that the motion of the 90N block impends down the plane? The coefficient of friction for entire surface = 1/3.
Sol.: Consider equilibrium of block 30N
∑V = 0;
R_{1} - 30cos θ = 0,
R_{1} = 30cos ...(i)
∑H = 0;
T - µR_{1} - 30sinθ = 0,
T = 10cos θ + 30sinθ ...(ii)
Consider the equilibrium of block 90N
R_{2} - R_{1} - 90cos θ = 0
R_{2} = 120cos ...(iii)
90sin θ - µR_{1} - µR_{2} = 0,
90sin θ = 10cos θ + 40sinθ ...(vi)
tanθ = 5/9 that is θ = 29.050