Calculate the value of force - frictionless 

A block weighing 5KN is attached to the chord that passes over the frictionless pulley, and supports weight of 2KN. The coefficient of friction in between block and floor is 0.35. Calculate the value of force P if (i) The motion is impending to the right  (ii) The motion is impending to the left.

Sol.: Case-1

From Free body diagram of the block,

∑V = 0→  -5 + R + 2sin30º = 0

R = 4KN

∑H = 0→  -P + 2cos30º - 0.35N = 0

P = 2cos30° - 0.35 × 4 = 0

P = 0.332KN                                                               .......Ans

Case-2: As the motion impends to left, the friction force is directed to right, from the FBD

of the block:

∑V = 0→  -5 + R + 2sin30° = 0

R = 4KN

∑H = 0→  -P + 2cos30° + 0.35N = 0

P = 2cos30° + 0.35 × 4 = 0

P = 3.132KN                                                               .......Ans