Determine least value of work:

Q. Determine least value of W as shown in the figure given below to keep the system of connected bodies in equilibrium µ for surface of contact between plane AC and block = 0.28 and that between the plane BC and block = 0.02

Sol.: For least value W, motion of 2000N block must be impending downward.

From the free body diagram of block 2000N as shown in the figure

∑V = 0

R₁  - 2000cos30° = 0

R₁ = 1732.06N                                                                                                           ...(i)

∑H = 0

T + µ₁R₁ - 2000sin30° = 0

T = 2000sin30° - 0.20 × 1732.06, T = 653.6N                                             ...(ii)

Now Consider the free body diagram of WN block, as shown in the figure

∑V = 0

R₂ = Wcos60° = 0

R₂ = 0.5W N                                                                                                            ...(iii)

∑H = 0

T - µ2R2 - Wsin60° = 0

653.6 = Wsin60° - 0.28 × 0.5W

WLEAST = 649.7N                                                                        .......ANS