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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
R2 = Wcos60° = 0
R2 = 0.5W N ...(iii)
T - µ2R2 - Wsin60° = 0
653.6 = Wsin60° - 0.28 × 0.5W
WLEAST = 649.7N .......ANS
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