A 10 kg block rests on a rough horizontal surface with μₛ = 0.5. A force F is applied at 37° above the horizontal. Take g = 10 m/s², sin37° = 3/5 and cos37° = 4/5. The minimum F required to just start the block is:
Options

Question

A 10 kg block rests on a rough horizontal surface with μₛ = 0.5. A force F is applied at 37° above the horizontal. Take g = 10 m/s², sin37° = 3/5 and cos37° = 4/5. The minimum F required to just start the block is:

Options

G1 Physics · Accepted Answer

At impending motion, F cosθ = μₛN and N = mg - F sinθ. Thus F cosθ = μₛ(mg - F sinθ). Hence F(cosθ + μₛsinθ) = μₛmg. F = 0.5×100/[0.8 + 0.5×0.6] = 50/1.1 = 45.45 N. Therefore none of the listed values would be exact; corrected answer is 45.45 N.