A $25,mathrm{kg}$ block rests on a rough horizontal surface. A horizontal force $P = 80,mathrm{N}$ is applied. If $mu_s = 0.35$, determine whether the block moves and find the friction…

Question

A $25,mathrm{kg}$ block rests on a rough horizontal surface. A horizontal force $P = 80,mathrm{N}$ is applied. If $mu_s = 0.35$, determine whether the block moves and find the friction force.

Accepted Answer

1. Draw the free-body diagram — Isolate the block: weight $W=mg$ down, normal $N$ up, applied $P$ to the right, friction $f$ opposing motion. 2. Vertical equilibrium — [ Sigma F_y = 0:; N - mg = 0 Rightarrow N = (25)(9.81) = 245.25,mathrm{N} ] 3. Maximum static friction — [ f_{max} = mu_s N = 0.35times 245.25 = 85.84,mathrm{N} ] Since $P=80,mathrm{N} < f_{max}$, the block does not move. 4. Actual friction force — [ Sigma F_x = 0:; f = P = 80,mathrm{N} ] The block stays at rest, $f = 80,mathrm{N}$ opposite to $P$.

numengineering.com

A $25,mathrm{kg}$ block rests on a rough horizontal surface. A horizontal force $P = 80,mathrm{N}$ is applied. If $mu_s = 0.35$, determine whether the block moves and find the friction force.

Ratings & comments