Friction Examples

A $500\ \text{N}$ block rests on a horizontal floor with $\mu_s=0.40$. A worker pushes horizontally with $150\ \text{N}$. Determine the friction force and whether the block moves.

The same $500\ \text{N}$ block is pushed horizontally. Determine the force needed to reach impending sliding.

For a contact with $\mu_s=0.45$, determine the friction angle.

A block rests on a rough incline with $\mu_s=0.60$ and no other applied force. Determine the ideal incline angle at impending downward sliding.

A rectangular monument weighs $100\ \text{kN}$, is $1.00\ \text{m}$ wide, and a horizontal force acts $2.00\ \text{m}$ above the base. The base has $\mu_s=0.50$. Determine whether sliding or tipping occurs first.

For the same $100\ \text{kN}$, $1.00\ \text{m}$-wide monument, the horizontal force is applied only $0.500\ \text{m}$ above the base. Determine the tipping threshold and compare it with the $50.0\ \text{kN}$ sliding threshold.

A rope is wrapped through $180^\circ$ around a fixed cylinder with $\mu_s=0.30$. Find the limiting tension ratio $T_2/T_1$.

A rope has $T_2=10.0\ \text{kN}$ on the high-tension side, $\mu_s=0.25$, and a wrap angle of $270^\circ$. Determine the limiting low-side tension $T_1$.

An $800\ \text{N}$ block rests on a horizontal surface with $\mu_s=0.35$. A force $P$ is applied $25.0^\circ$ above horizontal. Determine $P$ at impending sliding.

A $600\ \text{N}$ block is pushed by $P=120\ \text{N}$ at $20.0^\circ$ below horizontal. The surface has $\mu_s=0.30$. Determine the actual static-friction force and check whether sliding occurs.

A capstan must sustain a limiting tension ratio $T_2/T_1=4.00$ with $\mu_s=0.25$. Determine the required wrap angle.