Irodov Problem 1.194

Problem Statement

A block of mass m is pressed against a wall by a horizontal force F. The coefficient of static friction is μs. Find the minimum force F to prevent the block from sliding down.

Given

m, F horizontal, μs, vertical wall.

Concepts & Formulas

Normal force N = F. Max static friction f = μs·F (upward). For equilibrium: μs·F ≥ mg.

Step-by-Step Solution

Step 1: N = F (wall reaction).
Step 2: Friction f_max = μs·F must support weight mg.
Step 3: μs·F ≥ mg → F ≥ mg/μs.

Worked Calculation

F_min = mg/μs.

Boxed Answer

F_min = mg/μs

Physical Interpretation

The required force is inversely proportional to μs — a rougher wall needs a smaller pressing force to keep the block from sliding.