Questions: Dry Friction and Coulomb's Law

Question 1

A 10 kg block sits on a horizontal surface with μ_s = 0.4. The normal force is approximately 98 N, giving F_s,max = 39.2 N. A 30 N horizontal force is applied. What is the friction force?

• A. 39.2 N — always use F = μ_s·N for friction problems
• B. 29.4 N — use kinetic friction μ_k·N since a force is applied
• C. 30 N — friction matches the applied force exactly, since it does not exceed the maximum
• D. 0 N — the block is not moving so there is no friction

Answer: (C)

Friction is reactive: it takes whatever value equilibrium requires, up to its maximum. Here, equilibrium requires only 30 N of friction to balance the applied force, which is less than F_s,max = 39.2 N — so the block does not slide and friction equals exactly 30 N. Using μ_s·N always (option A) is the most common error — that value is the maximum, not the actual friction force. Using kinetic friction (option B) is wrong because the block is not sliding. The friction force is 0 only when no tangential force tends to cause sliding.

Question 2

An engineer needs to determine whether a crate will slide when pushed with force F. In which order should they proceed?

• A. Apply F = μ_k·N immediately, since that governs motion
• B. Assume the crate is sliding, calculate kinetic friction, and verify afterward
• C. First solve equilibrium equations to find what friction force is required; compare to F_s,max = μ_s·N to determine whether sliding occurs
• D. Use F = μ_s·N for the friction force regardless, since static friction governs impending motion

Answer: (C)

The correct procedure is: assume static equilibrium, solve for the required friction force from equilibrium equations, then compare to F_s,max = μ_s·N. If the required friction is less than or equal to the maximum, the crate stays put and friction equals the required value. If equilibrium would require more friction than the surface can provide, sliding occurs and you switch to F = μ_k·N. The friction state must be determined before you can write the correct friction equation — there is no shortcut.

Question 3

The friction force between two surfaces usually equals μ_s × N, regardless of the magnitude of the applied load.

• T. True
• F. False

Answer: False

F = μ_s·N gives the maximum static friction force — the upper limit, not the actual value. For any applied load that does not cause impending motion, the actual friction force is less than this maximum and is determined by equilibrium. Only at the instant of impending slip does the friction force reach μ_s·N. This reactive character distinguishes friction from most other forces in statics: you cannot write the friction force directly from geometry; you must first determine the friction state.

Question 4

Kinetic friction is smaller than maximum static friction, which is why it takes more force to start an object sliding than to keep it sliding once motion has begun.

• T. True
• F. False

Answer: True

μ_k < μ_s by definition of Coulomb's model. When a block is on the verge of sliding, the maximum static friction F_s,max = μ_s·N must be overcome. Once sliding begins, the friction drops to F_k = μ_k·N, which is smaller. This reduction is why you can feel a 'give' when you first budge a stuck object — the resisting force drops once motion starts. Practically, this means the force needed to maintain motion is less than the force needed to initiate it.

Question 5

What does it mean to say that friction is a 'reactive' force, and why does this require you to determine the friction state before writing the friction equation?

Model answer: A reactive force adjusts its magnitude in response to the loads applied to a system, rather than having a fixed value determined by geometry or material alone. Friction opposes the tendency of motion and takes whatever value equilibrium requires — from zero up to its maximum μ_s·N. Because friction can take any value in that range, you cannot write a single friction equation without first knowing which of the three states applies: static equilibrium (F < μ_s·N, determined by equilibrium), impending motion (F = μ_s·N, the tipping-point condition), or sliding (F = μ_k·N, once motion has started). Each state uses a different equation, and choosing the wrong one produces an incorrect answer.

This is the central challenge of friction problems in statics: unlike a pin joint or roller support, friction does not have a unique force determined by the geometry. You must make a judgment about the state first, then set up equations, then verify that your assumed state is consistent with the solution. If the check fails, you assumed the wrong state and must redo the analysis.