A 10 kg box rests on a horizontal surface with μ_s = 0.4 and μ_k = 0.3. You push it with a 20 N horizontal force. The maximum static friction force is 39.2 N. Is the box moving, and what is the friction force?
AYes, moving; friction = 29.4 N (kinetic friction)
BNo, stationary; friction = 39.2 N (maximum static friction)
CNo, stationary; friction = 20 N (static friction adjusts to exactly balance the applied force)
DYes, moving; friction = 39.2 N (static friction at maximum)
Static friction is a constraint force — it takes whatever value is needed to prevent sliding, up to its maximum. Since the applied 20 N is less than the maximum static friction of 39.2 N, the box doesn't slide. Static friction adjusts to exactly 20 N to maintain equilibrium. It only equals μ_s N at the moment of impending motion. This is the most common misconception: students assume friction always equals μN, but that is only true at the threshold of sliding.
Question 2 Multiple Choice
Why does it typically require more force to start an object sliding than to keep it sliding once motion begins?
AThe contact area between surfaces increases as the object begins to move, creating more resistance
BThe normal force decreases slightly once the object is in motion, reducing the friction
CThe coefficient of kinetic friction is smaller than the coefficient of static friction for most material pairs, so the friction force drops once sliding begins
DMomentum must be overcome before motion starts, adding to the required force
For most material pairs, μ_k < μ_s. Before sliding, static friction can provide up to μ_s N of resistance. Once sliding begins, friction drops to the fixed value μ_k N. This is why furniture is hardest to move when you first push it — you must overcome maximum static friction to initiate motion, but once it's sliding, the required force drops. Contact area and momentum are irrelevant; the coefficient values are the explanation.
Question 3 True / False
The friction force acting on a stationary object usually equals μ_s × N, where μ_s is the coefficient of static friction and N is the normal force.
TTrue
FFalse
Answer: False
This is the central misconception about static friction. Static friction is variable — it takes whatever value maintains equilibrium, which can be anywhere from zero up to μ_s N. It equals μ_s N only when the object is on the verge of sliding (impending motion). A box sitting undisturbed on a floor with no applied force has zero static friction, not μ_s N.
Question 4 True / False
Both the coefficient of static friction and the coefficient of kinetic friction between two surfaces are independent of the contact area between those surfaces.
TTrue
FFalse
Answer: True
This surprises many students who intuit that more surface area in contact means more friction. In the standard friction model, both μ_s and μ_k depend only on the material properties of the contacting surfaces (e.g., rubber on concrete vs. wood on wood), not on how large the contact patch is. A wide tire and a narrow tire of the same rubber compound on the same road surface have the same friction coefficients.
Question 5 Short Answer
A student says 'friction always opposes motion.' Why is this description incomplete, and what is the more precise statement?
Think about your answer, then reveal below.
Model answer: For kinetic friction, opposing the direction of sliding is accurate. But static friction opposes the tendency of relative motion — the direction the surface would slide if friction weren't present — which may differ from the direction of any actual motion. A book on an accelerating car experiences static friction acting forward (in the direction of motion) because that's what prevents the book from sliding backward relative to the car.
The distinction matters for free-body diagram analysis. Static friction acts to maintain the no-slip condition, so its direction is whatever is needed to prevent relative sliding — not necessarily opposite to the direction of travel. Always ask: 'Which direction would this surface tend to slide without friction?' Static friction opposes that tendency.