1.2.7 · D5Newton's Laws & Dynamics
Question bank — Coefficients of friction — measurement, material dependence
Before we start, one shared vocabulary reminder so every symbol is earned:
True or false — justify
Rubber-on-road can exceed 1 — is that allowed?
True. is just a ratio ; nothing forbids friction being larger than the normal force. Soft rubber interlocks so deeply that or more is real.
Doubling the mass of a block on a horizontal floor doubles
False. It doubles (hence the friction force ), but is the ratio and stays fixed — it's a property of the surface pair, not the load.
Standing a brick on its small end instead of its wide face changes
False. Apparent contact area does not enter . Real contact is only at asperity tips, whose total area tracks , not the footprint.
On a flat table with nothing pushing sideways, the static friction force is exactly
False. With no applied sideways force, friction is zero — it only supplies as much as needed. It reaches only at the verge of slipping.
The angle-of-repose method requires you to know the block's mass
False. Both driving term and normal term carry , which cancels: . A protractor is enough.
is genuinely constant for all sliding speeds
Mostly true as a first approximation, but not exactly — at very high speeds heating and material changes shift it. For introductory dynamics we treat it as constant.
For any surface pair, always holds
Almost always true — resting asperities cold-weld and interlock, needing extra force to break free. A rare few engineered pairs can nearly tie, but is not seen in normal materials.
On a frictionless incline the angle of repose is
True in the sense that : the block slides at the slightest tilt, so there is no non-zero "just holds" angle.
A block sitting still on a ramp below the slip angle has friction equal to
True. It isn't sliding, so along-slope forces balance: static friction rises to exactly match the driving component , which is less than the ceiling .
Adding oil between two steel plates lowers because it reduces the weight
False. Weight is unchanged; the oil film separates the asperities so they can't cold-weld, cutting the friction force for the same — see Lubrication & Tribology.
Spot the error
"On an incline, , so ." Where's the slip?
Wrong . On a tilted surface the normal force is , not . Only presses into the ramp; the rest drives sliding.
"Since , a sliding block always decelerates." What's missing?
The applied force. Kinetic friction alone would decelerate it, but if you keep pushing hard enough the net force can be zero (constant speed) or even forward. only tells you starting is harder than continuing.
"To get on a horizontal pull, read the spring while accelerating the box." Fix it.
Read it at constant velocity (). Only then does the applied force equal kinetic friction exactly; while accelerating, part of your pull goes into and pollutes the reading via Newton's Second Law.
"Bigger means the object is heavier." Correct this.
carries no information about weight; it's set by what the two surfaces are made of. A light Teflon puck and a heavy steel block can each have small or large depending only on their surface pair.
" is a property of steel, so steel always has ." Wrong how?
belongs to a pair, never one material. Steel-on-steel dry is , but steel-on-ice is and steel-on-oiled-steel is . You must always say "steel on what".
"At the verge of slipping, ." Spot it.
The right side should be the friction ceiling , not . The correct along-slope balance is , giving .
"Real contact area equals the block's footprint." Why is this wrong?
Surfaces touch only at microscopic asperity peaks, so real contact is a tiny fraction of the footprint and grows with as bumps flatten — that's precisely why apparent area drops out of .
Why questions
Why is dimensionless?
It's a force divided by a force (), so all units cancel, leaving a pure comparison number.
Why does the mass cancel in the incline method but the angle does not?
Every force term is proportional to , so dividing the along-slope by the perpendicular balance removes entirely, leaving only — an angle-only result.
Why must friction be modelled as an inequality for the static case?
Because static friction adapts to whatever push it must cancel; it has a maximum it cannot exceed, but below that it takes exactly the value needed for equilibrium. See Static vs Kinetic Friction.
Why does pressing two surfaces harder increase the grip force?
Harder pressing flattens more asperities into contact, increasing real contact area, and friction scales with that real area — hence with . This is the microscopic origin of .
Why do we draw a free body diagram before both measurement methods?
To identify every force and choose axes so that "no motion perpendicular to the surface" cleanly gives , and the along-surface balance isolates friction — without it the cancellation of is easy to botch.
Why is usually larger than at the microscopic level?
At rest the bumps have time to settle and cold-weld into each other's valleys; once moving they skim across the tops without settling, so less force sustains the motion.
Why can't we ask "what is the coefficient of friction of ice?" as a standalone question?
Friction arises from the interaction of two surfaces, so a single surface has no by itself — the meltwater and adhesion depend on what ice slides against.
Edge cases
If the ramp angle equals the slip angle exactly, is the block moving?
No — it is at the verge of slipping. Static friction is maxed at and the block is in the last instant of equilibrium; any nudge starts motion.
What is the friction force on a block resting on a perfectly horizontal, undisturbed surface?
Exactly zero. There is no sideways driving force for static friction to oppose, so it supplies nothing despite .
For (idealised frictionless pair), what is the angle of repose?
There isn't one above ; the block cannot resist any tilt, so it slides for any . This is the degenerate limit of .
As (imagine perfect grip), what happens to ?
: the block would cling until the ramp is nearly vertical. blows up exactly as the angle approaches a right angle.
A block slides up a rough incline after being launched — which way does kinetic friction point?
Down the slope, opposing the upward motion. Kinetic friction always opposes the direction of sliding, so together with gravity's along-slope pull it strongly decelerates the block — see Inclined Plane Dynamics.
If an object is in free fall (no surface contact), what is and hence ?
Both zero — with no surface pressing, , so . No contact means no friction, regardless of .
At exactly the constant-velocity slide angle, what is the net force along the ramp?
Zero — constant velocity means , so , giving .
Recall One-line self-test before you leave
is a ratio, belongs to a pair, ignores apparent area and weight, static ≥ kinetic, and is on a ramp — not . If any of those surprised you, revisit that trap above.
Connections
- Parent topic — full derivations behind these traps.
- Static vs Kinetic Friction — the inequality vs equality distinction.
- Normal Force — why on inclines.
- Newton's Second Law — why constant velocity is required to read .
- Inclined Plane Dynamics — friction direction on ramps.
- Free Body Diagrams — the tool behind every setup.
- Lubrication & Tribology — how films cut .