Friction
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Direct answer
Friction is the tangential contact force opposing relative sliding, or the tendency of it, between two surfaces. Static friction self-adjusts to demand, up to the limit f(max) = mu_s N; once sliding starts, kinetic friction acts with the nearly fixed magnitude f_k = mu_k N, with mu_k usually slightly below mu_s. JEE answers turn on judging the direction of friction and on knowing which regime the body is in.
What you must remember
- Static friction is variable: f_s is at most mu_s N. Kinetic friction f_k = mu_k N is approximately independent of speed and apparent contact area.
- Angle of repose: the block just slides on an incline when tan(theta) = mu_s; this equals the angle of friction, tan^-1(mu).
- Block sliding down a rough incline: a = g(sin theta − mu cos theta); decelerating while moving up: a = g(sin theta + mu cos theta).
- Least force to move a block on a rough floor, applied at angle theta: F = mu mg/(cos theta + mu sin theta), minimum at theta = tan^-1(mu), where F(min) = mu mg/sqrt(1 + mu^2).
- Maximum speed on a level curve: v(max) = sqrt(mu r g); on a frictionless banked road tan(theta) = v^2/(r g).
- Static friction can do positive, negative or zero work: it accelerates a block on an accelerating plank, yet does no work on a body rolling without slipping on a fixed surface.
- mu can exceed 1; the coefficient is a ratio of forces with no upper bound.
Common confusion
The commonest error is writing friction = mu N automatically. That equality holds only at limiting equilibrium or during sliding; otherwise friction is an unknown found from the equations of motion. The second error is direction: friction opposes relative slipping at the contact, not necessarily the body's motion — ground friction propels a car's driven wheel forward, and friction acts up the incline on a body rolling down it.
Exam-focused takeaway
JEE Main asks numerical-value questions on incline acceleration, the least pulling force at the optimum angle, connected blocks on rough surfaces and v(max) on curves. JEE Advanced prefers stacked blocks (which pair slips first?), friction on rolling bodies, pseudo-force analysis in accelerating frames, and cases where friction must first be tested against the static limit before sliding is assumed. Draw the free-body diagram, assume a friction direction, and let the algebra correct you.
Frequently asked questions
Does friction always oppose a body's motion?
No. It opposes relative sliding at the contact; friction from the ground is what accelerates a car's driven wheel and lets us walk forward.
Why does pulling at an angle reduce the force needed?
The upward pull component reduces the normal reaction and hence the limiting friction; the optimum angle is tan^-1(mu).
What is the angle of repose?
The least inclination at which a block starts sliding, given by tan(theta) = mu_s; it equals the angle of friction.
Can the coefficient of friction exceed one?
Yes — mu is a ratio of forces, not bounded by unity, and rubber on dry track exceeds 1.
Why is kinetic friction independent of the apparent contact area?
Real contact occurs only at tiny asperities: widening the area lowers the pressure per asperity, and the two effects cancel, leaving f_k = mu_k N.
Is the work of friction always negative?
No — static friction can do positive work (a block on an accelerating plank), while sliding friction on the sliding body is negative and dissipates energy as heat.