Physics · Laws of Motion · Chapter notes
Friction and Block Systems · Class 11 Notes
Class 11 notes on friction and block systems: the friction graph, the rough incline, blocks on blocks, pulleys and constraints, built to JEE Advanced depth. Free to read or download.
In short
Friction is the force students guess at. The fix is a test you can run every time: work out how much friction the situation needs, then compare it with the most that is available, which is μN. If the need is smaller, friction supplies exactly the need and nothing slips. If it is larger, the surfaces slide.
Contents
- ·How to Read This
- 1What Friction Actually Does static against kinetic
- 2The Friction Graph one picture for the whole chapter
- 3The Rough Incline three cases, one geometry
- 4Blocks on Blocks which surface slips first
- 5The Slip Test the algorithm that never fails
- 6Pulleys and Constraints when strings join the blocks
- ★Friction and Block Systems · Fact Sheet
How to Read This
- Friction sits in Laws of Motion, and it feeds Circular Motion and Work and Energy later.
- Blue marks a defining fact. Red marks a trap.
- Almost every mistake in this chapter comes from assuming a block moves when it does not, or assuming it does not when it does.
- Never write f = μN straight away.
- μN is the maximum friction available, not the friction acting.
- First find how much friction the situation needs.
- Only if that exceeds μN does anything slide.
What Friction Actually Does
- Friction opposes relative sliding between two surfaces in contact.
- Static friction acts when there is no sliding yet. It adjusts itself to match the applied force.
- Kinetic friction acts once sliding has begun. It is roughly constant.
- μ(k) is slightly less than μ(s), which is why a heavy box lurches forward once it finally moves.
- Friction does not depend on the area of contact, and it does not depend on speed.
The Friction Graph
f(static) ≤ μ(s)N and f(kinetic) = μ(k)N
Note the inequality on the first one. That is the whole point.
- Push a wall gently. Friction equals your push, which is nowhere near μN.
- μ(s)N is only the ceiling, reached at the instant of slipping.
- This is called limiting friction.
- Writing f = μN for a stationary block is the single commonest error in mechanics.
The Rough Incline
- Perpendicular: N = mg cosθ. Along the slope: the driving force is mg sinθ.
- If mg sinθ is less than μ(s)mg cosθ, the block stays put and friction equals mg sinθ.
- The steepest angle at which it still holds is the angle of repose, where tanθ = μ(s).
- Sliding down: a = g(sinθ − μcosθ). Pushed up: a = g(sinθ + μcosθ).
- The mass cancels in both, so a heavy block and a light block slide the same way.
Blocks on Blocks
- Push the lower block and friction has to drag the upper one along. F(max) = (M + m)μg.
- Push the upper block and friction is the only thing moving the lower one.
- The two answers are not the same, and questions are built on exactly that asymmetry.
- Always ask which block the applied force touches, before writing anything.
The Slip Test
- Assuming they slip when they do not gives a wrong acceleration for both blocks.
- Assuming they stay together when they slip gives a friction larger than physically possible.
- The test costs one line and removes the guess entirely.
- If they do slip, the top block gets a = μg and the bottom takes whatever is left.
Pulleys and Constraints
- A light string over a smooth pulley has the same tension throughout.
- An inextensible string forces the two blocks to share one magnitude of acceleration.
- A movable pulley has two string segments holding the load, so the upward force on it is 2F.
- That also halves the distance moved, which is why the work done comes out the same.
- For a hanging mass driving a block on a table: a = mg / (M + m), and T = Ma.
★ Friction and Block Systems · Fact Sheet
Every rule for revision day.
THE TWO LIMITS
f(static) ≤ μ(s)Nf(kinetic) = μ(k)N
μ(k) is slightly smaller.
THE BIG TRAP
Static friction is NOT μN.μN is only the ceiling,
reached at slipping.
ON AN INCLINE
N = mg cosθdriving force mg sinθ
mass always cancels.
ANGLE OF REPOSE
tan θ = μ(s)the steepest angle at which
the block still holds.
SLIDING DOWN
a = g(sinθ − μcosθ)Pushed up:
a = g(sinθ + μcosθ).
STACKED BLOCKS
Push lower: F = (M+m)μgPush upper: F = (M+m)μmg/M
Not the same answer.
THE SLIP TEST
1 assume together2 find friction needed
3 compare with μN.
IF THEY SLIP
Top block: a = μgBottom block takes the rest.
MOVABLE PULLEY
Two segments hold the load,so upward force is 2F
but distance is halved.
Before the exam
What the paper actually asks from this chapter
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