Friction

Static and kinetic friction

Narrated video. Transcript:

Try to push a heavy almirah across the floor. You push gently and nothing happens. Something is pushing back with exactly the same force.

That force is static friction. It acts along the surface of contact and opposes the motion that would happen without it.

Push a little harder: static friction grows to match. The applied force and the friction force grow together, always equal.

But static friction has a limit. Its maximum value is mu s times N, where N is the normal force and mu s is the coefficient of static friction.

So f s is less than or equal to mu s N. The limit depends on the two surfaces and on N, but not on the area of contact.

Push beyond the limit and the almirah starts to slide. Now kinetic friction acts: f k equals mu k times N.

Mu k is smaller than mu s. That is why it is hard to get something moving, but easier to keep it moving.

Watch the graph of friction against applied force: a straight rising line, a peak at mu s N, then a drop to a flat level at mu k N.

Slopes, rolling, and why friction helps

Narrated video. Transcript:

Put a block on a plank and slowly lift one end. For a while the block stays put. Static friction holds it.

Split the weight into two parts: m g sin theta along the slope, and m g cos theta into the slope. The normal force N equals m g cos theta.

Friction must balance m g sin theta. At the angle where the block just starts to slide, friction is at its limit: m g sin theta equals mu s m g cos theta.

Mass cancels, and tan theta equals mu s. This angle is the angle of repose. Measuring it is an easy way to find mu s.

Now roll a wheel instead. Ideally, the point touching the ground is momentarily at rest, so it does not slide. Rolling friction is much smaller than sliding friction.

That is why wheels, and ball bearings in machines, make moving loads so much easier. Lubricants like oil reduce friction too.

But friction is not always the enemy. To walk, your foot pushes back on the ground, and static friction pushes you forward.

A car’s tyres need friction to start, stop and turn. On an oily or icy road, with little friction, the wheels just spin.

Try it: block on an incline

Interactive simulation. Things to try:

• Raise the angle slowly. The block slides when mg sin θ becomes bigger than μs N.
• Compare that angle with the angle of repose readout, tan⁻¹ μs.
• Change the mass. Does the sliding angle change?
• Pick an angle between tan⁻¹ μk and tan⁻¹ μs, then give the block a nudge. Once it moves, it keeps sliding!

Quick check

A 2 kg box sits on a level floor with μs = 0.5. You push it sideways with a force of 6 N. What is the friction force on the box? (g = 9.8 m/s²)

1. 0 N
2. 3.8 N
3. 6 N
4. 9.8 N

Angle of repose

A block rests on a plank. The plank is tilted slowly until, at 15°, the block just begins to slide. What is the coefficient of static friction?

1. 0.26
2. 0.27
3. 0.97
4. It depends on the mass of the block

Summary

• Static friction: fs ≤ μs N
• Kinetic friction: fk = μk N (μk < μs)
• Angle of repose: tan θ = μs

• Static friction adjusts itself to stop sliding, up to a limit of μs N.
• Once sliding starts, kinetic friction μk N acts. It is smaller, so keeping an object moving is easier than starting it.
• Friction depends on the surfaces and the normal force, not on the area of contact.
• Rolling friction is much smaller than sliding friction. Friction also makes walking and driving possible.