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Push a heavy almirah across the floor and you know the feeling: nothing, nothing, then it suddenly gives and becomes easier to keep moving. Before you read on, predict: if you pull a block with a force that rises slowly from zero, what happens to the friction on it?
What happens to friction as you slowly pull harder on a block?
While the block stays still, friction exactly matches your pull. Static friction acts between surfaces that are not moving relative to each other, and it can take any value up to a maximum: fs ≤ μsN, where N is the normal force (OpenStax University Physics Volume 1, section 6.2).
So if you pull with 2 N, friction is 2 N. Pull with 6 N, and friction is 6 N. On a graph of friction against applied force, this part is a straight line through the origin with slope 1. It ends at μsN, the limiting friction. Pull a little harder and the block slips. If you have wondered why the answer for a block at rest is not simply μN, our post on why static friction is often less than μN works through it.
Why does friction drop when the block starts to slide?
Once the block moves, kinetic friction takes over, with size fk = μkN, and for most surface pairs μk is smaller than μs (OpenStax, section 6.2). So friction falls the instant the block starts sliding. OpenStax also notes that at small but nonzero speeds, friction is nearly independent of speed. With N unchanged, kinetic friction stays at μkN however hard you pull, so the graph runs flat after the drop.
Georgia State University's HyperPhysics site puts the shape in two sentences: "Static friction resistance will match the applied force up until the threshold of motion. Then the kinetic frictional resistance stays about constant" (HyperPhysics, friction plot).
OpenStax's table gives typical pairs (OpenStax, section 6.2):
Wood on wood: μs = 0.5, μk = 0.3
Dry steel on steel: μs = 0.6, μk = 0.3
Rubber on dry concrete: μs = 1.0, μk = 0.7
These are rough values that change with the surfaces; HyperPhysics reports typical classroom results of 0.4 static and 0.3 kinetic for wooden blocks.
How do you plot friction against applied force?
Take a 2 kg wooden block on a wooden table, pulled horizontally, with OpenStax's wood-on-wood values μs = 0.5 and μk = 0.3 (OpenStax, section 6.2) and g = 9.8 m/s².
Normal force: the pull is horizontal, so N = mg = 2 × 9.8 = 19.6 N.
Limiting friction: μsN = 0.5 × 19.6 = 9.8 N.
Kinetic friction: μkN = 0.3 × 19.6 = 5.88 N, about 5.9 N.
Plot it: a line from (0, 0) to (9.8, 9.8), a vertical drop to 5.9 N, then a flat line.
Some points on the graph:
Pull 4 N: friction 4 N, at rest
Pull 9.8 N: friction 9.8 N, just about to slip
Pull 10 N: friction 5.9 N, sliding, net force 4.1 N, acceleration about 2.1 m/s²
Pull 12 N: friction 5.9 N, sliding, net force 6.1 N, acceleration about 3.1 m/s²
The drop is 9.8 − 5.9 = 3.9 N, which is (μs − μk)N. That is the almirah lurch: when it slips, the friction holding it back falls by that amount, but your push does not, so the difference becomes acceleration.
What mistakes do students make with this graph?
Writing f = μsN for a block at rest. That is only the ceiling; below it, friction equals the pull.
Drawing kinetic friction rising with the pull. In this model it stays at μkN.
Joining the two parts with a smooth curve instead of a drop.
Assuming N = mg when the pull is at an angle. An upward tilt takes some weight off the floor, so N and both friction limits get smaller.
The school practical on finding limiting friction against normal reaction lets you see the first part of this graph with your own numbers.
How can you see the drop for yourself?
Tie a string to a thick book, put a rubber band in the middle of the string, and pull very slowly along a table. The band stretches while the book sits still, then the book jerks forward and the band relaxes a little. That relaxing is the drop to kinetic friction.
If you would rather watch the idea move first, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than to read; write your prediction down before you press play. For practice, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
For where μ came from, read how Coulomb worked out the laws of friction.
