Friction force

Pull a cupboard gently: it does not move. Pull harder: it still stays put, then begins to slide. Why does friction initially seem to change with our pulling force? And why could we not walk normally without friction?

If the cupboard stays still under a horizontal pull, what balances that pull? The floor resists relative sliding between the surfaces in contact. This is static friction. With a small pull, its magnitude equals the pull and its direction is opposite. Increase the pull within a certain range and friction increases too. But this adjustment has a limit. Once the force needed for equilibrium exceeds that limit, sliding starts.

Imagine a perfectly slippery floor. Your foot tries to push backwards but slips, barely accelerating you forwards. On an ordinary floor, the foot does not slip while pushing off: it pushes the ground backwards, and static friction from the ground pushes the foot forwards. So ‘friction always opposes the object's motion’ is wrong. Ask how the contacting surfaces slide, or would tend to slide, relative to each other.

Now the cupboard slides right over a stationary floor. Kinetic friction from the floor acts left on the cupboard, opposing relative sliding; its magnitude is measured in newtons. But put a block on a belt moving right and slipping underneath it: friction can accelerate the block to the right. The direction depends on the relative motion of the surfaces, not merely on the block's velocity relative to the room.

Press a sliding eraser harder against the table: it usually becomes harder to pull. We describe the contact loading using the normal force N, the force the support exerts perpendicular to its surface. Here N denotes a force; its unit is the newton. On a horizontal table, with no other vertical forces or acceleration, N = mg. Extra downward pressure increases N. An inclined support or other actions require a separate force analysis.

Experiments with dry surfaces often give the approximate relation Fтр = μN for kinetic friction. The dimensionless coefficient μ depends on the pair of materials and their surface condition. At fixed μ, doubling N doubles friction; lowering μ reduces friction at the same contact loading. The formula separates two ways to change resistance: change the surfaces or how strongly they are pressed together. It is an experimental model, not an exact law for every contact and speed.

Does a block at rest with no horizontal action experience friction μN simply because it touches the table? No: there is no horizontal force to balance, and static friction can be zero. Here Fтр = μN applies to sliding. Apparent contact area does not enter this simple model directly: turning the block onto another face need not change friction at the same N and μ. Real surfaces can behave beyond this approximation.

Put a load on wheels instead of dragging it across the floor. Its whole underside no longer has to slide continuously, so transport is usually easier. However, the wheel and support deform slightly during rolling, and some of the energy spent is not returned to motion. This produces rolling resistance, usually smaller than kinetic friction under comparable conditions. Grip between wheel and road is still needed: without it, accelerating, braking and turning are difficult.

A box is sliding; N = 60 Н, μ = 0,25. Find the friction force.

Sliding is already occurring, so the model Fтр = μN applies.

Fтр = 0,25·60 Н = 15 Н. The coefficient is dimensionless, so the result is in newtons.

The force opposes the box's motion relative to the surface.

15 Н opposite to relative sliding.

Friction opposes relative sliding or the tendency to slide. It can accelerate an object.

Static friction adjusts to other forces up to a limit and can be zero.

Fтр = μN approximates dry sliding. First establish the type of contact and the normal force.

The same force has different effects over large and small areas. This leads us to pressure.