Friction, drag and terminal velocity

Friction is a force that acts against motion when surfaces rub together. Air resistance and water resistance (drag) act against things moving through fluids, and they grow as speed increases. That is why falling objects reach a terminal velocity, and why stopping distances get much longer at high speed.

Key facts

  • Friction always acts opposite to the direction of motion (or attempted motion).
  • Friction is useful for grip and brakes, but wastes energy as heat in machines; lubricants reduce it.
  • Drag (air or water resistance) increases with speed; streamlined shapes reduce it.
  • Terminal velocity: drag has grown to equal weight, so the resultant force is zero and speed is steady.
  • Coefficient of friction: F = μN, so on flat ground the friction force is μmg.
  • Drag is roughly proportional to v² at high speed: double the speed, four times the drag.

Worked examples

Example 1

A toy car rolls 140 cm on lino but only 85 cm on carpet. How much further does it go on lino, and which surface has more friction?

  1. Mark how far the car went on each surface.
  2. Find the difference. 140 − 85 = 55 cm
  3. The carpet stopped the car sooner, so it has more friction.

Answer: 55 cm further; the carpet has more friction

Example 2

A 30 kg crate is pushed at a steady speed with a force of 120 N. What is the friction force?

  1. Steady speed means no resultant force: the forces are balanced.
  2. Friction acts backwards along the floor and is exactly as big as the push. friction = 120 N

Answer: 120 N, backwards

Example 3

An 80 kg skydiver feels 500 N of air resistance. Find her acceleration. (g = 9.8 N/kg)

  1. Her weight acts downwards. W = 80 × 9.8 = 784 N
  2. The forces are unbalanced: find the resultant. 784 − 500 = 284 N downwards
  3. Divide by the mass. a = 284 ÷ 80 = 3.55 m/s²

Answer: 3.55 m/s² downwards

Example 4

A car at 20 m/s brakes on a wet road with μ = 0.4. Find its braking distance. (g = 9.8 m/s²)

  1. Friction μmg = ma, so the mass cancels: a = μg. a = 0.4 × 9.8 = 3.92 m/s²
  2. Use v² = u² + 2as with v = 0. s = 20² ÷ (2 × 3.92) = 51 m

Answer: 51 m