Section 2.7: Friction & Applications

Friction is the resistive force that opposes relative motion between surfaces in contact. It is essential in everyday life, from walking to driving vehicles.

Types of Friction:
  • Static friction: Prevents motion until the applied force exceeds a maximum value \( f_s \le \mu_s N \).
  • Kinetic friction: Acts on moving objects \( f_k = \mu_k N \).
  • Rolling friction: Opposes rolling motion, typically smaller than kinetic friction.

Calculating Frictional Forces

The general formula for friction:

  • Static: \( f_s \le \mu_s N \)
  • Kinetic: \( f_k = \mu_k N \)

Where \(N\) is the normal force and \(\mu\) is the coefficient of friction.

Example 1

A 10 kg block rests on a horizontal surface with \(\mu_s = 0.4\). What is the maximum static friction force?

\( N = mg = 10 \times 9.8 = 98 \text{ N} \)

\( f_s^{\max} = \mu_s N = 0.4 \times 98 \approx 39.2 \text{ N} \)

Example 2

A 5 kg block slides on a surface with \(\mu_k = 0.2\). Find the kinetic friction force.

\( N = mg = 5 \times 9.8 = 49 \text{ N} \)

\( f_k = \mu_k N = 0.2 \times 49 \approx 9.8 \text{ N} \)

Practice Problems

  1. A 15 kg crate rests on a horizontal surface with \(\mu_s = 0.5\) and \(\mu_k = 0.3\). Calculate the maximum static friction and kinetic friction if moving.
  2. A 20 N horizontal force is applied to a 4 kg block on a surface with \(\mu_s = 0.6\). Will it move? If yes, find kinetic friction using \(\mu_k = 0.4\).
  3. An object on an incline of 30° has \(\mu_s = 0.35\). Determine if it slides.
  4. Calculate friction force for a 12 kg block on a 25° incline with \(\mu_k = 0.2\).
  5. A 50 kg box is pushed with 300 N on a surface where \(\mu_s = 0.4\). Determine motion and friction forces.