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
- 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.
- 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 \(\mu_k = 0.4\).
- An object on an incline of 30° has \(\mu_s = 0.35\). Determine if it slides.
- Calculate friction force for a 12 kg block on a 25° incline with \(\mu_k = 0.2\).
- A 50 kg box is pushed with 300 N on a surface where \(\mu_s = 0.4\). Determine motion and friction forces.