Section 2.2: Friction
This section covers friction, the resistive force that opposes relative motion between surfaces. We discuss static and kinetic friction and how to calculate them.
Key Formulas:
- Static friction: \( f_s \le \mu_s F_N \)
- Kinetic friction: \( f_k = \mu_k F_N \)
- \( F_N \) is the normal force between surfaces.
- Static friction adjusts to match applied force up to maximum \( f_s^{max} = \mu_s F_N \).
Example 1
A 10 kg block rests on a horizontal surface with µ_s = 0.4 and µ_k = 0.3. Determine the maximum static friction.
F_N = mg = 10*9.8 = 98 N
Maximum static friction: f_s(max) = µ_s F_N = 0.4*98 = 39.2 N
Example 2
The same block is pushed with a 50 N force. Determine acceleration if it moves (kinetic friction applies).
F_k = µ_k F_N = 0.3*98 ≈ 29.4 N
Net force: F_net = 50 – 29.4 ≈ 20.6 N
Acceleration: a = F_net/m = 20.6/10 ≈ 2.06 m/s²
Practice Problems
- A 15 kg block on horizontal table, µ_s = 0.5, µ_k = 0.4. Compute max static friction and acceleration if pushed by 80 N.
- Block of 8 kg on 30° incline, µ_s = 0.3, µ_k = 0.2. Find f_s(max) and f_k.
- A 10 kg crate on frictionless surface is pulled with 25 N. Find acceleration.
- Compare static and kinetic friction for a block on a slope of 25° with µ_s = 0.4 and µ_k = 0.3.
- A 5 kg box on horizontal floor, horizontal push 20 N, µ_s = 0.3, µ_k = 0.2. Determine if it moves and acceleration if it does.