friction (static vs kinetic)

Question

A horizontal force just sufficient to start motion of a 20 kg crate on a rough floor is 60 N. Once in motion, a constant force of 50 N keeps it moving at constant velocity. The ratio of coefficients μ_s / μ_k is (g = 10 m/s²).

RankGuru · Accepted Answer

1. **Static Case (Impending Motion)**: The force needed to start motion equals the limiting static friction $f_{s(max)}$.
   - $f_{s(max)} = \mu_s N = \mu_s (mg)$
   - $60 = \mu_s (20 	imes 10) = 200 \mu_s \implies \mu_s = \frac{60}{200} = 0.30$.
2. **Kinetic Case (Constant Velocity)**: Net force is zero; applied force equals kinetic friction $f_k$.
   - $f_k = \mu_k N = \mu_k (mg)$
   - $50 = \mu_k (200) \implies \mu_k = \frac{50}{200} = 0.25$.
3. **Calculate Ratio**: 
   - $\frac{\mu_s}{\mu_k} = \frac{0.30}{0.25} = \frac{30}{25} = 1.20$.
4. **Physics Insight**: Static friction is typically higher than kinetic friction.

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friction (static vs kinetic)

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