friction on incline

Question

A 5 kg block rests on a rough incline of angle 30°. Coefficient of static friction is 0.4. Will the block remain at rest? (g = 10 m/s²)

RankGuru · Accepted Answer

1. **Resolve Weight Components**:
   - Component down-slope ($F_{\parallel}$) $= mg \sin 30^\circ = 5 	imes 10 	imes 0.5 = 25$ N.
   - Component normal to slope ($N$) $= mg \cos 30^\circ = 5 	imes 10 	imes \frac{\sqrt{3}}{2} \approx 43.3$ N.
2. **Limiting Static Friction ($f_{max}$)**:
   - $f_{max} = \mu_s N = 0.4 	imes 43.3 = 17.32$ N.
3. **Comparison**: The force trying to pull the block down ($25$ N) is greater than the maximum force friction can provide ($17.3$ N).
4. **Conclusion**: Since $F_{\parallel} > f_{max}$, the block cannot remain at rest and will **slide down**.

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friction on incline

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