kinetic friction

Question

A block slides down a rough inclined plane of angle 45° with constant velocity. What is the coefficient of kinetic friction?

RankGuru · Accepted Answer

1. **Constant Velocity Condition**: Net force along the incline must be zero.
2. **Driving Force**: Gravity's component down the slope, $F_d = mg \sin 	heta$.
3. **Resistive Force**: Kinetic friction opposite to motion, $f_k = \mu_k N = \mu_k mg \cos 	heta$.
4. **Equate**: $mg \sin 	heta = \mu_k mg \cos 	heta$.
5. **Simplify**: $\mu_k = \sin 	heta / \cos 	heta = 	an 	heta$.
6. **Evaluation**: $\mu_k = 	an 45^\circ = 1$.

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