Question4. San Francisco has some pretty steep streets. Some of which have inclines of $25^{\circ}$. a. Draw a force diagram and obtain the $\Sigma \mathrm{F}$ equations for a car on such an incline. b. What static coefficient of friction is needed to prevent a car from sliding downhill? $\mathrm{FFS}_{\mathrm{F}}$

Studdy Solution
Calculate the static coefficient of friction ($\mu_s$):
The static frictional force is given by $f_s = \mu_s N$.
Substitute the expressions for $f_s$ and $N$: $$mg \sin \theta = \mu_s (mg \cos \theta)$$
Solve for $\mu_s$: $$\mu_s = \frac{mg \sin \theta}{mg \cos \theta} = \tan \theta$$
For $\theta = 25^\circ$: $$\mu_s = \tan 25^\circ$$
Calculate $\tan 25^\circ$ using a calculator: $$\mu_s \approx 0.466$$
The static coefficient of friction needed to prevent the car from sliding downhill is approximately:
$$\boxed{0.466}$$