## Related questions with answers

Question

The coefficient of static friction between the tires of a car and a dry road is $0.62$. The mass of the car is $1500$ kg. What max- imum braking force is obtainable $(a)$ on a level road and $(b)$ on an $8.6\degree$ downgrade?

Solution

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1 of 3$\textbf{(a)}$ The maximum braking force is equal to the maximum static friction force. The latter is given by Eq. 5-7:

$\begin{align*} F_{\text{braking}}=f_{s,max}=\mu_s N=\mu_s mg \end{align*}$

where we have substituted $N=mg$ since the road is level.

Inserting the numbers we get

$\begin{align*} &~ F_{\text{braking}}=0.62\cdot (1500\mathrm{~kg}) \left( 9.81\mathrm{~\frac{m}{s^2}} \right) \\ \implies &\boxed{F_{\text{braking}}=9123 \mathrm{~N}} \end{align*}$

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