A flat (unbanked) curve on a highway has radius of $100 \mathrm{m}$. A car rounds the curve at a speed of $20 \mathrm{m}/\mathrm{s}$, what is the minimum coefficient of friction that will prevent sliding?

Given in the question:

• Radius of unbanked curve of highway$=\mathrm{R}=100 \mathrm{m}$
• Speed of car $={\mathrm{V}}_{\mathrm{C}}=20 \mathrm{m}/\mathrm{s}$

Let the coefficient of friction [minimum] that will prevent sliding be ${\mathrm{\mu }}_1$

Here, $\frac{{{\mathrm{Mv}}_{\mathrm{c}}}^2}{\mathrm{R}}=$centripetal force acting on car

${\mathrm{\mu }}_1\mathrm{Mg}=$frictional force acting on car

$\mathrm{M}=$mass of car

Now applying equation of equilibrium, we get:-

$$\begin{gathered} \frac{{\mathrm{MVc}}^2}{\mathrm{R}}={\mathrm{\mu }}_1\mathrm{Mg} \\ {\mathrm{\mu }}_1=\frac{{{\mathrm{V}}_{\mathrm{c}}}^2}{\mathrm{gR}} \\ {\mathrm{\mu }}_1=\frac{{(20 \mathrm{m}/\mathrm{s})}^2}{10\mathrm{m}/{\mathrm{s}}^2\times 100 \mathrm{m}} \\ {\mathrm{\mu }}_1=0.4 \end{gathered}$$