Question

A car is travelling on a track which has radius of curvature $50\text{m}$. What is the maximum safe speed with which the car can travel on this track? Take $g=10{\text{m/s}}^2$. Assume coefficient of friction to be 0.8.

• A. $10\sqrt{3}\text{m/s}$
• B. $10\text{m/s}$
• C. $20\text{m/s}$
• D. $10\sqrt{5}\text{m/s}$

Answer 1

The correct option is C $20\text{m/s}$

In this case, the track is not banked, so component of normal is not available to support the requirement of centripetal force along the curve.
$\therefore$ The only reliability is on the frictional force between the track and wheels of car


Applying equation of circular dynamics on car:
$N=mg$ ......($i$) and
$f=\frac{m{v}^2}{r}$ .......($ii$)

Since we are asked for maximum safe velocity, we should consider limiting friction i.e $f_{max}=\mu N$ .....($iii$)

So, combining Eq.($i$), ($ii$), ($iii$):
$\frac{m{v}_{max}^2}{r}=\mu \times \left(mg\right)$
Putting $r=50\text{m}$,
$v_{max}=\sqrt{\mu gr}=\sqrt{0.8\times 10\times 50}=20\text{m/s}$