Question

A road is being designed for vehicles to travel at $80km/h$. The coefficient of friction between the road surface and the tyres is $0.2$. What should be the radius of an unbanked level turn on the road for vehicles to move without skidding? (in m)

• A. $251.90$
  
• B. $236.3$
  
• C. $215.3$
  
• D. $218.6$
  

Answer 1

The correct option is A $251.90$

Given that $v=80km/h=22.22m/s$ and $\mu =0.2$

assume that mass of vehicle is $m$

as the diagram(FBD) shows, if centrifugal acceleration $a_c$ applying on cycle is less than acceleration $a_f$ due to static friction then the cyclist will not slip down while taking turn

$N=mg...\left(1\right)f=\mu N...\left(2\right)$

from above two equations

$\Rightarrow f=\mu mg=2m$

$\Rightarrow a_f=\frac{f}{m}=\frac{2m}{m}=2m/s^2$

and $\Rightarrow F=m\frac{v^2}{R}$

$\Rightarrow a_c=\frac{F}{m}=\frac{\left(\frac{m{v}^2}{R}\right)}{m}=\frac{v^2}{R}=\frac{{22.22}^2}{R}m/s^2=\frac{493.9}{R}m/s^2$

if$a_c$$\le$$a_f$ so the cyclist will not slip down

$\Rightarrow \frac{493.9}{R}\le 2\Rightarrow R\ge 246.95mtr$

so the answer should be $\left(A\right)$