Question

A vehicle driving at $54km/h$ can safely negotiate a curved road of $50m$ radius. If the road is unbanked, find the co-efficient of friction between the road surface and the tyres.

• A. $0.96$
  
• B. $0.459$
  
• C. $0.36$
  
• D. $0.75$
  

Answer 1

Answer: (B)

$0.459$

Given that $=50km/h=\frac{125}{9}m/s$ and $R=50m$

assume that mass of vehicle is $m$

as the diagram(FBD) shows, if vehicle driven on a curved unbanked road, the friction force towards the center balance out the centrifugal force, we get three equations from here

$N=mg...\left(1\right)f=\mu N...\left(2\right)f=m\frac{v^2}{R}...\left(3\right)$

putting the valur of $N$ in eqn$\left(2\right)$ and then putting the valur of $f$ in eqn$\left(3\right)$

$\Rightarrow \mu =\frac{v^2}{Rg}=\frac{(\frac{125}{9}{)}^2}{50\times 10}=0.459$