Question

A circular race track of radius 300m is banked an angle of 15o. If the coefficient of friction between the wheel of the race car and the road is 0.2, what is the (a) optimum speed of the race car to avoid wear and tear on its tyres and (b) maximum permissible speed to avoid slipping.

Answer 1

Optimum speed = v₀ = [RgtanΘ]¹⁻₂

R= 300
theta = 15⁰
g= 10

so, v₀= √300 x 10 x tan 15
= 28.06 ms⁻²

2. max speed= Vm= √Rg  u+tan theta/ 1- utan theta
as u=0.2 

= √300 x 10  0.2+tan15/1- 0.2tan 15

= 38.13 ms⁻¹