Question

Consider the motion of a car around a banked curve. The angle of the bank with respect to the horizontal is 15.0 degrees, the speed of the car is 20.0 m/s, the radius of curvature for the curve is 30.0 m, and the coefficient of static friction is 0.500. The mass of the car is 1000 kg.

a) What is the frictional force?
b) Is there a speed at which the frictional force would be zero? If so, what is it?

c) What is the maximum speed of the car at which the car can take the curve without slipping?

Answer 1

(a) frictional force is given by

$f=\mu N=\mu *mgcos\theta$

$\Rightarrow f=0.500*1000*9.8*cos15.0^{\circ}$

$\Rightarrow f=4733.04N$

(b) In zero friction also, car can run on a banked road, and that speed is given by

$v=\sqrt{rgtan\theta }$

$\Rightarrow v=\sqrt{30.0*9.8*tan15.0^{\circ}}=8.88m/s$

(c) maximum speed of the car without slipping is

$v=\sqrt{rg\cdot \frac{\mu +tan\theta }{1-\mu tan\theta }}$

$\Rightarrow v=\sqrt{30.0*9.8\cdot \frac{0.5+tan15}{1-0.5*tan15}}=16.14m/s$