Question

Car A uses tires for which the coefficient of static friction is 0.330 on a particular unbanked curve. The maximum speed at which the car can negotiate this curve is 17.0 m/s. Car B uses tires for which the coefficient of static friction is 0.632 on the same curve. What is the maximum speed at which car B can negotiate the curve?

Answer 1

To maintain a circle, the friction force must equal the centripetal force, or

u*m*g=mv^2/r, where u*m*g is the frictional force, mv^2/r is the centripetal force.

Solving for v,

v^2=u*r*g

So (v_1)^2=u_1*r*g, (v_2)^2=u_2*r*g, so

(v_2)^2/(v_1)^2=u_2/u_1 -> (v_2)^2=(u_2/u_1)*(v_1)^2

-> (v_2)=sqrt(u_2/u_1)*v_1

In your case,

v_2=sqrt(0.632/ 0.330)*17.0 m/s=23.526m