Question

Car A uses tires for which the coefficient of static friction is 0.169 on a particular unbanked curve. The maximum speed at which the car can negotiate this curve is 23.7 m/s. Car B uses tires for which the coefficient of static friction is 0.826 on the same curve. What is the maximum speed at which car B can negotiate the curve?

Answer 1

Answer:

$v_B = 52.4 m/s$

Explanation:

For unbanked road the maximum friction force will provide centripetal force to the car.

So here we will have

$F_c = \frac{mv^2}{R}$

Since we know that centripetal force here is due to friction force

$F_c = F_f$

$\mu mg = \frac{mv^2}{R}$

now for two cars we will have

$\mu_A m_A g = \frac{m_A v_A^2}{R}$

also we have

$\mu_B m_B g = \frac{m_B v_B^2}{R}$

now by division of two equations

$\frac{\mu_A}{\mu_B} = \frac{v_A^2}{v_B^2}$

$\frac{0.169}{0.826} = \frac{23.7^2}{v_B^2}$

so we will have

$v_B = 52.4 m/s$