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

`v_B = 52.4 m/s`

Step-by-step explanation:

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

So here we will have

`F_c = (mv^2)/(R)`

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

`F_c = F_f`

`\mu mg = (mv^2)/(R)`

now for two cars we will have

`\mu_A m_A g = (m_A v_A^2)/(R)`

also we have

`\mu_B m_B g = (m_B v_B^2)/(R)`

now by division of two equations

`(\mu_A)/(\mu_B) = (v_A^2)/(v_B^2)`

`(0.169)/(0.826) = (23.7^2)/(v_B^2)`

so we will have

`v_B = 52.4 m/s`