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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?

Respuesta :

Answer:

[tex]v_B = 52.4 m/s[/tex]

Explanation:

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

So here we will have

[tex]F_c = \frac{mv^2}{R}[/tex]

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

[tex]F_c = F_f[/tex]

[tex]\mu mg = \frac{mv^2}{R}[/tex]

now for two cars we will have

[tex]\mu_A m_A g = \frac{m_A v_A^2}{R}[/tex]

also we have

[tex]\mu_B m_B g = \frac{m_B v_B^2}{R}[/tex]

now by division of two equations

[tex]\frac{\mu_A}{\mu_B} = \frac{v_A^2}{v_B^2}[/tex]

[tex]\frac{0.169}{0.826} = \frac{23.7^2}{v_B^2}[/tex]

so we will have

[tex]v_B = 52.4 m/s[/tex]

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