Question

A car moves on a horizontal track of radius r, the speed increasing constantly at rate dv/dt = a. The coefficient of friction between road and tyre is μ. Find the speed at which the car will skid.

• A. $\left\lbrack \left( \mu^{2}g^{2} + a^{2} \right)r^{2} \right\rbrack^{1/4}$
• B. $\sqrt{\mu gr}$
• C. $\left\lbrack \left( \mu^{2}g^{2} - a^{2} \right)r^{2} \right\rbrack^{1/4}$
• D. $\sqrt{ar}$

Answer 1

Answer: (C)

$\left\lbrack \left( \mu^{2}g^{2} - a^{2} \right)r^{2} \right\rbrack^{1/4}$

Answer 2

net acceleration is $\sqrt{a^{2} + \left( \frac{v^{2}}{r} \right)^{2}} \geq \mu g$ or

$\left( \frac{v^{2}}{r} \right)^{2}$ = μ²g² – a² or v = $\left\lbrack \left( \mu^{2}g^{2} - a^{2} \right)r^{2} \right\rbrack^{1/4}$.