Answer to Question #300123 in Physics for roy

Question

 A 1,000 kg car rounds a curve on a flat road of radius 50 meters at a speed of 50km/hour. Will the car follow the curve or will it skid? Assume a) the pavement is dry and the coefficient of static friction is u=0.60; b) the pavement is icy, coefficient of friction is u=0.25?

Answer 1

Given:

$R=50\:\rm m$

$v=50\:\rm km/hr=13.9\: m/s$

The maximum speed of the car to follow the curve satisfies an equation

$$\frac{mv_{\max}^2}{R}=\mu mg$$

or

$$v_{\max}=\sqrt{\mu g R}$$

(a)

$$v_{\max}=\sqrt{0.60*9.8*50}=17.1\:\rm m/s>13.9\: m/s$$

Hence, the car will follow the curve.

(b)

$$v_{\max}=\sqrt{0.25*9.8*50}=11.1\:\rm m/s<13.9\: m/s$$

Hence, the car will skid the curve.