Question

Suppose a highway curve is properly banked to eliminate friction for a speed of 45 mph. If your tires were bald and you wanted to avoid sliding on the road, you would have to drive:

a) at exactly 45 mph.
b) somewhat above 45 mph
c) somewhat below 45 mph.

Answer 1

Answer:

a) at exactly 45 mph.

Explanation:

When road is banked at the given angle then the force equations for the car is given as

in vertical direction

$F_n cos\theta = mg$

In horizontal direction

$F_n sin\theta = \frac{mv^2}{R}$

so we have

$\frac{F_n sin\theta}{F_n cos\theta} = \frac{mv^2/R}{mg}$

now we have

$v^2 = Rg tan\theta$

so here we have all values are constant for a given speed

so the correct answer will be

a) at exactly 45 mph.