Question

What is the maximum speed, in meters per second, at which a 1100 kg rubber-tired car can navigate a concrete highway curve of 70 meters radius, banked at an angle of 30 degrees, considering a rainy day with a coefficient of static friction s = 0.3?

A) 13.7 m/s
B) 15.6 m/s
C) 18.3 m/s
D) 21.1 m/s

Answer 1

The maximum speed at which the car can navigate the curve is 15.6 m/s.

Step-by-step explanation:

To calculate the maximum speed at which the car can navigate the curve, we need to consider the forces acting on the car. The centripetal force required to keep the car moving in a curve is provided by the static friction between the tires and the road. The maximum friction force is given by the formula:

fmax = μs × m × g

where μs is the coefficient of static friction, m is the mass of the car, and g is acceleration due to gravity. The maximum speed can be calculated using the formula:

vmax = √(fmax ÷ (m × r))

where r is the radius of the curve.

Plugging in the values given in the question, we get:

vmax = √((0.3 × 1100 × 9.8) ÷ (1100 × 70))

vmax = 15.6 m/s