A car travels around 200 m radius flat curve at 40 m/s at constant speed. What is the minimum static coefficient of friction which allows it to travel at this speed without sliding?
A)1.23
B)0.815
C)0.736
D)0.952
E)0.662

Question

Quizplus · Accepted Answer

The minimum static coefficient of friction can be calculated using the formula for centripetal force: $ f_s = \frac{v^2}{r} $, where $ v $ is the velocity and $ r $ is the radius. The frictional force must equal the centripetal force needed to keep the car on the curve, so $ \mu_s \cdot g = \frac{v^2}{r} $. Solving for $ \mu_s $, we get $ \mu_s = \frac{v^2}{g \cdot r} $. Substituting $ v = 40 \, \text{m/s} $, $ r = 200 \, \text{m} $, and $ g = 9.8 \, \text{m/s}^2 $, we find $ \mu_s \approx 0.815 $.

A Car Travels Around 200 M Radius Flat Curve at 40