A split highway has a number of lanes for traffic. For traffic going in one direction, the radius for the inside of the curve is half the radius for the outside. One car, car A, travels on the inside while another car of equal mass, car B, travels at equal speed on the outside of the curve. Which statement about resultant forces on the cars is correct?
A) The force on A is half the force on B.
B) The force on B is half the force on A.
C) The force on A is four times the force on B.
D) The force on B is four times the force on A.
E) There is no net resultant force on either as long as they stay on the road while turning.

Question

Quizplus · Accepted Answer

The centripetal force required to keep a car moving in a circle is given by the formula $F = \frac{mv^2}{r}$, where $m$ is the mass of the car, $v$ is the velocity, and $r$ is the radius of the circle. Since both cars have the same mass and are traveling at the same speed, but car A is on a path with half the radius of car B, the force on car A is twice as much as the force on car B. This is because the force is inversely proportional to the radius.

A Split Highway Has a Number of Lanes for Traffic