The Hills Motorway in Sydney 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 force on B is half the force on A.

Both cars experience a centripetal force while turning, which is provided by the frictional force between the tires and the road. The centripetal force is given by F = mv²/r, where m is the mass of the car, v is the speed, and r is the radius of the curve. Since the radius for the inside of the curve is half the radius for the outside, the centripetal forces required for cars A and B are different.

Let's say car A is turning with a radius of r/2 and car B is turning with a radius of r. Since they are traveling at the same speed, the centripetal forces required for them are:

FA = mv²/(r/2) = 2mv²/r
FB = mv²/r

Therefore, FA is twice as large as FB. However, the force of friction between the tires and the road provides the centripetal force for both cars, so the force on B must be twice the force on A to keep them both on the road. Therefore, the correct statement is:

The force on B is half the force on A.

The Hills Motorway in Sydney Has a Number of Lanes