A car moving at a constant speed goes around a curve of 400-ft radius and then goes around a second curve of 200-ft radius.The centripetal force acting on the car as it goes around the 200-ft radius curve is ___________ the value of the centripetal force acting on the car as it goes around the 400-ft radius curve.
A)one quarter
B)one half
C)the same as
D)twice
E)four times

Question

Quizplus · Accepted Answer

The centripetal force is directly proportional to the square of the velocity and inversely proportional to the radius of the curve. At a constant speed, the velocity will be the same for both curves. Therefore, the centripetal force will be inversely proportional to the radius. The centripetal force is proportional to 1/radius². So, the ratio of the forces will be (1/400²)/(1/200²), which simplifies to 1/4 or 0.25. This means that the force on the 200-ft radius curve is four times greater than the force on the 400-ft radius curve, or twice as much as in answer choice D. However, since this question asks for the ratio between them, the best choice is D.

A Car Moving at a Constant Speed Goes Around a Curve