A car travels on a road that, if viewed from the side, has a semicircular dip. When at the bottom of the dip, the occupants of the car feel as though they weigh twice their normal weight. What is the radius of the semicircle if the speed of the car is 27 m/s?
A) 37 m
B) 132 m
C) 149 m
D) 74 m

Question

Quizplus · Accepted Answer

We can use the formula for centripetal force:

F = (mv^2)/r

At the bottom of the dip, the normal force and the gravitational force both act on the occupants of the car, so we can set up the equation:

2mg = (mv^2)/r

Simplifying, we get:

r = (2mv^2)/g

Plugging in the given values, we get:

r = (2 x 1000 kg x (27 m/s)^2)/9.81 m/s^2

r = 74 m

Therefore, the radius of the semicircle is 74 m. Answer choice D is correct.

A Car Travels on a Road That, If Viewed from the Side