A car moving at a steady 10 m/s on a level highway encounters a bump that has a circular cross-section with a radius of 30 m.The car maintains its speed over the bump.What is the normal force exerted by the seat of the car on a 60.0-kg passenger when the car is at the top of the bump?
A)200 N
B)390 N
C)790 N
D)490 N
E)590 N

Question

Quizplus · Accepted Answer

At the top of the bump, the passenger is experiencing maximum apparent weight due to the normal force, which is equal to the sum of actual weight and the centripetal force required for circular motion. 
Using Newton's second law, 
Net force = mass x acceleration 
The only force acting in the vertical direction is the normal force. Therefore, 
Normal force - weight =  mv²/r 
where m is the mass of the passenger, v is the speed of the car, and r is the radius of the bump. 
Substituting the given values, 
Normal force - (60.0 kg)(9.81 m/s²) = (60.0 kg)(10 m/s)²/(30 m) 
Normal force = 390 N

A Car Moving at a Steady 10 M/s on a Level