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

Question

Quizplus · Accepted Answer

The force exerted by the seat of the car on the passenger is the normal force, which is equal to the weight of the passenger plus the centripetal force required to keep the passenger moving in a circle. The centripetal force is given by:$$F_c = mv^2/r$$where:* m is the mass of the passenger* v is the speed of the car* r is the radius of the circular pathIn this case, the mass of the passenger is 60.0 kg, the speed of the car is 10 m/s, and the radius of the circular path is 30 m. Therefore, the centripetal force is:$$F_c = (60.0 kg)(10 m/s)^2/30 m = 200 N$$The normal force is equal to the weight of the passenger plus the centripetal force, which is:$$F_n = mg + F_c = (60.0 kg)(9.8 m/s^2) + 200 N = 790 N$$Therefore, the force exerted by the seat of the car on the passenger is 790 N.

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