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 normal 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

At the bottom of the depression, the centripetal force required to maintain the motion of the car is given by:

F_c = m*v^2/r

where m = mass of the car + passenger, v = speed of the car, and r = radius of the depression.

The weight of the passenger (mg) and the normal force exerted by the seat (N) add up to balance the force of gravity acting on the passenger:

mg + N = F_c + mg

Simplifying this expression and substituting the given values, we get:

N = m*g - F_c
N = (60.0 kg)*(9.81 m/s^2) - (60.0 kg)*(10.0 m/s)^2/(30.0 m)
N = 790 N

Therefore, the normal 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