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 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 forces acting on the passenger are the normal force (N) from the seat and the gravitational force (mg). The net force provides the centripetal force needed to move in a circle. Thus, $N + mg = \frac{mv^2}{r}$. Rearranging for N gives $N = \frac{mv^2}{r} - mg$. Substituting $m = 60.0 \, \text{kg}$, $v = 10 \, \text{m/s}$, $r = 30 \, \text{m}$, and $g = 9.8 \, \text{m/s}^2$, we get $N = \frac{60 \times 100}{30} - 60 \times 9.8 = 200 - 588 = -388 \, \text{N}$. The negative sign indicates the direction of the force, but we are interested in the magnitude, which is 388 N, rounded to 390 N for significant figures.

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