Driving in your car with a constant speed of 12 m / s , you encounter a bump in

Question

Driving in your car with a constant speed of 12 m/s, you encounter a bump in the road that has a circular cross-section as indicated in the figure.

If the radius of curvature of the bump is 35 m, find the apparent weight of a 68-kg person in your car as you pass over the top of the bump.

Driving in your car with a constant speed of 12 m/s, you encounter a bump in the road that has a circular cross-section as indicated in the figure. If the radius of curvature of the bump is 35 m, find the apparent weight of a 68-kg person in your car as you pass over the top of the bump.

Explanation / Answer

While the car is driving on the bump, a centripetal acceleration acts toward the center of the radius of curvature. Take the direction toward the center as positive, this is also the direction of the weight of the person. The apparent weight of the person will be equal to the normal force. From Newton's 2nd law:

?F(c) = ma(c) = mg - n
n = mg - ma(c)

But a(c), centripetal acceleration, is equal to v

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