A car travels down a straight country road that leads over hills and through val

Question

A car travels down a straight country road that leads over hills and through valleys. On one particular stretch of road, the car encounters a hill that can be approximated as the top of a circle with a radius of 109 m. Later, the car comes to a dip with a radius of curvature of 85 m. Assume that the car maintains a constant speed of v=23 m/s as it goes over the hill and through the dip. The actual weight of the driver, as measured on a flat stretch of road, is 755 N.

A) What is the apparent weight of the driver at the top of the hill?

B) What is the apparent weight of the driver at the bottom of the dip?

Explanation / Answer

At the top of the hill,

N = mg + mv^2/r = 755/9.81 * (9.81 + 529/109) = 1128.51 N (ans)

At the bottom of hill,

N = mg - mv^2/r = 755/9.81 * (9.81 - 529/85) = 276.02 N (ans)

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