6. a car of mass m travels along the semicircular hills of radii r. the car maintains a constant speed v as it drives. find an expression for the normal force on the car at the bottom of the hill and at the top of the hill.

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smecloudbird17 smecloudbird17 · Answer 1 · 2022-08-28T07:51:16-04:00

The force pointing towards the center of the circle (i.e. down) is

Fnet = W – N = mg – N

The maximum value this can have occurs when N = 0, in which case for circular

motion we have

Fnet = mg – 0 = mg

so since the car is moving in a circle,

Fnet = mg = mv2/r

Hence the maximum speed is given when the force is this maximum:

v2 = gr

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