A motorcycle is traveling at a constant speed v when it happens upon a circular

Question

A motorcycle is traveling at a constant speed v when it happens upon a circular hill of radius r = 320 m. The motorist and motorcycle collectively have mass m = 159 kg.

What speed in m/s does the motorcycle have if the motorist feels weightlessness (i.e., has an apparent weight of zero) at the top of the hill?

If the motorist is traveling at the speed above and happens upon a hill with a radius 2r, what is the apparent weight of both the motorist and the motorcycle in Newtons at the top of the hill?

Explanation / Answer

at the top of the hill, net acceleration=g-(v^2/R)

where R=radius

so to feel no net force,

g=v^2/R

v=56 m/s

b)net accelration downward=g-(v^2/(2*R))

=g/2=4.9 m/s^2

so apparent weight=159*4.9=779.1 N

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