centripetal motion and weightlessness

[Chocolatebear89]

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The effect of weightlessness can be produced by flying a plane in a circular arc (i.e. ascending then descending in a smooth motion). If the speed of the plane is constant at 100 m/s, what is the radius of the arc that must be flown?


1,000 m
10,000 m
100 m
1,500

 

[ilovemcat]

The effect of weightlessness can be produced by flying a plane in a circular arc (i.e. ascending then descending in a smooth motion). If the speed of the plane is constant at 100 m/s, what is the radius of the arc that must be flown?


1,000 m
10,000 m
100 m
1,500

Fnet = Gravitational Force + Centripetal Force

Gravitational Force = ma = 10m
where m is some mass
and 10 (m/s squared) = acceleration

Centripetal Force = mv2/r
where m is some mass
and v2/r = acceleration

In order to be "weightless," Gravitational Force and Centripetal Force must cancel out. Therefore:

10m = mv2/r (Cancel out mass)
10 = v2/r

Solve for radius:
R = v2/10

We're told velocity is 100m/s so v2 = 10,000m/s2
10,000m/s2 divided by 10 m/s2 = 1,000 m

So the Answer would be A.) 1,000 m.