Here is the question I am stuck on:
A plane is to perform the top part of a vertical loop at a speed of 2.50x10^2 m/s. What radius arc must the plane make in order to give the passengers the sensation of weightlessness at the top of the loop?
If the plane makes an arc with a radius of 8.00x10^3m what is the reaction force from the plane onto a 75.0kg passenger when the plane is at the very top of the loop?
For the first question, would weightlessness be reached when mg=mv^2/r or when mg is greater than mv^2/r?
Any help is appreciated!
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Verified answer
a) Weightlessness is reached when g = v² / r.
g = 9.8m/s² = v² / r = (250m/s)² / r → r = 6380 m
b) LESS than the radius found above, so the reaction force would have to come from the seat belt (or the canopy). a = (250m/s)² / 8000m = 7.8 m/s², so that reaction force is
F = m(g - a) = 75kg * 2m/s² = 150 N (up)