## If a feather is dropped from a height, would its apparent weight be equal to its true weight or zero as in weightlessness.?

Question

I understand that the drag force acting on the feather would be abundant so it would reach terminal velocity soon and thus a = 0

So, apparent weight = m(g-a) = true weight.

But what bothers me is don’t all bodies accelerate with 9.8 m/s^2? So would the feather have acceleration 0 or 9.8?

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General Physics
2 years
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## Answer ( 1 )

In a gas, where there can be a terminal velocity, the drag is equal but opposite to the weight when the acceleration is zero.

So we can write D = kv^2 = mg = W which give us v = sqrt(mg/k) for the terminal speed. k = 1/2 rho Cd X where rho is air density, Cd is drag coefficient, and X is X-sectional area.

We note that the weight W = mg is still the weight. By definition, weight is the force of gravity. But the net force f = ma = W – D = 0, which means a = 0 which is why we are at the so-called terminal speed.

So there you are. The mass, m, has zero acceleration. If that mass is the mass of a feather, the feather has zero acceleration. It is, after all, the mass that’s falling at the constant speed called terminal velocity.