Air Lift

Calculating upward lift force on a hot air balloon?

A hot-air balloon consists of a basket, one passenger, and some cargo. Let the total mass be Mg. Even though there is an upward lift force on the balloon, the balloon is initially accelerating downward at a rate of g/3.

Find the upward lift L.
What fraction of weight must be dropped to make the balloon accelerate upward at a rate of g/2?

∑F = ma

F_up – W_baloon = m a

F_up – Mg = M (-⅓ g)

F_up = ⅔ Mg

∑F = ma

F_up – W_baloon’ = m a’

⅔ Mg – M’g = M (½ g)

M’ = (1/6)M

conclusion : (5/6) M must be dropped

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