Question

A hot-air balloon is accelerating upward under the influence of two forces, its weight and the buoyant force. for simplicity, consider the weight to be only that of the hot air within the balloon, thus ignoring the balloon fabric and the basket. the hot air inside the balloon has a density of ρhot air = 0.93 kg/m3, and the density of the cool air outside is ρcool air = 1.29 kg/m3. what is the acceleration of the rising balloon?

Answer 1

Let V = the volume of the balloon
Force of gravity = V * ?hot * g downward
Buoyant force = V * ?cool * g upward
Net upward force F = V * ?cool * g - V * ?hot * g

F = V g (?cool - ?hot)

Mass of the balloon m = V ?hot

a = F/m = V g (?cool - ?hot)/(V ?hot)

a = g(?cool/?hot - 1)

a = 9.8(1.29/0.93 - 1)

a = 3.79 m/s^2

Answer is 3.79 m/s^2