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 ñhot air = 0.93 kg/m3, and the density of the cool air outside is ñcool air = 1.29 kg/m3. What is the acceleration of the rising balloon?

Answer 1

Ignore mass of balloon and basket.

Consider 1 m^3 of hot air:
mass, m = 0.93 kg
net upward force, F
=(1.29-0.93)=0.36 kg
= 9.81*0.36 N
=3.53 N
acceleration
= F/m
= 3.53/0.93 m/s²
= 3.8 m/s²

Note: At this acceleration, air resistance is significant.

Answer 2

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