First the balloon is held fastened to the ground and the internal air is heated to steady-state temperature of θ3 = 110° C.

Question

Consider a hot-air balloon (open to atmosphere) with volume VB = 1.1 m3 . The mass of the balloon envelope, whose volume is to be neglected in comparison to VB, is m = 0.187 kg. The balloon shall be started, where the external air temperature is θ1= 20° C and the normal external air pressure is P0 = 1.013 × 105 Pa. Under these conditions the density of air is ρ1 = 1.2 kg/ m3.

First the balloon is held fastened to the ground and the internal air is heated to steady-state temperature of θ3= 110° C. The balloon is fastened with a rope. Find the tension in the rope.

Answer 1

The tension (FB) in the rope is the difference between the buoyant force FA and the weight force FG.

FB = VB ρ1 .g -(VB 3 + m) g

It follows with ρ3.T3 = T3 = ρ1 .T1

So, block will not move so total distance travelled = 2 + 1 = 3m.