A 50 m3 balloon is filled with hot air with a density of 0.9 kg / m3. The density of the ambient air is 1.3 kg / m3

A 50 m3 balloon is filled with hot air with a density of 0.9 kg / m3. The density of the ambient air is 1.3 kg / m3. What is the maximum mass that the ball can lift if the mass of its shell is 8 kg?

To calculate the value of the maximum mass of the load lifted by a given balloon, we will use the equation: Fa = Fт; ρw * g * V = m * g = (mo + mw + mg) * g, whence we express: mg = ρw * V – mo – mw = ρw * V – mo – ρsh * V.

Constants and variables: ρv – the density of the ambient air (according to the condition ρv = 1.3 kg / m3); V is the volume of the ball (V = 50 m3); mo is the mass of the shell (mo = 8 kg); ρsh – air density in the ball (ρsh = 0.9 g / m3).

Let’s perform the calculation: mg = ρw * V – mo – ρsh * V = 1.3 * 50 – 8 – 0.9 * 50 = 12 kg.

Answer: The cargo will have a mass of 12 kg.