How much volume should a balloon with hydrogen have to lift a person weighing 60 kg?

Given:

m = 60 kilograms – the mass of a person;

ro1 = 0.09 kg / m3 is the density of hydrogen;

ro2 = 1.29 kg / m3 – air density;

g = 10 Newton / kilogram – acceleration of gravity.

It is required to determine V (cubic meter) – what volume should be a balloon with hydrogen in order to lift a person of mass m.

In order for the ball to be able to lift a person, according to Newton’s first law, the equality must be fulfilled:

F1 + F2 = F3, where F1 is the force of gravity acting on a person, F2 is the force of gravity acting on a ball with hydrogen, F3 is the Archimedean force.

m * g + V * ro1 * g = V * ro2 * g;

m * g = V * ro2 * g – V * ro1 * g;

m = V * ro2 – V * ro1;

m = V * (ro2 – ro1);

V = m / (ro2 – ro1) = 60 / (1.29 – 0.09) = 60 / 1.2 = 50 m3.

Answer: the volume of the ball should be 50 m3.