Question

A balloon is released from a tall building. The total mass of the balloon including the enclosed gas is 2.0 kg. Its volume is 5.0 m3. The density of air is 1.3 kg/m3

Answer 1

Answer on Question #42610, Physics, Mechanics | Kinematics | Dynamics

Conditions:

1) A balloon is released from a tall building. The total mass of the balloon including the enclosed gas is $m = 2.0 \, \text{kg}$ . Its volume is $V = 5.0 \, \text{m}^3$ . The density of air is $\rho = 1.3 \, \text{kg/m}^3$ .

The most probable questions: what the resulting force acting on the balloon $(F = ?)$ ; what acceleration has the balloon without extra weight $(a = ?)$ ; what maximum weight can be carried by the balloon $(M_{\text{max}} = ?)$ .

Solution:

The balloon will hill his own weight $(m * g)$ and a force due to Archimedes' principle

$$F _ {a r c h} = \rho * V * g;$$

Resulting force: $F = F_{arch} - mg = \rho * V * g - mg = (\rho * V - m) * g = 45 \, N$ ;

The acceleration of the balloon has up direction: $ma = F$ ; $a = F / m = 22.5 \, m / s$ .

Maximum weight that can be carried with the balloon: $M_{\text{max}} = F / g = 4.5 \, \text{kg}$ .

Answer: $F = 45 \, N$ ; $a = 22.5 \, m/s$ ; $M_{\text{max}} = 4.5 \, kg$ .

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