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. Will the balloon rise, fall, or remain stationary; and why?
(A) The balloon will fall because the upward buoyant force is less than its weight.(B) The balloon will rise because the upward buoyant force is greater than its weight.(C) The balloon will fall because the downward buoyant force is greater than the upward buoyant force.(D) The balloon will fall because its density is greater than that of air.(E) The balloon will remain stationary because its density is less than that of air.

Answer 1

(B) The balloon will rise because the upward buoyant force is greater than its weight.

Explanation:

In order to evaluate what happens to the balloon, we need to compare the magnitude of the two forces acting on the balloon:

- Its weight, W, acting downward

- The buoyant force, B, acting upward

The weight of the balloon is given by:

$W=mg$

where

m = 2.0 kg is the mass of the balloon

$g=9.8 m/s^2$ is the acceleration of gravity

Substituting,

$W=(2.0)(9.8)=19.6 N$

The buoyant force on the balloon is given by:

$B=\rho V g$

where

$\rho = 1.3 kg/m^3$ is the air density

$V=5.0 m^3$ is the balloon's volume

$g=9.8 m/s^2$ is the acceleration of gravity

Substituting,

$B=(1.3)(5.0)(9.8)=63.7 N$

We observe that the buoyant force B is larger than the weight, so the balloon will accelerate upward, and the correct answer is

(B) The balloon will rise because the upward buoyant force is greater than its weight.

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