Chapter 20, Problem 31A

A helium-filled balloon pulls upward on its string. Your friend says the upward force is evidence that atmospheric pressure is greater at the bottom of the balloon than on the top. Another friend says such a small difference in altitude wouldn’t make a difference in atmospheric pressure. They both look to you for an answer. What do you tell them?

To determine

To Explain: A helium filled balloon pulls upward on its string.

Explanation of Solution

Introduction:

An object will rise up if the upward force is greater than the downward gravitational force. On other hand, it will sink if the downward force is greater than the upward force.

Helium is much lighter than air. It has a density of about 0.17 g per L, whereas air has density of about 1 g per L. So, the buoyant force acting on the helium filled balloon is more than the weight of the balloon itself. Buoyant force acts upward while weight acts downward.

Buoyant force = mass of air displaced $\times$ gravity

Weight = mass of helium balloon $\times$ gravity

It means “mass of air displaced” should be greater than the “mass of helium balloon” for it to float in air.

Now, mass = volume $\times$ density

Since whole helium balloon is inside the air, volume of air displaced is equal to the volume of balloon itself. It implies the volume effect is same for both masses.

Now, as the density of air is much greater than the density of helium, it gives mass of air displaced greater than the mass of helium balloon which means the buoyant force is larger.

Conclusion:

A helium filled balloon rises up in air because of larger buoyant force than its weight.