Buoyancy Question

[HopefulOncoDoc]

Hey guys, could someone please explain the reasoning behind this answer? Thanks!

To lift a 2000 kg load with a hot-air balloon rather than a helium-filled balloon, what changes to the balloon system should be made?

A. More ballast should be used in the hot-air balloon, since air is less dense than helium at the same temperature.
B. The volume of the hot-air balloon should be bigger, since air is more dense than helium at the same temperature.
C. A balloon with a smaller volume should be used, since air is more dense than helium at the same temperature.
D. No changes need to be made, since equal moles of air and helium occupy the same volume at the same temperature and pressure.

The answer is B. I understand that air is more dense than helium at the same temperature, but I can't seem to understand why a larger volume would be needed. Thanks.

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[billw]

The buoyant force is related to the volume of air displaced. You need to displace a little more air in order to compensate for the weight of the air that now fills the balloon. When the balloon was filled with helium, you did not need to displace as much air to counteract the force of gravity on the helium.

 

[BerkReviewTeach]

Hey guys, could someone please explain the reasoning behind this answer? Thanks!

To lift a 2000 kg load with a hot-air balloon rather than a helium-filled balloon, what changes to the balloon system should be made?

A. More ballast should be used in the hot-air balloon, since air is less dense than helium at the same temperature.
B. The volume of the hot-air balloon should be bigger, since air is more dense than helium at the same temperature.
C. A balloon with a smaller volume should be used, since air is more dense than helium at the same temperature.
D. No changes need to be made, since equal moles of air and helium occupy the same volume at the same temperature and pressure.

The answer is B. I understand that air is more dense than helium at the same temperature, but I can't seem to understand why a larger volume would be needed. Thanks.

To lift off from the ground, the balloon must accelerate upwards. This means that the force up should exceed the force down ever so slightly. The force down is the combined weight of the balloon, cargo, an ballast. By using hot-air, which is denser than helium, the system is heavier with the hot-air than helium. This means that the hot-air balloon requires a greater buoyant force in order to achieve liftoff than the lighter helium-filled balloon. The buoyant force is:

Fbuoyant = rhosurrounding air x g x Vballoon

The density of the surrounding air and the gravitational force constants can't be changed, so the only factor you can control is the volume of the balloon. In order to increase the buoyancy, the volume of the balloon must increase until the buoyant force once again exceeds the weight.

You could have also gotten the answer by POE. Choice A is factually wrong. Choice C is not a good choice, because a smaller volume would reduce the buoyant force, which is the opposite of what is needed to lift a heavier balloon system. Choice D is one of those tempting statements that is true, but completely irrelevent. Ideally the two gases occupy the same volume, but the question centers around forces and not the ideal gas law.

 

[jpatel]

A simple asnwer to this would be:


you want something less dense than air if your going to float the balloon

Lets say we pump the balloon with helium.
Helium is less dense, so it will float.

Now we pump air with the same balloon. But it will not float because air is not less dense than air.

Therefore, you must heat air to make it less dense and therefore, you must increase volume.

Ez as cake