Fluids - floating balloon problem

In summary, the conversation discusses a physics problem involving a helium-filled balloon and the maximum weight it can lift. The person is having trouble getting the exact answer and is seeking help with their equations. They provide their work and ask for assistance in finding the mistake. The conversation ends with a suggestion to double-check the value used for the density of air.
  • #1
Neuronic
3
0
Hi - I know this must be a basic question, but I'm doing this physics problem and I can't get the exact answer!

Here it is and my work along with it - can someone please tell me what I'm missing in my equations?

The problem is taken from the James Walker physics book - Chapter 15. Number 29.

A 0.12 kg balloon is filled with helium (density = .179 kg/m-cubed).
The balloon is a sphere with radius of 5.2 m. What is the maximum
weight the baloon can lift?

I keep getting something close to 6.4 kN, whereas the book says 5.7 kN.

My work:

volume of baloon (which is actually the volume of helium) = 4/3 pi
r-cubed = 588.9 m-cubed

bouyance force lifts the balloon upward, while the weight of the
balloon, the weight of the helium and the weight of the unknown weight
(ex. block) counteracts the bouyance force.

Bouyance force = (density of air) (g) (V) = (1.29) (9.8) (588.9) =
7453 N (upward force)

Weight total = weight of baloon material + (density of helium) (g) (V)
+ unknown weight = (.12)(9.81) + (.179)(9.81)(588.9) + unknown weight
= bouyance force

this would make the unknown weight = 6.4 kN

Not 5.7 kN


Please someone help? Thanks a bunch!
 
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  • #2
Your work looks OK to me. Double-check the value you are using for the density of air, since that depends on the assumed temperature and pressure.
 
  • #3
thanks a bunch!
 

1. What causes a balloon to float in the air?

The principle of buoyancy, which states that an object will float if it displaces an amount of fluid that weighs more than the object itself, is what causes a balloon to float in the air. In the case of a balloon, the gas inside the balloon is less dense than the surrounding air, causing it to rise.

2. How does the size of a balloon affect its ability to float?

The size of a balloon does not affect its ability to float as long as the amount of gas inside the balloon remains the same. However, a larger balloon may be able to displace more air and therefore, can hold more gas, allowing it to float for a longer period of time.

3. Does the type of gas inside a balloon affect its ability to float?

Yes, the type of gas inside a balloon does affect its ability to float. Helium, which is less dense than air, is commonly used to fill balloons and is the reason why they float. Other gases, such as hydrogen, can also be used but are less commonly used due to their flammable nature.

4. Can a balloon float in any type of fluid?

Technically, a balloon can float in any type of fluid as long as the amount of fluid it displaces weighs more than the balloon itself. However, due to the density of different fluids, a balloon may only float in certain types of fluids such as air or helium.

5. Why does a balloon eventually fall back down to the ground?

A balloon eventually falls back down to the ground due to a decrease in the upward force of buoyancy. As the gas inside the balloon escapes into the surrounding air, the density of the balloon increases and it becomes heavier than the air around it, causing it to no longer float and fall back down to the ground.

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