Calculate Volume of Balloon to Lift 3670 kg Package

  • Thread starter DDS
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In summary: You can divide g out of the equation to make the numbers easier to work with.Da*V = Dh*V + Mb +McNow, solve for V.V = Mb/(Da-Dh) + Mc/(Da-Dh) + Ma/(Da-Dh)You already know the values for Mb, Mc, and Da. You calculated Da correctly in your last post. You will need to calculate the mass of helium, Mh = Dh*V, using the density of helium you were given. Use the formula for density to find the volume of helium needed to lift the weight of the helium.Remember, the volume of helium is the same as the volume of air needed to lift the same
  • #1
DDS
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A 576 kg weather balloon is designed to lift a 3670 kg package. What volume should the balloon have after being inflated with helium at standard temperature and pressure in order that the total load can be lifted?

Am i missing something or is there more to this question there , there seems.

The balloon with a certain mass wants to lift an iditional mass therefore the combinded mass of the baloon is 4246 Kg

The dnesity of Helium at STP is 0.18 kg/m^3

and the relationship describing density is :

D=M/V rearrange for volume and and get Volume= mass/ density

V=4246 kg/ 0.18kg/m^3
V=23588.89 m^3 which is wrong...what am i missing here??
 
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  • #2
DDS said:
A 576 kg weather balloon is designed to lift a 3670 kg package. What volume should the balloon have after being inflated with helium at standard temperature and pressure in order that the total load can be lifted?

Am i missing something or is there more to this question there , there seems.

The balloon with a certain mass wants to lift an iditional mass therefore the combinded mass of the baloon is 4246 Kg

The dnesity of Helium at STP is 0.18 kg/m^3

and the relationship describing density is :

D=M/V rearrange for volume and and get Volume= mass/ density

V=4246 kg/ 0.18kg/m^3
V=23588.89 m^3 which is wrong...what am i missing here??

Your are missing Archimedes' Principle. The buoyant force on the balloon is equal to the weight of air that is displaced by the balloon.
 
  • #3
so the weight of the air displaced is equal to the weight of the balloon correct?

so

w=mg
w=5650.56 N

then i add this to the weight of my cargo load and divid over the density of helium??

which gives me

wc=mg
wc=(3670)(9.81)
wc=36002.7

36002.7 + 5650.56 = 41653.26

v=m/d
v=41653.26/0.18
v=231407 m^3??
 
  • #4
DDS said:
so the weight of the air displaced is equal to the weight of the balloon correct?

so

w=mg
w=5650.56 N

then i add this to the weight of my cargo load and divid over the density of helium??

which gives me

wc=mg
wc=(3670)(9.81)
wc=36002.7

36002.7 + 5650.56 = 41653.26

v=m/d
v=41653.26/0.18
v=231407 m^3??

41653.26 Newtons is the combined weight of the balloon and cargo. That is all you have so far. It is not a mass. You need to work on being consistent about dimensions, so that you don't do things like use a weight in a place where you need mass.

Use the weight you have calculated to continue the problem. You are going to fill a balloon with helium to displace the amount of air needed to lift the balloon. When you do this, don't forget that the helium in the balloon has weight of its own that must be lifted by the buoyant force. Once you correctly figure out the weight of the displaced air, you need to find the mass of the air before you calculate its volume.
 
  • #5
wow that just confused me because it seems like i have to find some many weights of so many things and I am only given two masses and a density of helium...is there any way to be more specifc with that i have to do... i learn and grasp things better via formula description
 
  • #6
This is what i have so far:

Wc=36002.7
Wb=5650.56
Wt=41653.26

Dhe=0.180

Fb= D*V*G
fb=(1000)(0.180)(9.81)
Fb=Whe=1765.8

now i believe that the weight of air is the sum of all my weight thus

Wa=43419.06


thus the mass of air is 43419.06/9.81=m
m=4426

v=m/d
4426/0.180
v=24588.89

please tell me I am right
 
  • #7
DDS said:
This is what i have so far:

Wc=36002.7
Wb=5650.56
Wt=41653.26

Dhe=0.180

Fb= D*V*G
fb=(1000)(0.180)(9.81)
Fb=Whe=1765.8

now i believe that the weight of air is the sum of all my weight thus

Wa=43419.06


thus the mass of air is 43419.06/9.81=m
m=4426

v=m/d
4426/0.180
v=24588.89

please tell me I am right

More dimensional inconsistencies

0.18 is a density, not a volume. You don't know the volume of the helium until the problem is solved.

Downward forces:
Weight of balloon [Newtons] Mb*g
Weight of cargo [Newtons] Mc*g
Weight of helium [Newtons] Mh*g = Dh*V*g

Upward forces:
Weight of displaced air [Newtons] Ma*g = Da*V*g

V is the same for the air and the helium

Upward forces must be the same magnitude as the downward forces. You will need to find the density of air at standard temperature and pressure. It depends on humidity, but you can assume dry air.
 
  • #8
its 1.28 kg/m^3 but what do i do what that
 
  • #9
would it be:

Vhe= Total mass/(Pair-PHe)
V=4246/1.1
v=4162.74
 
  • #10
DDS said:
its 1.28 kg/m^3

would it be:

Vhe= Total mass/(Pair-PHe)
V=4246/1.1
v=4162.74

My last post gives you everything you need to write an equation
Weight of balloon [Newtons] Mb*g
Weight of cargo [Newtons] Mc*g
Weight of helium [Newtons] Mh*g = Dh*V*g

Upward forces:
Weight of displaced air [Newtons] Ma*g = Da*V*g

V is the same for the air and the helium
Da*V*g = Dh*V*g + Mb*g + Mc*g

You now know every quantity in the equation except for V. Solve the equation for V. Notice that g is common to every term.
 

1. How can the volume of a balloon be calculated to lift a 3670 kg package?

To calculate the volume of a balloon needed to lift a 3670 kg package, you will need to use the formula: volume = weight of package / weight of air displaced. This will give you the minimum volume required for the balloon to lift the package.

2. What factors affect the volume of a balloon needed for lifting?

The volume of a balloon needed for lifting is affected by several factors, including the weight of the package, the weight of the air displaced by the balloon, the type of gas used to fill the balloon, and the altitude at which the balloon will be flying.

3. How do I determine the weight of air displaced by a balloon?

The weight of air displaced by a balloon can be determined by multiplying the density of air (approximately 1.2 kg/m³) by the volume of the balloon. This will give you the weight of the air that the balloon will displace when fully inflated.

4. Can the volume of a balloon be adjusted to lift heavier packages?

Yes, the volume of a balloon can be adjusted to lift heavier packages by either increasing the size of the balloon or using a gas with a lower density. However, it is important to note that there are limitations to how much weight a balloon can lift depending on its design and the environmental conditions.

5. Are there any safety considerations when calculating the volume of a balloon for lifting?

Yes, there are safety considerations when calculating the volume of a balloon for lifting. It is important to make sure that the balloon is properly designed and inflated to prevent any accidents. Additionally, the weight of the package should not exceed the lifting capacity of the balloon to ensure safe and successful flight.

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