Calculate Volume of Cargo Lifter for 160t Load | Cargolift Problem

[robax25]

Homework Statement

A cargo lifter needs to carry 160t and if the density of gas is 0.6125kg/m³. what is the volume of the Cargo lifter?

Homework Equations

F=ρ*Vc*g
ρ=density of the gas
Vc=Volume of the cargo lifter
F=1569600N/m²

The Attempt at a Solution

Vb=261224.4898 m³
I think my solution is wrong because it is too large.

 

[berkeman]

What's a cargo lifter? Like a balloon or something?

 

[robax25]

balloon

 

[haruspex]

I think my solution is wrong because it is too large.

Not only that, what would happen to your solution if the density were higher? Does that make sense?

 

[robax25]

if density is higher, my solution would decrease.

 

[haruspex]

if density is higher, my solution would decrease.

Right, whereas a denser gas will give you less lift, so you need more of it.
Another hint: what you have actually calculated is the volume of a vacuum needed to lift the cargo if the Earth's atmosphere were to consist of this gas.

 

[robax25]

yes, but it is too large.Is it possible to make in real?

 

[haruspex]

yes, but it is too large.Is it possible to make in real?

I get the feeling you have not understood the question. The gas is to go inside the balloon. What will be outside? Why will there be any lift?

 

[robax25]

Sorry I understand it fully.If you make such a big Vacuum Ballon, it is costly.

 

[jbriggs444]

Sorry I understand it fully.If you make such a big Vacuum Ballon, it is costly.

It is still not clear that you have understood the difficulty. If you filled a 260000 cubic meter balloon with lead (11340 kg/m³, how much payload could it lift?

See also lead balloon and Hindenburg (500,000 m³ of hydrogen for 500 tons lift).

 

[haruspex]

Sorry I understand it fully.If you make such a big Vacuum Ballon, it is costly.

We are not making a vacuum balloon, but your calculation in post #1 is exactly as though that is what we are doing.
Please answer my questions in post #8.

 

[robax25]

there is lift because the gas is less denser than air. It goes up automatically because gravity don't hold the gas.If you are talking about outside, ´The whole system works following pascal law.

 

[haruspex]

there is lift because the gas is less denser than air.

Yes.

It goes up automatically because gravity don't hold the gas

Gravity acts to pull the gas down, just like it does any other mass. But it pulls the air which would occupy the same space harder.
Use Archimedes' principle.