How Much Weight Can a 20.0 m³ Meteorological Balloon Lift?

[chawki]

Homework Statement

A meteorological balloon has volume of 20.0 m3 and a weight of 10.5 kg (gas included).
The density of the air is 1.18 kg/m3 and acceleration of gravity 9.81 m/s2

Homework Equations

What amount of cargo in kg can the balloon lift?

The Attempt at a Solution

Can you please advise about the starting point, it has certainly something to do with the density of air.
I'm using the principle PV=nRT but it's not taking me any further

 

[gneill]

Think buoyancy.

 

[chawki]

you're explaining me something difficult with something more difficult...some laws would be nice.
I think that to be able to lift some weight, the density inside the balloon should be greater than the air density...but then ?

 

[gneill]

you're explaining me something difficult with something more difficult...some laws would be nice.
I think that to be able to lift some weight, the density inside the balloon should be greater than the air density...but then ?

If the density inside the balloon were greater than that of air, then the balloon would be heavier than air and it would fall to the ground.

This is a buoyancy problem. I'm afraid there's no escaping it! You'll need to review your notes or text on the subject.

The balloon's volume is displacing a certain weight of air, replacing it with its own (less dense) weight of gas + balloon.

 

[chawki]

yes i was wrong about the density inside the ballon...it should be less than air of course..we heat air inside the balloon so that the density decrease.
you know, it would be nice to see the solution or half of it and i will try to understand it by my own..it have always worked for me.
but thank you for your help.

 

[chawki]

can someone tell me how can we use buoyancy here.

 

[gneill]

Buoyancy force acts upwards. Buoyant force magnitude is equal to the weight of the fluid (air in this case) displaced by the object. Whatever force is left over after you've subtracted out the weight of the object is the "lift" -- the lifting force available.

 

[chawki]

the lift force is like buyancy force (in air)?

 

[gneill]

the lift force is like buyancy force (in air)?

No, lift is what's left of the buoyancy force once the weight (due to gravity) of the object is subtracted.

 

[chawki]

The buoyant force = g(mass of the gas + cargo weight)?

 

[gneill]

The buoyant force = g(mass of the gas + cargo weight)?

Well, the "mass of the gas" should include the mass of the balloon's fabric and any other hardware associated with it, but yes that is the idea. When the forces balance as you have written, that is the maximum cargo weight, and the balloon and cargo will just hover.

 

[chawki]

i really need to understand buoyancy well..the formula that i have written above..got it when googling about buoyancy..still don't understand it well.and if it is the same in all cases?
all i know so far is that if we contrast water with the case of air..i know that the volume of the balloon equal the volume of air displaced.
where all this will lead us?

 

[chawki]

(10.5+x)/20 = m_air/1.18 ?

 

[gneill]

i really need to understand buoyancy well..the formula that i have written above..got it when googling about buoyancy..still don't understand it well.and if it is the same in all cases?
all i know so far is that if we contrast water with the case of air..i know that the volume of the balloon equal the volume of air displaced.
where all this will lead us?

Hopefully it will lead you to a class or textbook covering the topic! This is probably not the best place to learn a subject from scratch.

To answer your query, yes, buoyancy works in the same fashion for gases and liquids; any time you've got a displaced medium and gravity (or bulk acceleration) working.

 

[gneill]

First calculate the weight of air that is displaced by the balloon.

 

[chawki]

(10.5+x)/20 = m_air/1.18 ?

I think my formula here is wrong

 

[chawki]

First calculate the weight of air that is displaced by the balloon.

how can we calculate that?

 

[chawki]

The weight of air that is displaced by the balloon is the same the weight of the ballon.
m*g=1.18*20*9.81=231.51N

 

[gneill]

Okay, make it simple. You have the volume. You have the density of air. What is the mass of air that is displaced?

 

[chawki]

please check post #18
and sorry for being slow to understand today

 

[gneill]

please check post #18
and sorry for being slow to understand today

No problem. Some people think I'm like that all the time (of course, it depends on the topic!).

Okay, so you've determined that displaced air is producing a buoyancy force Fb = 231.51N.

Subtract from that the weight of the balloon and gas inside and you get

Fb - 10.5kg * 9.8m/s^2 = 231.51N - 103.0N = 128.5 N

That is then the net upward force available for lifting cargo.

How much mass can you lift with that force?

 

[chawki]

why we don't go simply with the basic idea of The volume of balloon = the volume of air displaced
and then...20=(10.5+x)/1.18 and then we find x=13.1kg?

 

[chawki]

No problem. Some people think I'm like that all the time (of course, it depends on the topic!).

Okay, so you've determined that displaced air is producing a buoyancy force Fb = 231.51N.

Subtract from that the weight of the balloon and gas inside and you get

Fb - 10.5kg * 9.8m/s^2 = 231.51N - 103.0N = 128.5 N

That is then the net upward force available for lifting cargo.

How much mass can you lift with that force?

OUPSOUPSOUPS... that's 128.5/9.81=13.1kg too

 

[chawki]

Dear gneil
I go to sleep now..i have no idea how I'm thinking or how i think it in post 22
good night, i will continue this tomorrow

 

[gneill]

I went the long way around so that you could see that there are forces involved; The displaced medium (air in this case) results in a buoyant force (in Newtons) when there is a gravitational field involved. You will come across problems involving buoyancy where it is essential that you understand where the forces involved are coming from, and in what directions they act.

 

[chawki]

is buoyancy related to weight or volume?
in the case of a ship, what would be the condition for floating or sinking?

 

[gneill]

is buoyancy related to weight or volume?
in the case of a ship, what would be the condition for floating or sinking?

A ship floats because it displaces its own weight in water before it's completely submerged -- it sinks until the weight of water displaced is equal to the weight of the ship. If it didn't displace its own weight in water before it is completely submerged, then its weight would be greater than the maximum possible buoyant force for the ship (the weight of water corresponding to the entire volume of the ship), and it would sink.

 

[chawki]

Can you please write that mathemaically in equation

 

[chawki]

Can we use Newton's second law to find F_buoyancy?

m*g-F_buoyancy=0
F=m*g
F=density of air*volume of balloon*g
F=1.18*20*9,81
F=231.5N

 

[gneill]

See http://theory.uwinnipeg.ca/physics/fluids/node10.html" .

 

[chawki]

I am very confused...
WHAT is the general starting point in these situations (i mean floating,lifting)
The volume of the object = the volume of fluid displaced
OR
The weight of the object = the weight of fluid displaced

I mean what is the condition of (floating,lifting) from which we start soving the problem

 

[gneill]

I am very confused...
WHAT is the general starting point in these situations (i mean floating,lifting)
The volume of the object = the volume of fluid displaced
OR
The weight of the object = the weight of fluid displaced

I mean what is the condition of (floating,lifting) from which we start soving the problem

Where is the starting point of a circle?

You calculate all the parameters (weights, displaced volume, lift) from the given information and compare them to see what will happen, or determine what is needed in order to make what you want to happen, happen.

Sometimes problems will specify that an object is floating. Sometimes it's sunk. Sometimes it's sinking or rising at a particular rate. Sometimes you're asked to calculate weight, or lift, or density, or determine how far a given object extends into a given fluid when it floats, or how much it protrudes above the surface. Problem writers can be devious in how they provide the information you need in order to solve the problem.

In all cases you need to determine the forces acting and how they depend upon the densities and geometry of the things involved.

 

[chawki]

Okay, make it simple. You have the volume. You have the density of air. What is the mass of air that is displaced?

why it's not 10.5 kg as given

 

[gneill]

why it's not 10.5 kg as given

Because that is the mass of the balloon, not the mass of the air displaced by the balloon.

 

[chawki]

Because that is the mass of the balloon, not the mass of the air displaced by the balloon.

so the weight of the balloon is simply 10.5*9.81=103.005 N ?

 

[gneill]

so the weight of the balloon is simply 10.5*9.81=103.005 N ?

Yes, that is the weight of the balloon and the gas inside it if the buoyancy is ignored.

 

[chawki]

Yes, that is the weight of the balloon and the gas inside it if the buoyancy is ignored.

While the weight of the air displaced is 1.18*20*9.81=231.51 N ?

 

[gneill]

Yes.

You know, I think we went through all this before...

 

[chawki]

Yes.

You know, I think we went through all this before...

yes i know. just let me get it right and step by step because I'm confused about it...

we have the weight of the displaced air, and the weight of the ballon.
and by law,
The buoyant force= weight of the displaced air-weight of the balloon ?
The buoyant force= 231.51-103.005 = 128.505 N (that's the buoyant force for a balloon of 10.5kg with volume of 20m³ and under the density of 1.18kg/m³)

 

[gneill]

The buoyant force is the equal to the weight of the displaced air. Period.

The lift force is equal to the buoyant force minus the weight of the materials making up the balloon -- that is, it is the force available for lifting cargo (you don't count the balloon as cargo).

 

[chawki]

The buoyant force is the equal to the weight of the displaced air. Period.

The lift force is equal to the buoyant force minus the weight of the materials making up the balloon -- that is, it is the force available for lifting cargo (you don't count the balloon as cargo).

ok. so Fb=weight of the materials making up the balloon + weight of cargo ?
but what is the weight of the materials making up the balloon here

 

[gneill]

ok. so Fb=weight of the materials making up the balloon + weight of cargo ?

If the balloon is hovering and not accelerating either up or down, yes.

but what is the weight of the materials making up the balloon here

Read the original problem statement.

 

[chawki]

this is seriously word complications..that's when i get lost
in post#23 you said the buoyant force is 231.51 N
isn't 128.505 N ?

 

[gneill]

The buoyant force is the equal to the weight of the displaced air. Nothing else. It's the upward force due to the displacement of the air. It does not include any other forces (like weights, loads, other external forces).

 

[chawki]

the buoyant force is the equal to the weight of the displaced air. Nothing else. It's the upward force due to the displacement of the air. It does not include any other forces (like weights, loads, other external forces).

... ... ...

 

[chawki]

... ... ...

i think we are always supposed to calculate the buoyant force, and if:
the buoyant force = weight of displaced fluid-weight of the objcet
and if:
the buoyant force is = the weight of the displaced air

HOW CAN THESE EQUATIONS BE SAME?

 

[gneill]

Forces of interest:

1. Weight of balloon
2. Buoyant force
3. Weight of cargo

The lift is what remains of the buoyant force when the weight of the balloon is subtracted... it's the force available to lift the cargo. In this case it's equal to the weight of the cargo, since the problem specifies the maximum cargo.

Note that the balloon will not be able to rise with its cargo because there's no unbalanced lift force left over to provide for acceleration. This is a condition referred to as "neutral buoyancy", where an object will neither sink nor rise.

 

[gneill]

i think we are always supposed to calculate the buoyant force, and if:
the buoyant force = weight of displaced fluid-weight of the objcet
and if:
the buoyant force is = the weight of the displaced air

HOW CAN THESE EQUATIONS BE SAME?

Why do you want to say that the buoyant force is equal to the weight of the displaced fluid minus the weight of the object? It is not. You are confusing lift with buoyant force.

Now, read carefully: The buoyant force is equal to the weight of the displaced air.
That is it. That is all. Nothing else. No other interpretation. No other factors. End of story.

To find out how much cargo can be lifted, you take the buoyant force and subtract the weight of the balloon. Whatever force remains is available to lift cargo.

 

[chawki]

Forces of interest:

1. Weight of balloon
2. Buoyant force
3. Weight of cargo

The lift is what remains of the buoyant force when the weight of the balloon is subtracted... it's the force available to lift the cargo. In this case it's equal to the weight of the cargo, since the problem specifies the maximum cargo.

Note that the balloon will not be able to rise with its cargo because there's no unbalanced lift force left over to provide for acceleration. This is a condition referred to as "neutral buoyancy", where an object will neither sink nor rise.

Buoyancy force=weight of ballon+the weight of cargo(lift force) ?

 

[gneill]

Yes. That is the equation that describes the situation put forth in the problem statement. So you should be able to solve for the weight of the cargo, right?