How Much Helium Is Needed to Lift a 320kg Load?

[poloboy]

Homework Statement

A balloon is to be filled with helium (density 0.178 kg/m^3) while the air outside has density 1.29kg/m^3. the mass of the empty balloon is 80kg and it is to lift a load of 240kg
what minimum volume is necessary for the lift off? assume that the balloon material and the load occupy negligible volumes.

Homework Equations

i am assuming that we are using P = m / V
it gives us all the necessary units to plug into this formula but my question is how do u put the 2 densities together into the equation?

The Attempt at a Solution

i think I'm suppose to use the P=m/v formula but i haven't figured out how the 2 densities are to fit together. the m = 80+240 = 320kg. can anyone point me in the right direction please.

 

[anathema]

Dear forum post author,

Thank you for your question. To solve this problem, you will need to use the equation P = m/V, where P is the density, m is the mass, and V is the volume. In this case, you are trying to determine the minimum volume necessary for the balloon to lift off, so you will need to rearrange the equation to solve for V.

First, let's plug in the given values for the densities and the mass:

P = m/V
0.178 kg/m^3 = (80kg + 240kg)/V

Next, we can simplify the equation by adding the masses together:

0.178 kg/m^3 = 320kg/V

Now, we can rearrange the equation to solve for V:

V = 320kg / 0.178 kg/m^3

V = 1797.75 m^3

Therefore, the minimum volume necessary for the balloon to lift off is 1797.75 m^3. I hope this helps and good luck with your calculations!

 

[ogb p]

I would approach this problem by first understanding the concept of density. Density is a measure of how much mass is contained in a given volume. In this case, we have two different densities, one for helium and one for air. The density of helium is much lower than that of air, which is why it can cause lift when used in a balloon.

To solve this problem, we can use the equation P = m/V, where P is density, m is mass, and V is volume. We know the mass of the empty balloon (80kg) and the mass of the load (240kg), so we can calculate the total mass of the balloon and load (320kg). We also know the density of helium (0.178 kg/m^3) and the density of air (1.29 kg/m^3).

To find the minimum volume needed for lift off, we can set up the following equation:

1.29 kg/m^3 = (80 + 240) kg / V

Solving for V, we get V = 320 kg / 1.29 kg/m^3 = 248.06 m^3.

This means that the minimum volume needed for lift off is 248.06 m^3. Any volume less than this will not provide enough lift to lift the balloon and the load.

It is important to note that this calculation assumes that the balloon material and the load occupy negligible volumes, as stated in the problem. If this is not the case, the actual minimum volume needed may be slightly different.

In conclusion, by understanding the concept of density and using the appropriate equation, we can calculate the minimum volume needed for lift off in this scenario.