Problem finding average density

[NeRdHeRd]

Homework Statement

Can anyone help me with this problem?

A balloon is released from a tall building. The total mass of the balloon including the enclosed gas is 2.0 kg. Its volume is 5.0 m^3. The density of air is 1.3 kg/m^3. What is the average density of the balloon?

2. The attempt at a solution

MY ATTEMPT:

density = mass/volume = 2/5 = .4 This is the density of the balloon and gas.

I'm tempted to leave this answer as it is but it just doesn't seem right.

I thought if I added the density of the air to the density of the balloon and then divided by two I would get and average.

EX. 1.3 + 0.4 = 1.7... 1.7/2 = 0.85 kg/m^3

Does this seem logical to you or are there some steps that I'm missing?

 

[JoAuSc]

I'm confused by the problem. "balloon" can either mean "rubber balloon + whatever's inside" or "rubber balloon". If the first definition is true, then your first answer of .4 kg/m^3 is correct.

If the second definition is true, you would find the mass of the air inside of a balloon of volume 5.0 m^3, assuming that the air inside the balloon has the same density as the air in the atmosphere. The problem is that then the air inside would seem to have more mass than both the air and the balloon together, which is nonsense.

In any event, you can't just add two quantities together and divide by two to get an average. That only works if you have two individual things. You would find the total mass of the system and the total volume of the system and divide one by the other.

 

[EnumaElish]

In any event, you can't just add two quantities together and divide by two to get an average. That only works if you have two individual things to be weighted equally in the averaging.

It is still possible to calculate a weighted average denstiy, as long as you weight each item with its share of the total volume.

 

[NeRdHeRd]

Unfortunately the problem does not state what type of gas is inside the balloon. But it does state that the total mass of the balloon and gas combined is 2.0 kg. I'm not sure if I should assume that the balloon is filled with air and not some other gas.

 

[EnumaElish]

I'd assume it's air, especially since the problem states its density.

 

[NeRdHeRd]

I'd assume it's air, especially since the problem states its density.

If that is the case then I'm completely confused. I guess since mass = density*volume the mass of the air inside the balloon would be 1.3 * 5 = 6.5 which is more than the combine mass of the air and balloon. I'M STUMPED!

 

[drpizza]

I think everyone's over-complicating this. You were correct the first time. Density = mass/volume. = .4kg/m^3.

The fact that you were given the density of air suggests to me that next, you're going to decide if this balloon will float away or sink to the ground. And, perhaps you'll also be asked to find the buoyant force and net force on the balloon.