# Homework Help: Density and Volume

1. Aug 8, 2010

### mizzy

1. The problem statement, all variables and given/known data
A balloon is to be filled with helium(density = 0.178kg/m^3) while the air outside has density of 1.29km/m^3. The mass of the empty balloon is 80.0kg 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.

2. Relevant equations

density = M/V

3. The attempt at a solution

2. Aug 8, 2010

### rl.bhat

The balloon will float when the weight of the displaced air is equal to the weight of the balloon with load.

Volume of the balloon = mass of the balloon/density of helium.

3. Aug 8, 2010

### mizzy

hmmm. not quite getting it.

This is archemides' principle right? so wouldn't the equation be:

density of balloon/ density of gas = volume of gas/ volume balloon??

4. Aug 8, 2010

### rl.bhat

Mass of the displaced air = Ma = (240 + 80 + VHe* ρHe) kg.

volume of the air = Ma/ρa = ...... = Volume of the balloon.

So Vb*ρa = (240 + 80 + VHe* ρHe) kg

Ηere volume of the balloon is equal to the volume of He.

5. Aug 8, 2010

### mizzy

k...just want to clarify. The balloon will float when the mass of the displaced air is equal to the weight of the balloon plus the load.

therefore,
Ma = (240 + 80)kg including helium??

how come is volume of air = volume of balloon?

sorry...a bit confused. I'm not great with this kind of physics.

6. Aug 9, 2010

### rl.bhat

(240 + 80)Kg is mass with out helium. Mass of the displaced air is equal to the (mass of helium + 240 + 80) kg. Balloon will float only when it is filled with the helium. Since the balloon material and the load occupy negligible volumes, volume of the helium = volume of the air.