# Density Problem

## Homework Statement

A good estimate for the volume of a particular hot air balloon is 2800 m3. Suppose the total load (passengers, fuel, balloon fabric, etc.) on a hot air balloon is 724 kg. In preparing to launch, the pilot heats the air inside to an average temperature of 210 oC, giving it a density of 0.95 kg/m3 (compared to a density of 1.2 kg/m3 for the air outside the balloon). [Note! This means that the total mass of the hot air balloon is 724 kg plus the mass of the hot air in the balloon!]

How much extra mass does the pilot need to keep in the basket in order to stay on the ground while all passengers are on board?

## The Attempt at a Solution

I'm really lost here. Any help would be great.

well so you want the balloon to stay on the ground, in other words: zero velocity

this means that all the forces acting on the balloon need to sum up to be zero

there's only going to be two forces acting on the balloon. The force due to gravity acting on the total mass of the system and the buoyancy force due to the difference in the density of the air inside the balloon compared to outside

so obviously, as given in the problem, the 724 kg mass is not going to be enough to keep it down, so you need to add some other force to that to equal the buoyancy force

So...
-9.8(negative because pushing down)*724 + 9.8*___=0?

well, no, you need to account for the buoyancy force