# Archimedes's Principle

#### aud11888

i don't see how this question give enough information to answer it..

"A lighter than air balloon and its load of passengers and ballast are floating stationary above the Earth. Ballast is the weight that van be dropped over board to make the balloon rise. The radius of the balloon is 6.25m. Assuming the density of air to be 1.29kg/m^3, determine the weight that must be dropped overboard to make the balloon rise 105m in 15 secs."

so far i've determined the balloon has to rise at a rate of 7m/s to reach 105m in 15seconds. I was then going to use the Buoyancy formula to figure out how much force is pushing up on the balloon, but i don't understand how to do that because i don't have the volume of the balloon..

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#### iNCREDiBLE

aud11888 said:
i don't see how this question give enough information to answer it..

"A lighter than air balloon and its load of passengers and ballast are floating stationary above the Earth. Ballast is the weight that van be dropped over board to make the balloon rise. The radius of the balloon is 6.25m. Assuming the density of air to be 1.29kg/m^3, determine the weight that must be dropped overboard to make the balloon rise 105m in 15 secs."

so far i've determined the balloon has to rise at a rate of 7m/s to reach 105m in 15seconds. I was then going to use the Buoyancy formula to figure out how much force is pushing up on the balloon, but i don't understand how to do that because i don't have the volume of the balloon..
You know the radius of the balloon <=> you know the volume.

aud11888 said:
i don't see how this question give enough information to answer it..

"A lighter than air balloon and its load of passengers and ballast are floating stationary above the Earth. Ballast is the weight that van be dropped over board to make the balloon rise. The radius of the balloon is 6.25m. Assuming the density of air to be 1.29kg/m^3, determine the weight that must be dropped overboard to make the balloon rise 105m in 15 secs."

so far i've determined the balloon has to rise at a rate of 7m/s to reach 105m in 15seconds. I was then going to use the Buoyancy formula to figure out how much force is pushing up on the balloon, but i don't understand how to do that because i don't have the volume of the balloon..
you can find the volume of the balloon from the radius of the balloon.

...and isn't the balloon going to accelerate once you change its mass? the buoyant force is going to stay the same, as the density of air is going to be the same, and the volume of the balloon will be the same. but the weight of the whole rig has just decreased, so the buoyant force will be greater than the weight, causing a nonzero net force upward, which will cause an acceleration upward.

#### aud11888

i still don't understand how to caluculate how much weight i need to get rid of to make the balloon rise at a specific rate...

#### Doc Al

Mentor
aud11888 said:
so far i've determined the balloon has to rise at a rate of 7m/s to reach 105m in 15seconds.
What you need to find is the acceleration of the balloon, not the average speed. Then find the net force that would provide that acceleration.

#### zwtipp05

aud11888 said:
i still don't understand how to caluculate how much weight i need to get rid of to make the balloon rise at a specific rate...
You know the distance to be traveled and the time it must travel that distance. you begin at v=0. So 105 m = .5 a (15 s)^2

Find your acceleration and you can work from there to find the force needed to make the balloon rise at the rate you need it too.

#### aud11888

how am i suppose to relate acceleration to force?

#### HallsofIvy

Homework Helper
If you do not know F= ma then you shouldn't be attempting this problem!

HallsofIvy said:
If you do not know F= ma then you shouldn't be attempting this problem!
harsh but...yeah, pretty true.

i suspect that this is toward the end of a physics 1 course without calc...

you should really know newton's second law by now.

you did free body diagrams earlier, right? ...drawing those will help with this problem and... all sorts of others.

you'll need two pictures: one when the balloon was in equilibrium (and take into account the individual forces acting on it) and another when the balloon starts having a net force acting on it (recall what i put in my earlier post).

then using the definition of buoyant force and such, you should be able to get the answer.

keep in mind that the mass of the balloon (and the stuff attached to it) changed, which caused it to acclerate upwards!

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