Fluids Question Regarding Density

[davidkis]

Homework Statement

A spherically shaped balloon has a radius of 11.5 m, and is filled with helium. How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 1200 kg?
Neglect the buoyant force on the cargo volume itself.

Homework Equations

Fb = (Mhe+800kg)g

The Attempt at a Solution

I used the above equation to determine the buoyant force acting on the balloon but didn't seem to work. I tried some other methods but i can't get how much it can lift. Need some explanation thanks.

 

[ideasrule]

What's the equation for the buoyant force on ANY object in ANY fluid? After getting that, draw a free-body diagram on the balloon and note that buoyancy must balance gravity if the balloon is to lift the heaviest possible load.

 

[davidkis]

still can't get it...seems like a easy question too.. i am setting Fb = 1200+m+g. I got force buoyant to be density of air (1.29 kg/m3) * Gravity * Volume. Which looks like 1.29*9.8*3583.477 = 1200+m+g. m is the mass of the cargo which i am solving for. i keep getting the mass of the cargo to be 3422.68 which is wrong. any ideas of where I'm messing up?

 

[ideasrule]

where did you get Fb=1200+m+g? It doesn't make sense because m has units of kg, while g has units of m/s^2.

Anyhow, draw a free-body diagram. Label all forces. Then write out Newton's second law. Don't take any shortcuts until you get more familiar with physics.