Finding mass of cargo dropped from hot air balloon

[Mike13]

Homework Statement

Some hot air balloonists find themselves accelerating downward with acceleration a at a moment when the mass of the balloon plus the passengers and cargo is M. They want to accelerate upwards at the same rate, so they toss out some of the cargo mass m (and maybe one or two of the balloonists). Determine m.
[/B]

Homework Equations

F=ma[/B]

The Attempt at a Solution

Ok, so I think the force on the hot air balloon initially moving downward is either Ma or M(a+g). I thought it would just be the total mass times the acceleration given in the problem but gravity still has to be considered right? And once the cargo is thrown out the total mass will be (M-m). I guess I just don't know how to isolate m. This is a review question for my final exam and my professor doesn't give answers to anything. Any help would be greatly appreciated![/B]

 

[SteamKing]

Homework Statement

Some hot air balloonists find themselves accelerating downward with acceleration a at a moment when the mass of the balloon plus the passengers and cargo is M. They want to accelerate upwards at the same rate, so they toss out some of the cargo mass m (and maybe one or two of the balloonists). Determine m.
[/B]

Homework Equations

F=ma[/B]

The Attempt at a Solution

Ok, so I think the force on the hot air balloon initially moving downward is either Ma or M(a+g). I thought it would just be the total mass times the acceleration given in the problem but gravity still has to be considered right? And once the cargo is thrown out the total mass will be (M-m). I guess I just don't know how to isolate m. This is a review question for my final exam and my professor doesn't give answers to anything. Any help would be greatly appreciated![/B]

Balloons work on buoyancy, so what happens when the buoyant force of the balloon equals its total weight?

 

[Mike13]

Balloons work on buoyancy, so what happens when the buoyant force of the balloon equals its total weight?

Wow, buoyancy? I was way off. I'm guessing if the total weight equals the buoyant force then the balloon is stationary? So its total weight is Mg, which ill set equal to the buoyant force? Wouldn't I need to take into account the gas in the balloon?

 

[SteamKing]

Wow, buoyancy? I was way off. I'm guessing if the total weight equals the buoyant force then the balloon is stationary? So its total weight is Mg, which ill set equal to the buoyant force? Wouldn't I need to take into account the gas in the balloon?

M would include the mass of the balloon (the basket, the envelope containing the gas, the gas itself, the passengers, etc.) Given the amount of acceleration the balloon experiences when it starts to drop, the balloon possibly has sprung a leak or something, but it is not yet in free-fall.

 

[Mike13]

M would include the mass of the balloon (the basket, the envelope containing the gas, the gas itself, the passengers, etc.) Given the amount of acceleration the balloon experiences when it starts to drop, the balloon possibly has sprung a leak or something, but it is not yet in free-fall.

Got it. Ill see if I can work it out. Thanks for the reply!