Solving Newtons Law Problem for Hot Air Balloon Mass of Ballast

[Ballox]

Homework Statement

A hot - air balloon experiences an acceleration of 1.10 m/s^2 [down]. The total mass of the balloon, the basket, and the contents of the basket is 315 kg.

The balloonist wishes to change the acceleration to zero. There is no fuel left to heat the air in the balloon. Determine the mass of the ballast that must be discarded overboard. [NEGLECT AIR RESISTANCE]

Homework Equations

Newtons second law equation : F = mA

Free body diagrams are also important

The Attempt at a Solution

I drew a free body diagram for the hot air balloon and I noticed there were two forces: The force of gravity and the upward (buoyant) force on the system. I calculated the upward force on the system to be approximately 2.7 * 10^3 N [up].

However I'm totally stuck on what to do next.
Please help and many thanks in advance!

 

[collinsmark]

Hello Ballox,

Welcome to Physics Forums!

I assume you know the gravitational force is equal to mg. The goal is to set the gravitational force equal to the buoyant force. "g" isn't about to change any time soon, so...

 

[benhou]

I am not sure how buoyant forces work. Does this buoyant change when force of gravity changes? If so, what is the formula for buoyant force?

 

[Ballox]

Hello Ballox,

Welcome to Physics Forums!

I assume you know the gravitational force is equal to mg. The goal is to set the gravitational force equal to the buoyant force. "g" isn't about to change any time soon, so...

So setting the gravitational force equal to the buoyant force would be:

mG = 2.7 * 10^3 N [up] ( I rounded this, it really should be around 2740.5 N)

Which we would solve for m as : 279.6 kg.

But this gives us the mass when when the gravitational force is equal to the buoyant force...so we have to subtract this mass from the mass of the entire system to determine the amount of mass that must be discarded overboard.

So I get :

315 KG - 279.6KG ~ 35 kg.

^
So I get the answer in the textbook! ^^;

Is this the right approach?

 

[collinsmark]

So I get :

315 KG - 279.6KG ~ 35 kg.

^
So I get the answer in the textbook! ^^;

Is this the right approach?

Looks good to me!

 

[Ballox]

Looks good to me!

Sweet. Thanks for your help.