Calculating Acceleration of Buoyancy Balloon Carrying 140kg

[febbie22]

Hi i have this question:

A balloon is filled with helium gas which weighs approximately one-seventh of what air weighs under identical conditions. The balloon has a diameter of 10 m and carries two people, each weighing 70 kg. Assume the density of air is 1.16 kg/m3 and neglect the weight of the ropes and cage. Determine:

(a) The acceleration of the balloon when it is first released

This is how I've been doing it

F= 1.16/7 * 9.81 * 523.6 = 852.7 - Buoyancy equation

Then i got the weight by doing

W= 140 * 9.81 = 1373.4

First of all I am not sure if these are right and if they were I've been taking away the buoyancy force from the weight to get 520.7

Then to get acceleration i divided it by the mass 140

to get 3.72

But the answer giving said its 16.465

Can anyone please tell me where I am going wrong thanks


And weirdly there's a secound question that's says find the maximum load that it can carry and the answer is 520.61 which is very close to my answer

Cheers

 

[febbie22]

Surely someone can help me?

 

[Doc Al]

(a) The acceleration of the balloon when it is first released

This is how I've been doing it

F= 1.16/7 * 9.81 * 523.6 = 852.7 - Buoyancy equation

What does Archimedes' principle tell you that the buoyant force equals?

The buoyant force is an upward force; the weights of the people and the balloon are downward forces.

 

[febbie22]

yeah, i thought i should take away the weight of the balloon and the people from the buoyancy force and that would leave me the force pushing it up and accelerating it. is this wrong.

does the buoyancy force=weight

 

[Doc Al]

yeah, i thought i should take away the weight of the balloon and the people from the buoyancy force and that would leave me the force pushing it up and accelerating it. is this wrong.

No, that's not wrong.

does the buoyancy force=weight

Buoyant force = weight of the displaced fluid (air, in this case)

 

[febbie22]

so should i calculate the weight of the air using -
row(density of air) * 9.81 * volume of balloon

then do the buoyancy force minus the weight of air and the weight of the people(m*g)

but if this is correct I am not sure why my buoyancy force is lower than the weight as the weight of the air that i calculate is 5958.3 N compared to my buoyancy force of 852.7

thanks for you help so far,

 

[Doc Al]

so should i calculate the weight of the air using -
row(density of air) * 9.81 * volume of balloon

Yes. That will give you the buoyant force.

then do the buoyancy force minus the weight of air and the weight of the people(m*g)

That should be minus the weight of the balloon (filled with helium, not air) and the weight of the people. That will give you the net force on the balloon+people.

but if this is correct I am not sure why my buoyancy force is lower than the weight as the weight of the air that i calculate is 5958.3 N compared to my buoyancy force of 852.7

Your calculation of the buoyant force is incorrect:

F= 1.16/7 * 9.81 * 523.6 = 852.7 - Buoyancy equation

You divided by 7. (That gives you the weight of the balloon, not the buoyant force.)