Calculating Acceleration of Buoyancy Balloon Carrying 140kg

In summary, the conversation discusses the method for calculating the acceleration of a balloon when it is first released, taking into account the weight of the balloon, people, and the buoyant force of the air. There is some confusion about how to calculate the buoyant force, but it is clarified that it is equal to the weight of the displaced air. The correct equation to calculate the buoyant force is given as density of air multiplied by 9.81 (acceleration due to gravity) and the volume of the balloon. The net force on the balloon and people should be calculated by subtracting the weight of the balloon and people from the buoyant force.
  • #1
febbie22
37
0
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 accleration 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
 
Physics news on Phys.org
  • #2
Surely someone can help me?
 
  • #3
febbie22 said:
(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.
 
  • #4
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
 
  • #5
febbie22 said:
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)
 
  • #6
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,
 
  • #7
febbie22 said:
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:
febbie22 said:
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.)
 

1. How do you calculate the acceleration of a buoyancy balloon carrying 140kg?

To calculate the acceleration of a buoyancy balloon carrying 140kg, you will need to use the equation F=ma, where F is the force, m is the mass and a is the acceleration. In this case, the mass will be the combined mass of the balloon and the 140kg weight. To determine the force, you will need to calculate the buoyant force acting on the balloon, which can be found by using the equation Fb=ρVg, where ρ is the density of the fluid, V is the volume of the displaced fluid, and g is the acceleration due to gravity. Once you have calculated the force, you can plug it into the equation F=ma to find the acceleration.

2. What is the role of buoyancy in calculating the acceleration of a buoyancy balloon carrying 140kg?

Buoyancy plays a crucial role in determining the acceleration of a buoyancy balloon carrying 140kg. Buoyancy is the upward force exerted by a fluid on an object immersed in it. In this case, the buoyant force is what allows the balloon to float in the air. By calculating the buoyant force, we can determine the net force acting on the balloon and use it to calculate the acceleration.

3. How does the density of the fluid affect the acceleration of a buoyancy balloon carrying 140kg?

The density of the fluid has a direct impact on the acceleration of a buoyancy balloon carrying 140kg. This is because the buoyant force is directly proportional to the density of the fluid. This means that as the density of the fluid increases, the buoyant force also increases, resulting in a higher acceleration for the balloon. Similarly, if the density of the fluid decreases, the buoyant force and acceleration will also decrease.

4. What other factors can affect the acceleration of a buoyancy balloon carrying 140kg?

Aside from density, there are a few other factors that can affect the acceleration of a buoyancy balloon carrying 140kg. These include the volume of the displaced fluid, the weight of the balloon and the 140kg weight, and the acceleration due to gravity. As mentioned earlier, the volume of the displaced fluid is used to calculate the buoyant force, which in turn affects the acceleration. The weight of the balloon and the 140kg weight will also impact the overall mass and therefore the net force and acceleration. Finally, the acceleration due to gravity is a constant value that will also play a role in the calculation.

5. What is the significance of calculating the acceleration of a buoyancy balloon carrying 140kg?

Calculating the acceleration of a buoyancy balloon carrying 140kg is important in understanding the behavior and performance of the balloon. It can also be useful in designing and optimizing the balloon for a specific purpose. For example, if the acceleration is too low, the balloon may not be able to lift the 140kg weight, and adjustments may need to be made to increase the acceleration. On the other hand, if the acceleration is too high, it may result in instability or other issues that could affect the balloon's flight. By accurately calculating the acceleration, we can ensure the safe and efficient operation of the buoyancy balloon carrying 140kg.

Similar threads

Buoyancy and helium balloons
    • Introductory Physics Homework Help
Replies
3
Views
3K
Can a Helium-Filled Weather Balloon Accelerate Upwards Faster Than Gravity?
    • Introductory Physics Homework Help
Replies
2
Views
996
Balloon Accel: Find 16.4 m/s^2
    • Introductory Physics Homework Help
Replies
4
Views
1K
Moles of gas helium balloon; buoyancy; PV=nRT
    • Introductory Physics Homework Help
Replies
3
Views
7K
How Hot Must the Air in a Balloon Be to Lift a Given Mass?
    • Introductory Physics Homework Help
Replies
7
Views
3K
Buoyancy force of a hot-air balloon
    • Introductory Physics Homework Help
Replies
6
Views
8K
A Helium Balloon and Buoyancy
    • Introductory Physics Homework Help
Replies
1
Views
9K
Calculate velocity of helium baloon
    • Introductory Physics Homework Help
Replies
11
Views
2K
How fast does the balloon accelerate upwards?
    • Introductory Physics Homework Help
Replies
4
Views
11K
Bouyant force accelerates released balloon
    • Introductory Physics Homework Help
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top