Fluid Mechanics of a balloon

In summary, the problem involves a helium-filled balloon tied to a 2 m long string. The balloon has a mass of 0.25 kg and a radius of 0.4 m. The string has a mass of 0.05 kg. The task is to find the length h of the string that is lifted off the ground when the balloon is released. The relevant equation is P = P0 + pgH, where P is pressure, P0 is atmospheric pressure, p is density, g is gravity, and H is height. The density of the balloon can be found using its mass and volume, and the height h can be determined using the given information.
  • #1
Terrence
3
0

Homework Statement


A helium filled balloon is tied to a 2 m long uniform string of mass 0.05 kg.The balloon is spherical
with a radius of 0.4 m. When released it lifts a length h of the string off of the ground. Find the length h given that
the balloon has a mass of 0.25 kg.


Homework Equations



I think...

P = P0 + pgH

P is pressure, P0 is atmospheric pressure, p is density, g is gravity, H is height

The Attempt at a Solution



I'm really lost on this one...

I know desity is mass/volume, so I guess I can use .25 for mass and (4/3)pi*r3 to find the balloon's density. But I don't know the importance of the string's mass or how I am supposed to use all this information to find how high the balloon goes.
 
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  • #2
Terrence said:

Homework Equations



I think...

P = P0 + pgH

P is pressure, P0 is atmospheric pressure, p is density, g is gravity, H is height

The Attempt at a Solution


Is this the relevant equation? What is the meaning of H? The height of what? And what pressure is p?

ehild
 

1. What is the physics behind a balloon inflating and flying?

The inflation and flight of a balloon is governed by the principles of fluid mechanics. When the balloon is filled with air, the air molecules inside the balloon become more densely packed and create pressure, causing the balloon to expand. As the pressure inside the balloon increases, it pushes against the surrounding air molecules, creating lift and allowing the balloon to fly.

2. How does the shape and size of a balloon affect its flight?

The shape and size of a balloon play a crucial role in its flight. The larger the balloon, the more surface area it has to interact with the surrounding air molecules, creating more lift. The shape of the balloon also affects its aerodynamics and can impact its flight path and stability.

3. What is the role of buoyancy in the flight of a balloon?

Buoyancy is a force that acts opposite to the gravitational force and is responsible for the lift of a balloon. As the balloon is filled with air, it becomes less dense than the surrounding air and experiences an upward buoyant force. This force allows the balloon to rise and stay afloat in the air.

4. How does the temperature of the air inside a balloon affect its flight?

The temperature of the air inside a balloon is crucial for its flight. As the air inside the balloon is heated, it expands and becomes less dense, causing the balloon to rise. On the other hand, if the air inside the balloon cools, it becomes more dense, and the balloon will start to descend.

5. What are the potential hazards of flying a balloon?

While hot air balloons are generally considered safe, there are some potential hazards that should be taken into consideration. These include sudden changes in weather conditions, such as strong winds or thunderstorms, which can impact the flight path of the balloon. Additionally, improper handling or maintenance of the balloon can also lead to accidents. It is essential to follow all safety precautions and guidelines when flying a balloon.

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