Why Does a Balloon Fall Up in an Elevator?

In summary: The pressure gradient is just a result of the acceleration.In summary, the conversation discusses the scenario of being in an elevator accelerating downwards and holding a balloon. The question arises about what will happen to the balloon if the thread holding it snaps. While the balloon experiences no buoyancy inside the elevator, there is confusion about its behavior in an inertial frame of reference. The expert explains that the force of buoyancy is frame independent and there is none in this case due to the absence of air pressure gradient in the elevator. The conversation also considers the possibility of the elevator being a sealed box, in which case the air inside would also accelerate and create a pressure gradient. However, even with zero acceleration, there is still a pressure gradient caused by the
  • #1
hachikuda
1
0
Imagine you are in an elevator accelerating downwards with acceleration g, holding a balloon (which would fly upwards if left outside). Now if the thread you are holding snaps, what will happen to the balloon?
Since the acceleration felt inside the elevator is 0, the balloon should not experience any buoyancy and continue to stay at the same position.

The difficulty I am having in understanding is, if this experiment is observed from outside (i.e. from an inertial frame of reference), the balloon seems to be in a free fall towards the ground, where as it should actually be rising up.

Where is the mistake?
 
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  • #2
What about the air in the elevator? Should we suppose it moves together with the elevator?

If yes, then as soon as the thread snaps, the force of drag will be acting on the balloon, which makes the whole thing quite difficult.

If no, then the dynamics of the balloon will not be affected by the motion of the elevator after the thread snaps.
 
  • #3
hachikuda said:
The difficulty I am having in understanding is, if this experiment is observed from outside (i.e. from an inertial frame of reference), the balloon seems to be in a free fall towards the ground, where as it should actually be rising up.
Why should it be rising up in the inertial frame? The force of buoyancy is frame independent, and there is none, because there is no air pressure gradient in the elevator. Since gravity is the only force acting on the balloon in the inertial frame, it accelerates down.
 
  • #4
A.T. said:
The force of buoyancy is frame independent, and there is none, because there is no air pressure gradient in the elevator.

That is not true if the elevator is (approximately) a sealed box. In that case, the air inside the elevator is also accelerating, and the force causing the acceleration is a pressure gradient between the floor and the roof of the elevator.

Even when the acceleration is zero, the buoyancy force is just another name for the resultant force on the object caused by the pressure in the fluid. With no acceleration, there is still a pressure gradient, caused by the weight of the fluid. That statement is rather more "obvious" if you think about why pressure in water increase with depth, but the same is true of air.
 
  • #5
There is no pressure gradient. The elevator is in free fall.
 
  • #6
AlephZero said:
the air inside the elevator is also accelerating, and the force causing the acceleration is a pressure gradient between the floor and the roof of the elevator.
No, the force causing the acceleration is gravity.
 

Related to Why Does a Balloon Fall Up in an Elevator?

What is the difference between buoyancy and gravitation?

Buoyancy and gravitation are two important forces that affect objects in fluids such as water or air. Buoyancy is the upward force exerted by a fluid on an object immersed in it, while gravitation is the downward force exerted by the Earth's mass on all objects. Buoyancy is caused by differences in pressure between the top and bottom of an object, while gravitation is caused by the mass of an object and the Earth's gravitational pull.

How does buoyancy affect the weight of an object in water?

When an object is submerged in water, it experiences an upward force from the water called buoyancy. This force counteracts the weight of the object, resulting in a decrease in its apparent weight. The amount of buoyancy an object experiences depends on its volume and the density of the fluid it is submerged in. Objects with a higher volume and/or lower density will experience more buoyancy and appear lighter in water.

What is the relationship between an object's density and its buoyancy?

Density is a measure of an object's mass per unit volume. The denser an object is, the more mass it has in a given volume, and the more it will sink in a fluid. Objects with a lower density will experience more buoyancy and float in fluids. The density of an object also affects the amount of water it displaces, which is a key factor in determining the amount of buoyancy it experiences.

How does the shape of an object affect its buoyancy?

The shape of an object plays a significant role in determining its buoyancy in a fluid. Objects with a larger surface area will experience more buoyancy than objects with a smaller surface area. This is because a larger surface area means a larger volume of fluid is displaced, resulting in a greater upward force. Additionally, objects with a streamlined shape, such as a boat, will experience less resistance from the fluid and therefore have greater buoyancy.

What is the difference between positive and negative buoyancy?

Positive buoyancy occurs when an object is less dense than the fluid it is submerged in and therefore experiences an upward force, causing it to float. Negative buoyancy, on the other hand, occurs when an object is more dense than the fluid and therefore sinks. Neutral buoyancy is when an object's density is equal to the fluid and it remains suspended in the fluid without sinking or rising.

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