# A hellim ballon in a bus

#### rbwang1225

1. Homework Statement
Consider a hellium balloon with negiligible mass in the bus with all windows closed.
When the bus is acclerating in $\mathbf a=a \mathbf i$, where $\mathbf i$ is the unit vector in the positive x direction, describe the status of the ballon and explain the reason.
If we consider the massive balloon, does your answer change?
Explain the reason.
(Status: Does it tilt or not? What are the tilting diraction and angle?)

2. Homework Equations
Buoyent force $ρgV$

3. The Attempt at a Solution
I know the answer might be $tan\theta=\frac{g}{a}$ or something like this, but I don't really the reason behide this.
I think it is related to physics in noninertial frames.

Any help would be appreciated.
Sincerely.

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#### Borek

Mentor
Forget about the bus for a moment. What usually happens to the helium filled balloon and why?

#### rbwang1225

The balloon will float in the air because of the density of the helium is smaller than that of air.
I just got a new idea, but don't know if it's right or not.

Because of the total force is $\mathbf B+m\mathbf g$ which equals $m\mathbf a$, and I think the direction of the gravity is the same, therefore it is the change of the buoyant force that causes the change of the status of the balloon.

#### Borek

Mentor
The balloon will float, or ascend?

#### rbwang1225

Sorry, bad english, the balloon will ascend.

#### Borek

Mentor
OK, why does it ascend?

#### rbwang1225

Because the pressure at the lower part of the balloon is greater than the upper part of it, and, the buoyant force is larger than the gravitational force, the balloon ascends.

#### Borek

Mentor
OK, but why do these differences exist? Do they exist in the zero gravity environment?

#### Chestermiller

Mentor
If the balloon is not on a string held by someone, where do you think the balloon is located vertically before the bus starts to accelerate?

(a) in mid air
(b) at the roof of the bus.

If your answer is (b), what do you think the magnitude of the force is that the roof exerts on the balloon?

#### rbwang1225

OK, but why do these differences exist? Do they exist in the zero gravity environment?
No, they always exist in a gravitational environment.
As for the reason of these differences, I don't really understand your question, sorry...

#### rbwang1225

If the balloon is not on a string held by someone, where do you think the balloon is located vertically before the bus starts to accelerate?

(a) in mid air
(b) at the roof of the bus.

If your answer is (b), what do you think the magnitude of the force is that the roof exerts on the balloon?
My answer is (b), but I don't really know how to figure out the direction and magnitude of the normal force exerted by the roof and the buoyant force which, I think, has something to do with the condition of the windows.

Last edited:

#### CWatters

Homework Helper
Gold Member
I think we should consider it to be floating up in the air and it is on a sting held by a student.
or at least assume that the balloon is weighted so it has a tendency to float one way up eg with the knot pointing downwards.

Perhaps it would help the OP to remember that when the bus is stationary gravity (an acceleration) is pulling the air vertically downwards. What happens when the bus and the air in it are also accelerating in another direction. It helps if you have ridden on a bus standing up!

#### Borek

Mentor
Let me reword the original problem. Imagine you have a helium filled balloon in the standing bus. Obviously, the balloon goes up till it stops at the roof and it stays there. Now, what will happen when the bus starts to move?