Discover the Physics Behind Balloon Movement in a Stopped Car

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When a car traveling at constant speed suddenly decelerates, a balloon inside the car moves backward relative to the car. This occurs due to a pressure gradient created by the deceleration, where the air inside the car maintains its speed, resulting in higher pressure at the front. As the car slows down, the balloon experiences a difference in pressure, causing it to move toward the area of lower pressure at the back. This phenomenon contrasts with a pendulum, which would swing forward in the same situation. Understanding this behavior highlights the effects of pressure dynamics in a decelerating environment.
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Homework Statement


Question 20
You are traveling at constant speed in an airtight car with a
balloon floating motionless next to you. Suddenly, you slam
on the brakes so as to stop the car quickly. During decceleration,
with respect to the car the balloon
(a) moves forward; (b) remains motionless;
(c) moves backward; (d) can move forward or backward.


Homework Equations


No Equations


The Attempt at a Solution


The correct answer is c, that it moves backwards. Can someone explain why?
Thanks
 
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Great problem. I don't know why. I can do some handwaving and say the air in the car, relative to the ground, has the same average speed as the car, as of course does the balloon. So when the car abruptly decelerates you get a gradient of pressure from highest to lowest from the windshield backwards, and this pressure change develops rapidly.

But this is one answer I might need to empirically validate.
 
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Yes, it is because of a pressure gradient, inside the car the front part is in higher pressure, because as the car is decelerating the air tends to maintain the same speed so the majority of the air goes to the front part of the car, like there was some gravity attracting the air to there. If the pressure in the front part of the balloon is greater than the pressure behind he goes backwards. But if you have a pendulum, it would move forward.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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