A ping-pong ball attached to a string in a jar of water

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SUMMARY

The discussion analyzes the behavior of a ping-pong ball attached to a string in a jar of water when the jar is accelerated to the right. As the jar accelerates, the ping-pong ball perceives "down" as the bottom left of the jar, causing it to move to the right. This movement is explained by the creation of a pressure gradient in the liquid due to the acceleration, similar to the effects of gravitational acceleration on atmospheric pressure. The ball moves towards the region of lower pressure, which is aligned with the direction of the jar's acceleration.

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duoshock
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Consider a ping-pong ball attached to a string.

The string is secured at the bottom of a big jar, and water is used to fill the jar

The ping pong ball then floats inside the water, pulling the string upwards

What happens to the ping-pong ball when the jar of water is accelerated to the right?

any explanations using the concepts in physics? appreciate someone who understands the dynamics well to give a reasonable analysis. Thanks
 
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Just my guess...

While the jar was accelerating to the right, the ping pong ball would percieve "down" as being towards the bottom left of the jar. So it would move to the right in response.
 
A pressure gradient is created in the atmosphere due to the weight of the air. That is the atmospheric pressure is higher at the bottom than at higher elevations due to the weight of the atmosphere above it. This gradient exists solely due to gravitational acceleration. Any object less dense than the local air will move in the direction of decreasing pressure. A similar situation arises due to the acceleration of the container. A pressure gradient is created in the liquid due to its acceleration. A little bit of thought should convince you that a higher pressure will exist in the liquid on the opposite side than that in which it is accelerated in (similar to people being spun inside a circular structure), that is the liquid at the front is pushing "down" on the liquid at the rear of the container due to the acceleration. The ball will then move towards the region of lower pressure in the liquid, that is in the direction in which the container is being accelerated in.
 
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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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