/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 11 A helium-filled balloon stops ri... [FREE SOLUTION] | 91影视

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Chapter 15: Problem 11

A helium-filled balloon stops rising long before it reaches the "top" of the atmosphere, but a cork released from the bottom of a lake rises all the way to the surface. Why the difference?

Short Answer

Expert verified
The difference in the behavior of the balloon and the cork is due to the significant change in the density of air with height (lighter as we go up) compared to the inconsiderable change in the density of water with depth. This causes the buoyant force upward on the helium balloon to decrease as it ascends, causing it to stop at a point, while the cork continues to rise under buoyancy until it reaches the water鈥檚 surface.

Step by step solution

01

Understand Buoyancy

Buoyancy is a force that is exerted by a fluid (liquid or gas) on an object submerged in it. This force is upward and its magnitude is equal to the weight of the fluid displaced by the object. When an object is immersed in a fluid, buoyant force helps the object to float. For the object to rise up, the buoyant force must be greater than the weight of the object.
02

Balloon Scenario

When helium-filled balloon is released into the atmosphere, it starts rising because the weight of the air it displace is more than its own weight (Helium is lighter than air). Now, as the balloon rises, the air pressure and density decreases. This means the weight of air displaced by balloon also decreases. When the balloon reaches a height where weight of air displaced is equal to the weight of the balloon, it stops rising.
03

Cork Scenario

Conversely, when a cork is released from the bottom of a lake, it rises to the surface of the water. This happens because the cork's density is less than the water's density, and the buoyant force is greater than the cork's weight. Unlike in the atmosphere, the density of the water doesn't change significantly with depth, so the cork continues to rise until it reaches the surface.

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