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Chapter 11: Problem 22

An ice cube floats in a glass of water. As the ice melts, what happens to the water level? A. It rises. B. It remains the same. C. It falls by an amount that cannot be determined from the information given. D. It falls by an amount proportional to the volume of the ice cube. E. It falls by an amount proportional to the volume of the ice cube that was initially above the water line.

Short Answer

Expert verified
B. It remains the same.

Step by step solution

01

Understanding the State of the Ice Cube

As stated, the ice cube is floating in the glass of water. This means that it is in equilibrium; the weight of the water displaced is equal to the weight of the ice cube.
02

Interpreting the Melting Ice Cube

As the ice cube melts, it changes its state from solid to liquid without any mass loss. The water formed by the melting ice cube will occupy the same space that was initially displaced by the ice cube when it was in its solid state.
03

Determine the Water Level after Ice Melts

Since the melted ice cube forms water occupying the same volume as the displaced water volume when it was solid and floating, the water level in the glass remains the same after the ice has fully melted.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Buoyancy
Buoyancy is a force that acts upwards on objects submerged in a fluid like water. This force is what keeps objects like ice cubes afloat. Buoyancy is derived from Archimedes' Principle. This principle states that an object submerged in a fluid experiences an upward force equal to the weight of the fluid displaced by the object. This means that objects in a fluid will float if the buoyant force is equal to or greater than the weight of the object.
  • Ice cubes float because the buoyant force is equal to their weight.
  • Larger volumes displace more water and experience larger buoyant forces.
  • The name "buoyancy" comes from the successful balance of these forces.
When an ice cube is placed in water, it displaces an amount of water equal to its weight, causing it to float at the surface.
Displacement
Displacement is a vital aspect of understanding how floating objects behave in water. It refers to the amount of water pushed aside or displaced by an object submerged or floating in fluid. When ice floats, it displaces water equal to the ice cube's weight.
  • An ice cube floating on water displaces a volume of water equal to its weight.
  • The volume of water displaced matches the volume of the submerged part of the ice cube.
  • As ice melts, this displaced water volume becomes the melted water itself.
So, when the ice cube melts, the water level does not change, because the water that formed upon melting exactly fills the space of the displaced water.
Equilibrium
Equilibrium is a state in which opposing forces or influences are balanced. In the context of floating ice, it describes a situation where the weight of the ice cube is precisely counteracted by the buoyant force from the displaced water. This equilibrium keeps the ice cube at rest, floating at the surface without sinking or rising.
  • When an ice cube is floating, it is in equilibrium.
  • The weight of the water displaced is equal to the weight of the ice cube itself.
  • As the ice melts, the equilibrium shifts but maintains the overall water level unchanged.
The principle of equilibrium ensures that the water level remains constant when the ice cube melts, since the change in state from ice to water does not alter the total volume displaced.
Floating Ice
Floating ice is a classic example used to illustrate the concepts of buoyancy and displacement. When ice floats, it shows how an object can sit at the surface of a liquid because of the balance of forces. Floating ice in a glass of water exemplifies these principles in daily life.
  • The ice cube's density is less than that of water, allowing it to float.
  • As it melts, no additional water is displaced beyond the original volume that kept it afloat.
  • This shows how floating objects utilize Archimedes' Principle to remain buoyant.
This practical application helps us visualize how forces work in the natural world, confirming why the water level remains constant as the ice fully melts.

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Most popular questions from this chapter

You are given two objects of identical size, one made of aluminum and the other of lead. You hang each object separately from a spring balance. Because lead is more dense than aluminum, the lead object weighs more. Now you weigh each object while it is submerged in water. Will the difference between the weight of the aluminum object and weight of the lead object be greater than, less than, or the same as it was when the objects were weighed in air?

An elephant that has a mass of \(6000 \mathrm{~kg}\) evenly distributes her weight on all four feet. (a) If her feet are approximately circular and each has a diameter of \(50 \mathrm{~cm}\), estimate the pressure on each foot. (b) Compare the answer in part (a) with the pressure on each of your feet when you are standing up. Make some rough but reasonable assumptions about the area of your feet.

The return-air ventilation duct in a home has a cross-sectional area of \(900 \mathrm{~cm}^{2}\). The air in a room that has dimensions \(7 \mathrm{~m} \times 10 \mathrm{~m} \times 2.4 \mathrm{~m}\) is to be completely circulated in a 30 -min cycle. What is the speed of the air in the duct?

If the gauge pressure is doubled, the absolute pressure will A. be halved. B. be doubled. C. be unchanged. D. be increased, but not necessarily doubled. E. be decreased, but not necessarily halved. SSM

Two wooden boxes of equal mass but different density are held beneath the surface of a large container of water. Box A has smaller average density than box B. When the boxes are released, they accelerate upward to the surface. Which box has the greater acceleration? A. Box A B. Box B C. They are the same. D. We need to know the actual densities of the boxes in order to answer the question. E. It depends on the contents of the boxes. SSM
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