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Cube in water

Imagine that you have a solid cube composed of Material X. You put the cube into a beaker filled with water. The cube sinks to the bottom of the beaker and sits there, at rest, on the bottom.

Which of the following statements are true? (Give ALL correct answers: B, AC, BCD, ... , or None)

A) The buoyant force on the cube is less than its own weight
B) The cube displaces an amount of water less than its own volume
C) The cube of Material X weighs less than a cube of water the same size
D) The normal force exerted by the bottom of the beaker on the cube is greater than the weight (in air) of the cube
E) The substance must be more dense than water

Solution Preview

Please see the attached file.

Answer: A and E are true.
There are two forces acting on the cube while it is going down.
The buoyant force = volume of cube * density of water (fluid displaced).
The force of gravity = volume of cube * density of the cube. This is equal to its weight.
When the cube gets to the bottom of the beaker there will be a third force acting on it: the normal force.
Since the cube ...

Solution Summary

This solution looks at density, volume and force calculations of a cube in water.

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