AP Physics 2 : Archimedes' Principle
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Example Questions
Example Question #1 : Archimedes' Principle
Which of the following is a statement of Archimedes' principle?
Buoyant force is the weight of the mass of an immersed object
Buoyant force is the weight of the mass of water displaced by an immersed object
Buoyant force is the weight of the volume of water displaced by an immersed object
Buoyant force is the weight of the surface area displaced by an immersed object
Buoyant force is the weight of the volume of water displaced by an immersed object
Archimedes' Principle states: When a body is completely or partially immersed in a fluid, the fluid exerts an upward force on the body equal to the weight of fluid displaced by the body. Thus, the buoyant force is dependent on the density of the liquid and volume of the immersed object, regardless of the object's mass or surface area.
Example Question #1 : Archimedes' Principle
A spherical ball of density 
We can use Archimedes's Principle to solve this problem which states that the upward buoyant force on an object is equal to the weight of the fluid that the object displaces. Therefore, if an object is floating, the upward buoyant force is equal to the weight of the object. So, let's begin by calculating that. We are given the radius of the object and told that it is a sphere. Therefore, we can use the expression for the volume of a sphere:
Now multiplying this by the density, we get:
This is also going to be the mass of the water displaced. We can therefore calculate the volume of water displaced:
Example Question #1 : Archimedes' Principle
If a 
To answer this question, we'll need to consider the object submerged under water, and then use a force diagram in order to see which forces are acting on it.
The forces that are relevant to this question are the vertical forces, or those acting in the y-direction. Pointing down, we have the force due to gravity, which is the object's weight. Pointing upward is the bouyant force.
Next, we can expand each of the variables in the above expression.
Note that the depth in which the object was submerged is extraneous information.
Example Question #1 : Archimedes' Principle
A ball of mass 
None of these
The volume displaced will equal the volume of the ball.
Example Question #1 : Archimedes' Principle
How much of an iceberg is submerged below the water if the density of ice is 
Cannot be determined without knowing the mass of the iceberg.
The volume of the submerged mass is the volume of the mass proportional to the density of the solid to the density of the fluid.
Determine the amount of ice that is submerged.
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