AP Physics 2 : Archimedes' Principle

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 water displaced by an immersed object

Buoyant force is the weight of the mass of 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

Explanation:

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 #2 : Archimedes' Principle

A spherical ball of density  has a radius of . If the ball is placed on the surface of water and released, how much of the ball becomes submerged in the water?

Explanation:

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 #2 : Archimedes' Principle

If a  object with a volume of  is submerged  below water, what is the net force acting on the object?

.

Explanation:

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 #4 : Archimedes' Principle

A ball of mass  is lightly dropped into a tub with a base of . After it sinks to the bottom, the water rises by . Determine the density of the ball.

None of these

Explanation:

The volume displaced will equal the volume of the ball.

Example Question #3 : Archimedes' Principle

How much of an iceberg is submerged below the water if the density of ice is  and the density of water is ?

Cannot be determined without knowing the mass of the iceberg.