AP Physics 2 : Buoyant Force

Example Questions

Example Question #11 : Buoyant Force

Suppose that two different balls of equal volume are submerged and held in a container of water. Ball A has a density of  and Ball B has a density of . After the two balls are released, both of them begin to accelerate up towards the surface. Which ball is expected to accelerate faster?

Ball A and Ball B will have the same acceleration

There is no way to determine the relative acceleration of the two balls

Ball B will have greater acceleration

Neither ball will accelerate

Ball A will have greater acceleration

Ball A will have greater acceleration

Explanation:

In this question, we're presented with a situation in which two balls of different densities but equal volumes are held underneath the surface of a container of water. Then, each ball is released and allowed to accelerate up to the surface. The question is to determine how the acceleration of each ball compares to the other. In order to answer this, let's start by imagining all of the forces acting on the submerged ball.

In the x-direction, the forces acting to the left of the ball are exactly equal to the forces acting on the right of the ball. Therefore, all of the forces acting in the x-direction cancel out, resulting in a net force of zero in the x-direction.

In the y-direction, we have to consider two things. The first is the upward buoyant force caused by the displacement of water. Since both balls have an identical volume, both of them displace the same amount of water. Consequently, both balls will experience the same upward buoyant force. However, we must also consider the downward force caused by the weight of the ball itself. In this scenario, the downward weight of Ball B is greater than that of Ball A.

We can write the net force acting on the ball in the y-direction as the difference between the upward buoyant force and the downward weight as follows:

Due to the fact that Ball A has a smaller weight (a smaller  component in the above equation), the result is that the net upward force is greater than that of Ball B. Thus, we would expect Ball A to have a greater acceleration.

Example Question #12 : Buoyant Force

Determine the net force (including direction) on a gold  marble of radius in liquid mercury .

down

up

up

down

down

down

Explanation:

Consider all the forces on the gold marble:

Recall the equation for buoyant force:

Substitute:

Find the mass of the marble:

Plug in values:

Note how the buoyant force points up while the gravitational force points down.

Example Question #11 : Fluid Statics

Determine the buoyant force on an object of volume in a fluid of density

Explanation:

Use the equation for buoyant force:

Where is the density of the medium around the object in question

is the gravitational acceleration near the surface of the earth

is the volume of the object in question

Convert  into

Plug in values:

Example Question #14 : Buoyant Force

A balloon of mass  is inflated to a volume of  with pure . Determine the buoyant force it will experience when submerged in water.

None of these

Explanation:

Use the equation for buoyant force:

Where

is the density of the medium

is the acceleration due to gravity

is the volume

Plugging in values:

Example Question #15 : Buoyant Force

Will a ball of mass  and radius  sink or float in water?

Not enough information

It will be partially submerged

Float, but only because of surface tension

Sink

Float

Sink

Explanation:

Determining density:

Volume of a sphere:

Combining equations:

Converting to and plugging in values:

It is denser than water, so it will sink.

Example Question #16 : Buoyant Force

A block of mass  and volume  is held in place under water. What is the instantaneous acceleration of the block, and in what direction, when it is released?

Explanation:

According to Archimedes's principle, when the block is placed under water, 3.5L of water are displaced. We can then calculate the buoyant force provided by the water:

Where:

Plugging in our values to the first expression:

Then we can use Newton's 2nd law to determine the acceleration of the block:

There are two forces acting on the block, gravity and buoyancy, and they are in opposite directions. If we designate a downward force as positive, we get:

Substituting in the expression for force due to gravity:

Rearranging for acceleration:

Substituting in values:

Example Question #17 : Buoyant Force

A scuba diver with a total mass  is dressed so his density  and is holding a spherical ball with a volume  while submerged in water. What is the density of the ball if the upward acceleration of the ball and diver is ?

Explanation:

Where there are 4 total forces acting on the scuba diver and ball: gravity and buoyancy acting on both the scuba diver and the ball. However, the diver has the same density as the water, so the gravitational and buoyancy forces acting on the diver will cancel out. If we designate an upward force as being positive, we can say:

(1)

Where:

Where:

So,

Plugging these expressions back in to expression (1), we get:

Now let's start rearranging for the density of the ball:

Example Question #18 : Buoyant Force

A block of mass  is sinking in water at a constant velocity. There is a  constant drag force of  acting on the block. What is the volume of the block?

Explanation:

Since the block is traveling at a constant velocity we can say:

There are 3 forces acting on the block: gravitational, buoyant, and drag force. If we denote a downward force being positive, the expression becomes:

Where:

Substituting these in:

Where according to Archimedes's principle:

Plugging this in:

Rearranging for volume:

Plugging in values:

Example Question #19 : Buoyant Force

A bowling ball with mass  and radius  is submerged under water and held in place by a string. What is the tension in the string?

Explanation:

Since the ball is held in place, we know that:

There are three forces acting on the ball: gravitational, buoyant, and tension. If we denote a downward force as positive, we get:

(1)

And using Archimedes's principal:

Where:

Plugging all of these into expression (1), we get:

Plugging in our values, we get:

Example Question #20 : Buoyant Force

A semi-hollow, spherical ball with an empty volume of  is submerged in water and has an initial mass of . The ball develops a leak and water begins entering the ball at a rate of . How long does it take before the buoyant force on the ball is equal to the gravitational force?

Explanation: