AP Physics 2 : AP Physics 2

Study concepts, example questions & explanations for AP Physics 2

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Example Questions

Example Question #21 : Fluids

A nitrogen bubble of radius  is pumped into a bathtub from rubber tubing. Determine the net force on the bubble. The density of nitrogen is 

Possible Answers:

None of these

Correct answer:

Explanation:

The mass of the bubble will also be related to density and volume:

Plugging in values:

Example Question #551 : Ap Physics 2

A log has half of its volume out of the water. It weighs  and has a volume of . What is the buoyant force on the log?

Possible Answers:

The density of the log must be known to answer this question

Correct answer:

Explanation:

Since half of the log is floating above the water, the buoyant force must equal the gravitational force on the log for the net force to equal .

Example Question #32 : Fluid Statics

Blake drops a spherical ball of density  and radius  into a lake of material of density . How far will the bottom of the ball be submerged? 

Possible Answers:

Correct answer:

Explanation:

When the ball is stably submerged (no longer accelerating), the buoyant force will equal the gravitational force.

Let the mass of the ball be .

       

The buoyancy force is equal to the weight of the material the ball displaces, which is .

 is the volume of the material the ball displaces.

We need the mass of the ball in terms of its density, which is .

From equation ,

Solving for  we get

.

This is the entire volume of the ball, so the whole ball is submerged. 

Here is a more complicated route to the solution that would be necessary if the density of the water was greater than the ball:

Using the geometry of a spherical cap, you'll find the volume as a function of the depth  is . Setting this equal to volume displaced we get

In order for these to equal

This can also be done conceptually by realizing in order for the buoyant force to equal the gravitation force, the whole ball must be submerged since the density of the ball and water are equivalent. 

Note*: Any answer greater than  would also be acceptable since the ball would still be completely submerged, and the buoyancy force would still equal the gravitation force. However, the only answer choice greater than or equal to  is , so that is the answer.

Example Question #32 : Fluid Statics

Suppose that three different balls with equal volumes are submerged in water. Ball A has a density of , ball B has a density of , and ball C has a density of . What is true regarding the rate at which balls A, B, and C will float to the top?

Note: The density of water is .

Possible Answers:

Ball A will rise to the top first, followed by ball B, and lastly by ball C.

Ball C will rise to the top first, followed by ball B, and ball A will sink.

All three balls will sink at the same rate.

Ball C will rise to the top first, followed by ball B, and lastly by ball A.

Ball B will rise to the top first, followed by ball C, and ball A will sink.

Correct answer:

Ball C will rise to the top first, followed by ball B, and ball A will sink.

Explanation:

In this question, we're told that three balls of differing densities are submerged in water. We're then asked to determine the relative rates at which the balls will rise to the surface.

To begin, it's important to realize that whenever an object is submerged under water, there are two main forces acting upon it. One of these is the gravitational force, which points downwards. The other main force is the buoyant force, which acts upwards on the object. Because these two forces act in opposite directions, they can either cancel each other out partially or even completely.

Ball A, which has a density greater than water's, will not float to the surface but will rather sink to the bottom. This is because the gravitational force of ball A will be greater than the buoyant force from the displaced water. Consequently, there will be a net force downward.

For balls B and C, both of them have a density less than water. Hence, each of them will experience a net upward force and will thus rise to the surface. However, the magnitude of the upward force that each experiences will be different. This net upward force will, in turn, influence the degree to which each ball accelerates and will thus affect the rate at which they rise to the surface.

Ball B has a greater density than ball C. As a result, its gravitational force constitutes a greater downward force compared to ball C. The significance of this is that the net upward force for ball B will be lower than that of ball C. Thus, ball C will rise to the surface faster than ball B because it is enacted on by a greater net upward force.

So all in all, ball B and C will both float to the top. Ball C will reach the surface faster than ball B. Ball A, however, will sink to the bottom.

Example Question #1 : Pressure

At what depth within a salt water solution will the gauge pressure be equal to three times the atmospheric pressure?

 

Possible Answers:

Correct answer:

Explanation:

We can begin this problem by writing the equation for pressure.

We have to remember that the value of atmospheric pressure is equal to 1atm, which is also equal to 101325Pa.

Now, if we set the gauge pressure equal to three times the atmospheric pressure, we can solve for the depth.

Example Question #2 : Pressure

A cube with a volume of  is submerged a glass of fluid. The pressure at the top of the cube is 104kPa and the pressure at the bottom of the cube is 106kPa. What is the fluid's approximated density?

Possible Answers:

Correct answer:

Explanation:

The cube has a volume of . It is necessary to know the sidelength of the cube to know the height of the cube.

Use the pressure formula.

Rewrite the equation to solve for (rho density of the fluid) then plug in known values.

This is approximately 

Example Question #2 : Pressure

A bathysphere is designed to keep the pressure of the air inside at 1atm  so that divers do not suffer from decompression when returning to the surface. The the bathysphere has a circular hatch whose diameter is . What is the net force on the circular hatch when the bathysphere is at a depth of  in the ocean? The density of ocean water is .

Possible Answers:

Correct answer:

Explanation:

Pressure increases with depth according to:

Since the pressure at the surface of the ocean is the same as the pressure inside the bathysphere, we can ignore both. (This is called gauge pressure, or pressure above one atmosphere). Find the pressure at our depth:

Find the area of the hatch, and use the definition that force is pressure times area:

Example Question #1 : Pressure

A U-shaped tube is filled with equal amounts oil and water, with the interface of the two liquids at the middle of the tube (bottom of the "U"). The tube is open to atmospheric pressure  at either end. Given that the density of oil  is less than the density of water , the height of the column of oil  will be __________ the height of the column of water .

Possible Answers:

higher than 

equal to 

Cannot be determined without knowing the amount of each fluid

lower than

Correct answer:

higher than 

Explanation:

The interface between the liquids occurs at the bottom of the tube. Here, the pressure is the same. We also know that the tube is open to atmospheric pressure at the top of each side of the tube. Thus, we can create two equations for the pressure at the interface and set them equal to each other: 


By setting these equal to one another the result is: 
 
Since the density of water is greater than that of oil, we can conclude that the height of the oil column will be greater than that of the water. 

Example Question #1 : Pressure

Before you embark on a road trip, you check your tires to ensure that there is enough air in them. You find that they have a pressure of 25psi. What kind of pressure is this? 

Possible Answers:

Absolute pressure 

Atmospheric pressure 

Total pressure 

Gauge pressure

Correct answer:

Gauge pressure

Explanation:

The pressure in a tire is a gauge pressure; the 25psi is the difference between the pressure in the tire and atmospheric pressure, and does not add atmospheric pressure to reach the measured number. Absolute pressure adds these quantities together. 

Example Question #2 : Pressure

Calculate the difference in pressure, , between the surface of a lake and a depth of  below the surface. 

Possible Answers:

Correct answer:

Explanation:

The pressure at the lake's surface is just the atmospheric pressure, . The pressure at depth  below the surface is . Therefore, the pressure difference is given as .

We can then substitute the values in to arrive at the answer in :

Recall that this pressure is known as gauge pressure, and that the total pressure at the point underwater in the lake includes gauge pressure and atmospheric pressure.

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