# AP Physics 2 : Pressure

## Example Questions

### Example Question #11 : Pressure

Consider the three differently shaped containers, as shown. Each container is filled with water to a depth of . In which container is the pressure the greatest at the bottom?

Container C

It cannot be determined without knowing the volume of water in each container.

Each container has the same pressure at the bottom

Container A

Container B

Each container has the same pressure at the bottom

Explanation:

In this question, we're told that three containers of different shapes are filled with water. We're also told that each container has the same depth of water.

To find the pressure at the bottom of any of the containers, we'll need to remember the equation for pressure.

Since each of the containers is open to the atmosphere, we can disregard the term for atmospheric pressure in the above expression. Therefore, the absolute pressure becomes the gauge pressure.

Also, since each container is filled with water, the density of the fluid in each container is identical. Moreover, the depth we are considering for each container is also the same. Therefore, the pressure at the bottom of each container is exactly the same.

### Example Question #12 : Pressure

A ball with radius  is submerged in syrup at a depth of . What is the total force from pressure acting on the ball?

Explanation:

The total pressure on the ball includes both hydrostatic and atmospheric pressure:

We are given the atmospheric pressure, so we just need to determine the hydrostatic pressure using the following expression:

Plugging in values:

Therefore,

Now to determine the force on the ball, we need it's surface area. For a sphere:

Then,

### Example Question #13 : Pressure

Pressure exerts a force of  spherical ball with radius . The ball is submerged in the ocean which has a density of . How deep is the ball?

Explanation:

We can calculate the total pressure on the ball from the given force and radius:

Where for a sphere:

There are two pressures that combine to the total pressure on the ball: hydrostatic and atmospheric.

Since the ball is submerged in the ocean, we know that the surface of the water is at sea level and thus has a pressure:

Also, we can calculate the hydrostatic pressure with the following expression:

Where density is of the ocean and the height is the depth of the ball. Plugging this into our last expression, we get:

Rearranging for height:

### Example Question #14 : Pressure

A ship has crashed and is currently sinking to the bottom of the ocean. At time , the ship is at a depth of  and has reached a terminal velocity of  downward. What is the hydrostatic pressure on the ship at time ?

Explanation:

To determine the hydrostatic pressure, we need to know the depth of the ship at time t = 12s. We can determine this with the following expression:

Then using the expression for hydrostatic pressure:

### Example Question #15 : Pressure

Someone who is down on their luck throws a dime down a deep well. At time , the dime's velocity is immediately reduced to   as it hits the water and begins accelerating down at a rate . How much time has passed when the hydrostatic pressure on the coin is ?

Explanation:

Given the hydrostatic pressure, we can calculate the depth that this occurs at:

Rearranging for height:

Plugging in our values, we get:

We can then use the following kinematics equation to determine how much time has passed:

If we designate the downward direction as positive and plugging in values to the kinematics equation, we get:

Rearranging, we get:

Since we can't have a negative time, the first one is the answer.

### Example Question #16 : Pressure

A vertical, cylindrical tube is filled to a height of  with mercury. Then, the tube is filled to a total height of  with water. What is the hydrostatic pressure in the tube at a height of ?

Explanation:

We will use the expression for hydrostatic pressure for this problem:

In this scenario, the pressures from each material are additive. Therefore:

Plugging in expressions:

Plugging in values:

Note how we used 0.9m for the height of mercury since we are asked for the pressure at a height of 0.5m.

### Example Question #17 : Pressure

A U-shaped tube is filled with water, however the openings on either ends have different cross-sectional areas of  and . If a force of  is applied to the opening that is  in area, how much force will be exerted on the other end of the tube?

Explanation:

The following formula on pressure and area is used:

We substitute our known values and solve for F2 to obtain the output force:

Therefore the correct answer is  of force.

### Example Question #51 : Fluid Statics

A cube with a mass of  and sides of length  rests on a table. What pressure does this cube exert on the table?

Explanation:

The formula for pressure is given as:

Where  is pressure in pascals,  is force in newtons, and  is area in meters squared. By substituting our known values we can solve for pressure:

### Example Question #52 : Fluid Statics

Consider the diagram of a hydraulic lift shown below.

Based on this diagram, which of the following statements is true?

The pressure on the right side is greater than the pressure on the left side

The pressure on the left side is greater than the pressure on the right side

The force on the right side is greater than the force on the left side

None of these statements are true because the pressure and force on both the left and right side are equal

The force on the left side is greater than the force on the right side

The force on the right side is greater than the force on the left side

Explanation:

In this question, we're shown a hydraulic lift. A lift such as this functions to transmit a smaller force into a larger force via an incompressible liquid. From the diagram shown, we're asked to determine the relative values of the pressure and force on the right and left sides.

A hydraulic lift is able to transmit a small force into a larger force due to the liquid it contains being unable to compress. What this means is that when a force is applied to a given area of the liquid, this pressure is transmitted to all parts of the liquid. Therefore, at any given point, the pressure at all points within the lift will be equal. Thus, we can rule out the answer choices that list pressure.

But what about the forces? If the pressure is the same everywhere in an incompressible liquid, does this also mean the force is the same everywhere? The answer is no. Since pressure depends on the ratio of force to area, equal pressure does not mean equal force, because the area on which the force is acting must be taken into account. We can show this with the following expressions.

As can be seen from the above expression, the output force is greater than the input force by a factor equal to the ratio of the areas on which each force acts. In other words, to maintain constant pressure, a greater area will mean a greater force. Thus, from the diagram, we can see that the force on the right () will be greater than the force on the left ().

### Example Question #51 : Fluids

A girl is standing on two feet. She then stands on one foot. How does the pressure on her foot compare to when she is standing on two feet?

It is doubled

None of these

It is cut in half

Impossible to determine