Watch Fluids Video 4. Bernoulli’s Discuss video on ... Unit... · Theorem Study for Quiz ......

AP Physics 2 Unit 1. Fluids Name:_______________________ Accept that some days you're the pigeon, and some days you're the statue. - unknown

1

Date

Zero Hour

(7:15 starting

time)

In Class

Homework to completed that

evening (before coming to next

class period)

8/16 Tues (A) Intro to AP Physics 2 and

Intro to Fluids

Watch: Fluids video 1. Fluids,

Density and Hydrostatic Pressure

8/17 Wed (A)

Discuss video: density,

pressure and force

relationships

8/18 Thur (B) Pressure and Force in fluids

Summer videos

Watch: Fluids video 2. The Buoyant

Force.

8/22 Mon (A) Discuss video: Buoyant

Forces, sinking and floating.

8/23 Tue (B) Unknown Density

Lab Buoyant Force work

Study for Quiz

Watch Fluids video 3. Fluids in

Motion and the Continuity Equation

8/25 Thur (B) Quiz over Static Fluids

Discuss video on fluid flow

Watch Fluids Video 4. Bernoulli’s

Principle

8/29 Mon (A)

LSM

Discuss video on Bernoulli’s

Effect and Torricelli’s

Theorem

Study for Quiz

8/30 Tues (B) Leaky Bucket Lab Quiz over Flowing Fluids

Finish Packet Study for Unit Test

9/1 Thur (B) Unit Test Fluids and Lab

Practical

* Question types for online WSQ:

Confusion: anything you need clarification, further understanding about that I can help you

with

HOT: Higher Order Thinking - a good discussion question for the class like something the

teacher would ask but you can answer

Example: An example problem for students to work on in class, you must also provide a

worked out solution

Unit Video Guided Notes

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Concept 1 & 2 Learning Objectives:

Matter has a property called density.

The student is able to predict the densities, differences in densities, or changes in densities under different

conditions for natural phenomena and design an investigation to verify the prediction.

The student is able to select from experimental data the information necessary to determine the density of an object

and/ or compare densities of several objects.

Hydrostatic Pressure: The student is able to state the relationship between force and pressure to make

calculations related to a moving fluid.

Video 1. Guided Notes: Read through the questions below, then watch the video,

answer the following questions. Pause as needed.

Questions:

What is a fluid:

What is mass density, its equation and SI units

What is the conversion between g/cm3 to kg/m3

How is the density of a liquid different from that of a gas and why?

What are the two reasons given for why density is a valuable tool (in what ways did I use density in the video)?

How is Force related to pressure?

What is the SI unit of pressure?

How does the pressure change with depth? What is the pressure in a fluid caused by?


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If the pressure due to the fluid is greater lower then higher, how can a fluid be static? Draw a Freebody diagram of the forces on a section of fluid in a beaker.

What does the phrase “water seeks its own level” mean and how does that relate to pressure

What is the value of atmospheric pressure in units of Pascals and atms

What is the difference between absolute pressure and gauge pressure?

What is the equation for hydrostatic pressure of a liquid with density at depth d. Label each component as either absolute, gauge, or atmospheric (provided that the outside pressure is due to the atm)

How are barometers and manometers similar? How are the different?

Summarize: on the google form write a summary about what you learned from the video. Make sure to include; information on what density is and how it is useful, how and why pressure changes in a fluid (and what does density have to do with pressure?), and how you calculate hydrostatic pressure in a fluid.

Problems to try before class (show your work below) & type you answers into the google form where indicated.

1. An object has a density : a. Suppose each of the objects 3 dimensions are increased by a factor of 2 without changing the material of

which the object is made. Will the density change? If so, by what factor? Why?

b. Suppose each of the objects 3 dimensions are increased by a factor of 2 without changing the objects mass. Will the density change? If so, by what factor? Why?

2. You are scuba diving in the ocean ( =1025 kg/m3). When you are 20 m below the surface what is your absolute pressure (in pascals)?


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Concept 3. Learning Objectives: Contact forces result from the interaction of one object touching another object and they arise from interatomic electric

forces. These forces include tension, friction, normal, spring and buoyant. The student is able to represent forces in diagrams or mathematically using appropriately labeled vectors with

magnitude, direction, and units during the analysis of a situation.

The student is able to explain and calculate the buoyant force



Questions:

What causes the upward buoyant force on an object in a fluid?

Explain Archimedes Principle.

Why is the buoyant force the same on totally submerged rock or totally submerged piece of wood if their volume is the same?

What is the equation for buoyant force? How else can I calculate buoyant force?

When is the volume of the object equal to the volume of fluid displaced?

In terms of forces why do some objects sink?

In terms of forces, when do objects float?


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Why is it difficult to totally submerge a beach ball?

What determines how much of a floating object is below the surface of the fluid?

For the problem shown at the end of the video: Draw your freebody diagram on the box below: Write your sum of forces equation here: Show your work for finding the buoyant force here: Show your work for finding the tension in the rope here:

Summarize: on the google form write a summary about what you learned from the video. Make sure to include; why you feel lighter in water, what causes the buoyant force and why some objects sink while others float.

Problems to try before class (show your work below) & type you answers into the google form where indicated. 1. What is the tension in the string in the figure to the right? 1. If boats are made with steel, which has a higher density then water, why do they float?


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Concepts 4 – 6 Learning Objectives: The continuity equation describes conservation of mass flow rate in fluids. Examples should include volume

rate of flow, mass flow rate.

The student is able to make calculations of quantities related to flow of a fluid, using mass

conservation principles (the continuity equation).

Bernoulli’s equation describes the conservation of energy in fluid flow. The student is able to use Bernoulli’s equation to make calculations related to a moving fluid. The student is able to use Bernoulli’s equation and/or the relationship between force and pressure to

make calculations related to a moving fluid.

The student is able to use Bernoulli’s equation and the continuity equation to make calculations related

to a moving fluid.

The student is able to construct an explanation of Bernoulli’s equation in terms of the conservation of

energy.



Questions:

What are the two types of fluid flow and how are they different?

What are the three assumptions that we will make for moving fluids?

What is volume rate of flow? What are the two equations that can be used to calculate it? What are the units of volume rate of flow?

Why does the velocity of a fluid increase when the cross sectional area decreases?

What is the equation of continuity?

For the hose problem (d1 = 2 cm v1= 4m/s, d2 = ?, v2 = 16 m/s) What is d2? Show your work below:


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What causes the fluid to speed up as it moves into the smaller section of pipe?

Fluid moves from a section of pipe with a large diameter to a section with a small diameter. Compare the velocity and pressure of the fluid in each section of pipe.

What is the Bernoulli effect and how does it explain how roofs coming off in high winds?

Summarize: on the google form write a summary about what you learned from the video. Make sure to include; volume flow rate and the equation of continuity and why we need to assume that fluids are incompressible for these concepts to apply to moving fluids, also discuss velocity and pressure changes as a function of pipe cross sectional area and how this leads to the Bernoulli effect.

Problems to try before class (show your work below) & type you answers into the google form where indicated. 1. Water flowing through a 2.0 cm diameter pipe can fill a 300 L bathtub in 5.0 min. What is the speed of the water in the pipe? 2. Water flows through a garden hose that has a diameter of 2.50 cm at a speed of 5.25 m/s. What is the speed of the water when it spurts out of a nozzle that has a diameter of 0.120 cm?


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Questions:

What causes work to be done on a moving fluid?

What is the equation for work in terms of pressure?

In a horizontal pipe what type of energy does the work create?

What is the equation of kinetic energy of a fluid of a known density, but not known mass

What is the equation for gravitational potential energy of a fluid be written for a fluid of a known density, but not known mass

Write the equation for Work = K + Ug in terms of the variables Pressure, density, velocity, height, etc.

Write Bernoulli’s equation (the rearranged equation of above)

Work out the problem from the video here. Show all work!

What are the two criteria that must exist in order to use Torricelli’s Theorem?


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What is the equation for Torricelli’s Theorem and what are some example situations that you could use it to solve for fluid exit speed?

Summarize: on the google form write a summary about what you learned from the video. Make sure to include; How Bernoulli’s equation was derived (what concept is it derived from), the assumptions we must make about the fluid in order to use it and what Torricelli’s theorem is and what types of situations it is useful for.

Problems to try before class (show your work below) & type you answers into the google form where indicated.

1. What does the top pressure gauge in the figure to the right read (oil = 900 kg/m3)?

In Class Work

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Concept 1 – 2: In class problems:

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4. Rank in order, from largest to smallest, the pressure pA to pF in the container shown to the right.

Order: Explanation:

5. Rank in order, from largest to smallest, the pressure pA to pD in containers A through D at the depths indicated by the dashed line.

Order: Explanation:

6. A and B are rectangular tanks full of water. The have equal depths, equal

thicknesses (the dimension into the page) but different widths. a. Compare the forces the water exerts on the bottoms of the tanks. If FA large

than, smaller than, or equal to FB? Explain.

b. Compare he forces the water exerts on the sides of the tanks. Is FA larger than, smaller than, or equal to FB? Explain.

7. In the figure to the right is pA large than, smaller than or equal to pB? Explain. 8. The figure shows a manometer like that in Figure 13.10 of your book, but the height of the

liquid is higher on the left side than on the right. Is this possible? If not why not? If so what can you say about the gas pressure in the tank?

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9. A submarine in the Pacific Ocean cruises along at a depth of 678 m. If the density of sea water is 1025 kg/m3 a. Find the absolute pressure on the sub

b. Find the force exerted by the water on a hatch that measures 1.00 m by 1.50 m. 10. You can trap liquid in a drinking straw by placing the tip of your finger over the top while the straw is in the liquid,

and then lifting it out. The liquid runs out when you release your finger. a. What is the net force on the cylinder of trapped liquid?

b. Three forces act on the trapped liquid. Draw and label all three on the figure.

c. Is the gas pressure inside the straw, between the liquid and your finger, greater than, less than, or equal to atmospheric pressure? Explain, basing your explanation on your answers to parts a and b.

d. If your answer to part c was “greater” or less” how did the pressure change from the atmospheric pressure that was present when you placed your finger over the top of the straw?

11. How could you use a barometer to measure the height of a tall building? What assumptions would you have to

make for your measurement to be valid?

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12. (AP 2004B2). While exploring a sunken ocean liner, the principal researcher found the absolute pressure on the robot observation submarine at the level of the ship to be about 413 atmospheres. The density of seawater is 1025 kg/m3 . a. Calculate the gauge pressure on the sunken ocean liner. b. Calculate the depth D of the sunken ocean liner.

c. Calculate the magnitude F of the force due to the water on a viewing port of the submarine at this depth if the

viewing port has a surface area of 0.0100 m2.

Suppose that the ocean liner came to rest at the surface of the ocean before it started to sink. Due to the resistance of the seawater, the sinking ocean liner then reached a terminal velocity of 10.0 m/s after falling for 30.0 s. d. Determine the magnitude a of the average acceleration of the ocean liner during this period of time.

e. Assuming the acceleration was constant, calculate the distance d below the surface at which the ocean liner reached this terminal velocity.

f. Calculate the time t it took the ocean liner to sink from the surface to the bottom of the ocean.

In Class Work

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Concept 3: In class problems: 13. A cubical block is observed to float in a beaker of water. The block is then held near the

center of the beaker as shown and released. a. Describe the motion of the block after it is released.

b. In the space provided, draw a free-body diagram for the block before it is released and for the block the instant it is released. Show the forces the water exerts on each of the surfaces of the block separately. Make sure the label for each force indicates: - the type of force, - the object on which the force is exerted, and – the object exerting the force.

c. Rank the magnitude of the vertical forces in each free body diagram. i. Before it is released

ii. The instant is released

d. Did the relationship between pressure and depth effect the magnitudes of any of the vertical forces? If so how?

e. In the box at the right, draw an arrow to represent the vector sum of the forces exerted on the block by the surrounding water. How did you determine the direction? Is this the net force on the block?

f. Is the magnitude of the sum of the forces exerted on the block by the water greater than, less than, or equal to the weight of the block? Explain.

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14. The experiment above is repeated with a second block that has the same volume and shape

as the original block. However, this block is observed to sink in the water. a. In the space provided, draw a free-body diagram for the block before it is released and

for the block the instant it is released. Show the forces the water exerts on each of the surfaces of the block separately. Make sure the label for each force indicates: - the type of force, - the object on which the force is exerted, and – the object exerting the force.

b. Compare the free body diagram for the block that sinks to the one you drew in the previous problem for

the block that floats. Which forces are the same in magnitude and which are different?

c. Do any forces appear on one diagram but not on the other?

d. In the box at the right, draw an arrow to represent the vector sum of the forces exerted on the block by the surrounding water. How does this vector compare to the one you drew for the block that floats? (consider both magnitude and direction)

e. Imagine that you were to release the sinking block at a much greater depth. State whether each of the following forces on the block would be greater than, less than, or equal to the corresponding forces on the block above.

i. The upward force on the bottom surface of the block

ii. The downward force on the top surface of the block.

iii. The vector sum of the forces on the block by the surrounding water.

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15. In general, does the buoyant force on an object that is completely submerged in an incompressible liquid depend on: a. The mass or weight of the object? Explain.

b. The depth below the surface at which the object is located? Explain.

c. The volume of the object? Explain. 16. Consider two blocks of the same size and shape: one made of aluminum; the other of brass. Both blocks sink in

water. The aluminum block is placed in a graduated cylinder containing water. The volume reading increases by 3 mL. a. By how much does the volume reading increase when the brass block is placed in the cylinder? Explain.

b. Does the volume of water displaced by a completely submerged object depend on i. The mass or weight of the object? Explain.

ii. The depth below the surface at which the object is located? Explain.

iii. The volume of the object? Explain.

iv. The shape of the object? Explain.

17. What is Archimedes’ Principle: 18. Consider the following statement made by a student:

“Archimedes’ principle simply means that the weight of the water displaced by an object is equal to the weight of the object itself.”

Do you agree with the student? Explain.

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19.

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20. Three blocks of identical size, A, B and C, are to be gently placed into a large tank of water. Bock A has a

density of 2 g/cm3, block B has a density of 0.9 g/cm3, and block C has a density of 0.5 g/cm3. On the figure, draw and label each block in its final equilibrium in the water.

21. Rank in order, from the largest to smallest, the densities of blocks A, B, and C.

Order: Explanation:

22. Blocks A, B, and C have the same volume. Rank in order, from largest to smallest, the sizes of the buoyant forces FA, FB, FC on A, B, and C. Order: Explanation:

23. You need to determine the density of a ceramic statue. If you suspend it from a spring scale, the scale reads

28.4 N. If you then lower the statue into a tub of water so that it is completely submerged, the scale reads 17.0N. What is the density of the statue?

24. What is the (a) buoyant force acting on a cube of copper that measures 2.00 cm on its each side if it is immersed in a beaker of water?

(b) the apparent weight of the cube if it is resting on the bottom of the beaker? (density of copper: 8.9 x 103 kg/m3)

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25. A solid sphere has a radius of 15.0 cm and a mass of 1.05 kg. It sinks to the bottom of the ocean to a depth of

9,550 m. (a) Draw a FBD on the circle to the right showing all the forces acting on the ball at this depth. (b) What is the pressure experienced by the ball at that depth due to the water? (c) What is the force exerted on the surface of the ball by the water. (d) What is the buoyant force acting on the ball? 26. A fishing line is attached to one of those bobber deals that is 5.00 cm in diameter and has a mass of 5.00 g. A

lead weight is attached to the line. What is the mass of the lead if the bobber is floating half submerged?

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27. (AP 2005B5) A large rectangular raft (density 650 kg/m3) is floating on a lake. The surface area of the top of the

raft is 8.2 m2 and its volume is 1.80 m3. The density of the lake water is 1000 kg/m3. a. Calculate the height h of the portion of the raft that is above the surrounding water. b. Calculate the magnitude of the buoyant force on the raft and state its direction. c. If the average mass of a person is 75 kg, calculate the maximum number of people that can be on the raft without the top of the raft sinking below the surface of the water. (Assume that the people are evenly distributed on the raft.)

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28. (2010 Form B # 6) An object is suspended from a spring scale first in air, then in water, as shown in the figure

above. The spring scale reading in air is 17.8 N, and the spring scale reading when the object is completely

submerged in water is 16.2 N. The density of water is 1000 kg/ m3 .

(a) Calculate the buoyant force on the object when it is in the water.

(b) Calculate the volume of the object.

(c) Calculate the density of the object.

(d) Explain how the absolute pressure at the bottom of the water change if the object was removed?

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29. (AP 2010B2) A large pan is filled to the top with oil of density O . A plastic cup of mass mC ,

containing a sample of known mass mS, is placed in the oil so that the cup and sample float, as

shown above. The oil that overflows from the pan is collected, and its volume is measured. The

procedure is repeated with a variety of samples of different mass, and the pan is refilled each

time.

(a) On the dot below that represents the cup-sample system, draw and label the forces (not components) that act on

the system when it is floating on the surface of the oil.

(b) Derive an expression for the overflow volume VO (the volume of oil that overflows due to the floating system) in

terms of O, mC , mS, and fundamental constants. If you need to draw anything other than what you have shown in

part (a) to assist in your solution, use the space below. Do NOT add anything to the figure in part (a).

Assume that the following data are obtained for the overflow volume VO for several sample masses mS . Sample mass mS (kg)

0.020

0.030

0.040

0.050

0.060

0.070

Overflow volume V0 (m3)

29x10-6

38x10-6

54x10-6

62x10-6

76x10-6

84x10-6

(c) Graph the data on the axes below, plotting the overflow volume as a function of sample mass. Place numbers and units on both axes. Draw a straight line that best represents the data.

(d) Use the slope of the best-fit line to calculate the density of the oil.

(e) What is the physical significance of the intercept of your line with the vertical axis

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Concept 4-5: In class problems: volume rate of flow/equation of continuity 30. A stream flows from left to right through the constant-depth channel shown below in an overhead view. A 1 m

x 1m grid has been added to facilitate measurement. The fluids flow speed at A is 2 m/s.

a. Shade in squares to represent the water that has flowed past point A in the last two seconds. b. Shad in squares to represent the water that has flowed past point B in the last two seconds. Explain why

you shaded that many squares. 31. A stream of water gets narrower as it falls from a faucet. Explain this phenomenon using the equation

of continuity. 32. Water flows through a rubber hose that is 2.85 cm in diameter. If the hose is coupled into a nozzle that has a

diameter of 0.450 cm where its velocity is 135 m/s, what is its velocity in the hose?

33. For an incompressible fluid, the volume flow rate must stay constant due to the law of conservation of mass. So what happens when a pipe splits? a. Starting with the volume rate equation (Volume/time), write an equation in terms of area and

velocity for fluid starting at point A and splitting into pipes B and C. (you will need this for question 39 below)

b. How does the velocity in pipe B change if pipe C is plugged so water can’t flow through it?

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Bernoulli Effect: 34. Liquid flows through a tube whose width varies as shown to the right. The

liquid level is shown for pipe A, which is open at the top, but not for pipes B and C. Draw an appropriate level of liquid in pipes B and C to indicate the fluid pressures at those points.

35. Gas flows through a pipe. You can’t see into the pipe to know how the inner diameter changes. Rank in order, from largest to smallest, the gas speeds v1 to v3 at points 1, 2, and 3.

Order: Explain:

36. For the Venturi tube shown to the right.

a. Compare the velocity in the first section of pipe (between 1 and 2) to the velocity in the second section of pipe (between 3 and 4). Explain this result using concepts you have learned in the video.

b. Write a short paragraph explaining why the liquid is higher in the vertical pipes in the first second of pipe compared to the later section.

c. In the vertical pipes, why does d1 = d2 and d3 = d4? 37. Wind blows over a house. A window on the ground floor is open.

a. Is there an air flow through the house? If so, does the air flow in the window and out the chimney, or in the chimney and out the window? Explain.

b. What quantities would you need to know in order to calculate the lift force on the roof?

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38. This is a cross sectional view of an airplane wing (with streamline patterns of air above and below the wing). a. Why are wings shaped this way?

b. Explain lift on an airplane wing in terms of Bernoulli’s effect.

c. Explain lift on an airplane wing in terms of Newton’s third law. 39. Using what you know about the Bernoulli Effect, draw the direction of the force of the wind on the sail. A keel

is a board that projects into the water below the boat (see picture to the right). What is the role of the keel and why can it be smaller than the sail and still perform its function??

The long, white board on the right-hand side of the picture is the keel. Normally you don't see the keel since it's underwater.

Concepts 6. Flowing Fluids: Bernoulli’s Equation

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Concept 6: In class problems: 40. In the video I said that gaining elevation should also result in the reduction in pressure. Explain why? 41. Why can’t you use the hydrostatic pressure equation from video 1 to solve for pressure in moving fluids? (take

a look at Bernoulli’s equation and see if you see a component that resembles it)

42. The 3.0 cm diameter water line in the figure to the right splits into two 1.0 cm diameter pipes. All pipes are circular and at the same elevation. At point A, the water speed is 2.0 m/s. a. What is the water speed at point B?

b. If the gauge pressure at point A is 50 kPa, what is the gauge pressure at point B? 43. (AP2008B4) A drinking fountain projects water at an initial angle of 50° above the

horizontal, and the water reaches a maximum height of 0.150 m above the point of exit. Assume air resistance is negligible. a. Calculate the speed at which the water leaves the fountain.

b. The radius of the fountain's exit hole is 4.00 x 10-3 m. Calculate the volume rate of flow of the water.

c. The fountain is fed by a pipe that at one point has a radius of 7.00 x 10-3 m and is 3.00 m below the fountain's opening. The density of water is 1.0 x 103 kg/m3. Calculate the gauge pressure in the feeder pipe at this point.


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44. (AP2008Bformb4) A fountain with an opening of radius 0.015 m shoots a stream of water vertically from ground level at 6.0 m/s . The density of water is 1000 kg/m3 a. Calculate the volume rate of flow of water.

b. The fountain is fed by a pipe that at one point has a radius of 0.025 m and is 2.5 m below the fountain's opening. Calculate the absolute pressure in the pipe at this point.

c. The fountain owner wants to launch the water 4.0 m into the air with the same volume flow rate. A nozzle can be attached to change the size of the opening. Calculate the radius needed on this new nozzle.

45. (AP2009Bformb3) An underground pipe carries water of density 1000 kg/m3

to a fountain at ground level, as shown to the right. At point A, 0.50 m below ground level, the pipe has a cross-sectional area of 1.0x10-4 m2. At ground level, the pipe has a cross-sectional area of 0.50x10-4 m2. The water leaves the pipe at point B at a speed of 8.2 m/s. a. Calculate the speed of the water in the pipe at point A.

b. Calculate the absolute water pressure in the pipe at point A.

c. Calculate the maximum height above the ground that the water reaches upon leaving the pipe vertically at ground level, assuming air resistance is negligible.

d. Calculate the horizontal distance from the pipe that is reached by water exiting the pipe at 60o from the level ground, assuming air resistance is negligible.


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46. (AP2005Bformb5) A large tank, 25 m in height and open at the top, is completely filled with saltwater (density 1025 kg/m3). A small drain plug with a cross-sectional area of 4.0 x 10-5 m2 is located 5.0 m from the bottom of the tank. The plug breaks loose from the tank, and water flows from the drain. a. Calculate the force exerted by the water on the plug before the plug

breaks free.

b. Calculate the speed of the water as it leaves the hole in the side of the tank.

c. Calculate the volume flow rate of the water from the hole. 47. (AP2007formb4) A cylindrical tank containing water of density 1000 kg/m3 is filled

to a height of 0.70 m and placed on a stand as shown in the cross section above. A hole of radius 0.0010 m in the bottom of the tank is opened. Water then flows through the hole and through an opening in the stand and is collected in a tray 0.30 m below the hole. At the same time, water is added to the tank at an appropriate rate so that the water level in the tank remains constant. a. Calculate the speed at which the water flows out from the hole.

b. Calculate the volume rate at which water flows out from the hole.

c. Calculate the volume of water collected in the tray in t = 2.0 minutes.

d. Calculate the time it takes for a given droplet of water to fall 0.25 m from the hole.

AP Physics 2 Unit 1. Fluids Practice Questions

(answers at end of multiple choice questions)

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1. In the figure to the right, fluid fills the container as shown above. At which of the

indicated points is the pressure the greatest? a. A b. B c. C d. D e. E

2. A cart full of water travels horizontally on a frictionless track with initial velocity v.

As shown in the diagram, in the back wall of the cart there is a small opening near the bottom of the wall that allows water to stream out. Considering just the cart itself (and not the water inside it), which of the following most accurately describes the characteristics of the cart? Speed Kinetic Energy (A) stays the same stays the same (B) increases increases (C) stays the same increases (D) increases stays the same

3. A student places several ice cubes in a glass and fills the glass with water. After the ice cubes

melt, will the water level in the glass

(A) rise a small amount

(B) fall a small amount

(C) remain at the same level

(D) not enough information given 4. A 4.0 kg solid sphere, made of a metal whose density is 4000 kg/m3, is suspended by a cord. The density of

water is 1000 kg/m3. When the sphere is completely submerged in the water, the tension in the cord is closest to: a. 50 N b. 0 N c. 40 N d. 30 N e. 20N

5. A vertical cylinder attached to the ground is partially evacuated to a pressure of 10,000 Pa by a

vacuum pump. An airtight lid of radius 5 cm and mass 400 g is placed on its top. A rope is tied to

the lid and a force of 800N vertically upward is applied. Which of the following best describes the

result of the force applied to the rope?

(A) The lid pops off the container and then accelerates upward at roughly 2000 m/s2.

(B) The lid pops off the container and then accelerates upward at roughly 220 m/s2.

(C) The lid pops off the container and then accelerates upward at roughly 0.23 m/s2.

(D) The entire container, with sealed lid, remains stationary.

AP Physics 2 Unit 1. Fluids Practice Questions

(answers at end of multiple choice questions)

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6. The Bernoulli Effect is responsible for the lift force on an airplane wing. Wings must therefore be designed so as to insure that

a. air molecules will be deflected upward when they hit the wing. b. wings are thick enough to create a significant pressure difference between the top and bottom surfaces of

the wings because of the different heights of these surfaces. c. air molecules move more rapidly past the lower surface of the wing than past the upper surface. d. air molecules move more rapidly past the upper surface of the wing than past the lower surface. e. air molecules will be deflected downward when they hit the wing.

7. Water flows through a section of thick piping with some velocity v as shown in the

diagram at right. Based on the diagram, in which direction would you expect water to

flow through the narrow section?

(A) to the right

(B) to the left

(C) remain stagnant

(D) not enough information given 8. Water flowing through a pipe suddenly comes to a section of pipe where the pipe diameter decreases to 5% of its previous value. If the speed of the water in the larger section of the pipe was 25 m/s, what is the speed in this smaller section?

a. 500 m/s b. 10,000 m/s c. 25 m/s d. 1.25 m/s e. 0.63 m/s

Use the scenario below to answer questions 9-10.

You have two identical large jugs with identical small holes on the side near the bottom. One jug is filled

with water (=1.0 g/cm3) and the other is filled with liquid mercury (=13.6 g/cm3). The jugs are sitting on

a table and liquid in each jug squirts into separate containers on the floor.

9. Which container must be closer to the table?

(A) The container catching water.

(B) The container catching mercury.

(C) The containers need to be same distance from the table.

10. Which container will empty more quickly? (Ignore viscosity.)

(A) The container catching water.

(B) The container catching mercury.

(C) The containers will empty at the same rate. Answers to Multiple choice: 1) e, 2) B, 3) C, 4) D, 5) B, 6) D, 7) A, 8) B, 9) C, 10) C

AP Physics 2 Answers to Numerical and Ranking Fluids Questions

34

4. A = B = C > D > F > E

5. All equal

6. a. A > B b. same

7. Equal

9. a) 6900 kPa b) 1.0 x 107 N

12. a) 412 atm (or 4.17 x 107 Pa) b) 4151 m c) 417,000 N d) 0.33 m/s2 e) 149 m f) 430 s

20.

21. A > C > B

22. Same

23. 2,500 kg/m3

24. a) 0.0784 N b) 0.619 N

25. b) Pgauge = 9.6 x 107 Pa or Ptotal = 9.7 x 107 Pa c) 2.7 x 107 N d) 142 N

26. 0.028 kg

27. a) 0.076 m b) 11,500 N up c) 8 people

28. a) 1.6 N b) 1.63 x 10-4 m3 c) 11,143 kg/m3 d) less

29. b) Vo = (ms+mc)/o d) inverse of slope so ~ 900 kg/m3 e) volume of oil displaced by cup

30.

32. 3.37 m/s

34.

35. 2 > 1 > 3

36. V1 < V2, P1 > P2

42. a) 9 m/s b) 11,500 Pa

43. a) 2.24 m/s b) 1.13 x 10-4 m3 /s c) 31,600 Pa

44. a) 0.004 m3/s b) 143, 000 Pa c) 0.012 m

45. a) 4.1 m/s b) 131,000 Pa c) 3.43 m d) 5.9 m

46) a) 12.1 N b) 20 m/s c) 7.9 x 10-4 m3/s

47) a) 3.7 m/s b) 1.16 x 10-5 m/s c) 0.0014 m3 d) 0.0624 s

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