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|  | Fluids on the AP Physics B Exam
Beginning in 2002, the AP Physics B Examination began to include fluid dynamics questions. According to the current AP Physics B Course Description, the following topics may be tested.
II. A. Fluid Mechanics 6%
- Hydrostatic Pressure
and
- Buoyancy
- Fluid Flow Continuity A1v1 = A2 v2
- Bernoulli's Equation
A close examination of the appearance of these topics on previously released free-response questions may be instructive. The table below maps the appearance of fluids on the AP Physics B Exam since 2002, including the number of points assigned to particular concepts.
| Year |
Question |
Pressure |
Buoyancy |
Flow |
Bernoulli |
| 2002 |
B6 |
|
b(2), c, d(5) |
|
|
| 2002 Form B |
N/A |
|
|
|
|
| 2003 |
B6 |
a(2), b(1) |
c(5) |
|
|
| 2003 Form B |
B6 |
|
|
bi(3) |
bii(2) |
| 2004 |
B2 |
a(2), b(3), c(2) |
|
|
|
| 2004 Form B |
B2 |
b(3), c(3), d(3), e(2) |
|
|
|
|
Note that this analysis includes only free-response questions, as no multiple-choice questions have been released within this time frame. All of the above questions as well as their solutions are available on the Physics B Exam Questions page.
 The Physics B Exam
The main impetus of each of these questions is summarized below:
2002: Find the density of a liquid using a spring scale and a submerged object of known volume.
2002B: (Not applicable)
2003: Calculate gauge and absolute pressure, as well as the tension needed to lift a submerged object.
2003B: Calculate fluid speed in a pipe and the pressure at the end of the pipe at a different elevation.
2004: Calculate gauge and absolute pressure, as well as the force on an underwater window.
2004B: Calculate gauge and absolute pressure, as well as the force needed to open an underwater hatch.
This survey reveals that all of these topics have been tested in some form on either Form A or Form B of the AP Physics B Exam. However, no single question has ever addressed all of these topics. The question that follows is an attempt to include all the major concepts of fluid dynamics in one (rather convoluted) question. It is presented as a tool for instructors to use at the end of the fluid dynamics unit in order to assess student understanding and to hopefully encourage a "deep" discussion of this topic.
A Study in Fluids
Gil is a perfectly spherical fish bred specifically for use in physics problems. Gil has a mass of 33.5 kg. By inflating and deflating his air bladder, Gil has the ability to change his volume within certain limits. His mass does not change appreciably during these volume changes. Gil sleeps in a small cylindrical chamber that is connected to a larger chamber by a tapering passageway. The walls of both chambers are aluminum (shown here as transparent for clarity) with a small glass window (diameter = 0.4 m) in the larger chamber. Both chambers are sealed by large (thin) floating weights that can move up and down the cylinders as their respective water levels change. Gil is initially 5 m from the bottom of the smaller cylinder.
(A) Both tanks are filled with water (p = 1000 kg/m3). The small weight has a mass of 10,000 kg and a radius of 2 m. The large weight has a mass of 2,000,000 kg (yes, it's a LARGE weight) and a radius of 10 m. If the water level in the small cylinder is 15 m from the floor, what is the water level in the large cylinder? The system is in equilibrium.
(B) Gil adjusts his position in the tank by changing the amount of air in his air bladder (and thus changes his volume). What must Gil's radius be in order for him to remain stationary in the water tank?
(C) Gil wants to rise to the top of his tank. If he doubles his radius, what will his resultant acceleration be? The frictional force between Gil and the water can be neglected.
(D) How long will it take for Gil to strike the floating weight at the top of his tank? Ignore the effects of friction and turbulence. What will be his speed at this time?
(E) In order to conduct an experiment, a scientist wishes to force Gil into the larger tank. She accomplishes this by adding an additional 63,000 kg weight to the smaller cylinder. Qualitatively describe the acceleration and speed experienced by the small disk as it descends.
(F) Calculate the initial accelerations of both the small and large weights at the moment that the 63,000 kg mass is added. Are these two values the same? Why or why not?
(G) What will the water level of each tank be when equilibrium is once again reached?
(H) Gil is carried along by flowing water and forced into the large tank. If Gil enters the wider end of the connecting passageway (rpassage = 2 m) with a speed of 3.2 m/s, with what speed will he enter the large tank (rpassage = 0.5 m)? Gil is too lazy to do anything to affect this motion.
(I) Some time later Gil wanders over to the window in the large tank. What is the average pressure being exerted by the water on the 0.4 m diameter window?
(J) The window will shatter when subjected to a force of 150,000 N. How much force must Gil apply in order to shatter the window?
(K) Once the glass shatters, water begins to exit the large tank. Assuming that the water in the tank is moving very slowly, with what speed does water exit the tank?
(L) How far from the base of the large tank does Gil strike the floor?
(M) Before exiting the tank, the pressure inside Gil's body was equal to the pressure of the water in the tank. How much force must be exerted by Gil's body to maintain his structural integrity? Assume that the force is applied at the outside surface of Gil's body. Use the radius calculated in part (B).
Click here to view the answers and commentary!
David Castro taught AP Physics (B and C), AP Calculus (AB and BC), and AP U.S. and European History in a teaching career spanning 14 years, including 5 years as a master AP Physics teacher. In 1997, he received a Special Recognition Teaching Award, and in 2002 his combined AP Physics and AP Calculus syllabus was published in the AP Physics Teacher's Guide. Active as an AP Physics consultant in the Southwest Region since 1995, his areas of expertise include Pre-AP middle school science, AP Vertical Teams, as well as interdisciplinary physics/calculus. He also serves as a Reader for AP Physics. Mr. Castro recently joined the Charles A. Dana Center at the University of Texas, where he continues to focus on providing support for science educators.
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