Introduction
Fluid mechanics was added to the AP Physics B curriculum relatively recently, in 2002. Consequently, relatively few authentic AP fluids questions are available for classroom use. This Featured Question is similar in scope and difficulty to an AP Exam question.
The AP fluids curriculum includes four subtopics:
- Hydrostatic pressure
- Buoyancy
- Fluid flow continuity
- Bernoulli's equation
The first two of these deal with static fluids. Hydrostatic pressure has been the subject of two AP Physics B Exam questions in the past few years; buoyancy appeared in questions on both the 2002 and 2005 exams.
A common feature of the previous AP static fluids questions is that they combine fluids concepts with Newtonian mechanics. The addition of fluid mechanics to the AP curriculum presents teachers with an opportunity to communicate the cumulative nature of physics. AP students must be able to do more than simply recite the equations for hydrostatic pressure
(
) and buoyant force (
). They need to go beyond simply calculating a pressure or a force. AP-level students must carry over their fundamental knowledge of mechanics into the realm of fluids.
In particular, static-fluid questions tend to focus on static equilibrium. The added difficulty in a fluids question is that the buoyant force must be calculated from the weight of the displaced water. But the general problem-solving principles -- drawing a free-body diagram, setting the sum of the upward forces equal to the sum of the downward forces -- are the same as always.
The 2005 buoyancy question asked students to calculate the maximum number of people that a raft of given dimensions could hold. This Featured Question also involves a raft, but this time, weight is added to the raft from below. This situation provides an additional challenge: since the weights themselves are submerged, they also experience a buoyant force.
You can present this question to students in a variety of ways. The PDF "Five-Part Question" below can printed and used as a test or quiz question; the student is guided through a solution in five steps. This style is typical of an AP free-response question. Space is available for students to answer each part. Allot about 15 to 17 minutes for a cold approach to this question.
A simpler and more open-ended statement of the question is in the PDF titled "Open-Ended Question." I suggest using this statement as a homework assignment in which students have the opportunity to collaborate after their initial efforts. If you assign the question in this form, it becomes extraordinarily important to insist on a thorough presentation of the approach and reasoning used to get to the solution; a sample handwritten solution is included here as well.  Five-Part Question (.pdf/45KB)
Open-Ended Question (.pdf/26KB)
Sample Handwritten Solution (.pdf/137KB)
And finally, once students have had some time to grapple with the question, you can assign the follow-up quiz.
Click here to view the answers and commentary!
[Inspired by Douglas C. Giancoli, Physics: Principles with Applications, 5th ed., chapter 10, problem 32.]
Correlation to the Topic Outline in the Course Description
II.A.2. Fluid mechanics: Buoyancy (p. 16)
I.B.1. Newton's laws of motion: Static equilibrium (p. 15)
Greg Jacobs teaches AP Physics B and C at Woodberry Forest School in central Virginia. He is a graduate of Haverford College, and has a master's degree in engineering from Northwestern University. When he is not teaching, Greg broadcasts Woodberry Forest varsity baseball games over the Internet; he is a reporter for STATS, Inc., covering baseball, basketball, and football; and he is a Reader and consultant for the College Board's AP Physics program. Greg lives on campus at Woodberry with his wife Shari and their son Milo Cebu.
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