Survival Guide to Concourse PhysicsDavid Zych ’00Concourse tutor (Fall 1997 - Spring 2000)August 1999IntroductionThe purp ose of this document is to give you a clear picture of what we expect from you in Concourse Physics.When I was a Concourse student, very little of this was written down anywhere. I picked some things upby talking to the course staff, but I had to learn a lot by trial and error. I wrote the original version of thisdocument in the fall of 1997 as an email to the Concourse ’01 class, after I graded their first problem setand realized that they were confused about many of the same issues that had confused me during my ownfreshman year. I have since rewritten it, added more examples, and included several new pieces o f advicethat I have found myself dispensing fr equently over the past few years. The guide is a bit long, but that’sbecause I have tried to make it as clear as possible. I hope you will find it helpful.The Prose Requirement: How to Get Credit for Your SolutionsThe course syllabus emphasizes that your solutions to problems in the course are to be written up in coherentEnglish. This “prose requirement” is one of the defining characteristics of Concourse physics, and we takeit very seriously.This idea will be new for most of you, because it contrasts sharply with most high school physics classes.In high school, the objective was simply to get the a ns wer (usually by randomly throwing equations at theproblem until you find one that “works”). Here at MIT, the objective is to demonstrate to the grader thatyou unders tand how to solve the problem. You may assume that the grader is reasonably intelligent andknows physics. However, the grader cannot read your mind, so you must show your work and write proseto explain anything tha t is not clear about how you solved the problem. The grader sho uld never look atyour paper and wonder how you g ot from step 3 to step 4 – if it is not clear, then you a re not doing yourjob pro perly.Sample ProblemA b ox of mass 2 kg is pushed along a frictionless table with a force of 10 N. Find the accelera tion of the box.Acceptable Answer #1By Newton’s Second Law, the acceleration of the box isforce on boxmass of box. Thus a =10 N2 kg= 5ms2This is actually more prose than you need for a problem like this one, but it illustrates the kind o f thingyou might write in order to clarify how you went about solving the problem.Acceptable Answer #2a =Fm=10 N2 kg= 5ms2This is a more efficient solution to the same problem. It contains no actual English prose at all, butsince the first stepa =Fmis a well-known equation of physics, anyone re ading the solution can easily tell1that the problem is being solved using Newton’s Second Law. No further expla nation is necessary, becausenothing is unclear.An Insufficient Answera =10 N2 kg= 5ms2Here, it is not clear how the problem is being solved. A grader can justifiably ask, “How do you knowthat a =10 N2 kg? Where did you get that from?” Of course, in a simple problem such as this one, a gra dercould easily use his or her own problem-solving skills to figure out where that equation came from, but thepoint is that the grader should never have to figure out what you did; it should be obvious from readingyour solution.Distinguishing P hysics from MathematicsFrom our physics-centric point of view, mathematics is a tool (actually, a large collection of tools) that weuse to help us solve physics problems. The solution to a physics problem usually involves three distinctphases:1. Translate the pr oblem from physical language (physical quantities, verbal descriptions of what’s hap-pening in the problem, pictures, etc) to mathematical language (variables and equations).2. Use mathematics to manipulate the equations and solve for the values of a ny unknown variables.3. Translate the answer from mathematical language (the value of a va riable) back to physical language(a verbal statement about the physical situation).Phase 2 of this process involves only mathematics; it does not contain any physics at all. All of thephysics happens in phases 1 and 3. This doesn’t mean that you won’t spend a significant amount of timeon phase 2; in fact, for many problems you’ll spend most of your time on phase 2. What it does mean isthat you need to make a conscious effort to really pay attention to what goes on in pha ses 1 and 3 and tryto understand it; the ar t of problem so lving is subtle, and many students allow themselves to get so boggeddown in the details of the mathematics that they completely lose sight of the physics. Try not to let thishapp e n to you.Please note that the pros e requirement does not require you to explain every mathematical step of yoursolution – only the steps that req uire logical clarification. We assume that you understand algebra by now,and it would be a colossal waste of everyone’s time (yours and the grader’s) to have you write out prosefragments such as “now multiply both sides of the equation by 3.” Once you have written down an equation,you may algebraically transfo rm it as much as you like w ithout any further explanation. Just be s ure thatyou adequa tely explain how you got the first equation; that’s the physics part of the problem.ExampleA boulder is falling from a high cliff (neglect air resistance). At time t = 0, its velocity is 7 m/s downwardand it is 500 m above the ground. Find the time t at which the boulder is 150 m above the gr ound.SolutionLet y be the height of the boulder above the ground.y = y0+ v0t +12at2(A)(150 m) = (500 m) + (−7ms)t +12(−9.8ms2)t2(B)t = 7.8 s (C)2So the boulder is 1 50 m above the gro und at time t = 7.8 seconds.First we write down the general form of the equation we want to use as our mathematical model (A).Next, we incorporate the details of the physical problem into the model (B). Using algebra, we solve thisequation fo r the variable that represents the quantity we’re interested in (C). Finally, we translate ourmathematical solution into a physical statement that answers the question posed by the problem.You’ve probably noticed that this solution does not include any of the intermediate algebraic steps neededto get from (B) to (C). Including these intermediate steps in your own solutions is pr obably a good idea,because it will greatly reduce the frequency of careless mistakes in your answers; however, the omitted stepsare not strictly necessary from a physics point of view, so the
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