PROBLEM SOLVING SUGGESTIONS

CF - Convert Givens to SI Units First.

If you convert the values given into the correct SI units at the start of the problem, then any subsequent answer you find - for any variable - will automatically have correct SI units for that variable. See UX for a table of SI units. When a problem has several parts, this procedure saves time since you will not need to convert the answer you find in each part to SI units separately. Moreover, it is usually mathematical-ly easier to convert the values given, rather than the final answers. The units of the final an-swer are usually a more complicated mathematical expression of units than those of the units given.

DHW - Done a Hard Way.

Your answer is correct, but the method you have used is not the easiest way to solve this type of problem. You have overlooked something useful. There is a simpler way that is shorter and less complicated.

DOW - Done an Old Way.

Although the method you are using is correct, you missed a chance to delve into the relevant physics in this section and use it to solve this problem. You do not need to use your method to solve this problem. Note that when I construct an exam question (to test your understanding of the physics principle involved in this part of the book) I always make sure that the question can not be solved by the old method. I purposely chose a problem that could be solved by a prior method so that you could cross correlate the two methods if you had difficulty understanding the current principles involved.

DS - Draw Sketch or Picture."One sketch is worth a thousand words".

Make a sketch that reflects, schematically, the process and the data given in the problem. Making a sketch is an important or-ganizational aide in casting the problem into a visual structure that summarizes - at a glance - all the relevant information that you need to solve the problem.

MU - Method Unorganized.

Your solution is too slapdash and unorganized. As the problems get more difficult, your lack of a systematic approach will get you into trouble even if you are able to find the correct answers to this question. While the problems are still relatively sim-ple, practice putting more structure into the way you write down and solve prob-lems. The rest of the "PROBLEM SOLVING SUGGESTIONS" contain techniques that can help you put more order into your solutions. Also see the "Problem Solving Overhead Notes"

LG&U - Label the Givens and Unknowns.

Every quantity you handle in a problem needs a tag to distinguish it from other quan-tities. This is especially true if there are several quantities that are similar. A good example is the applied force Fapp, the force of friction Ff, the centripetal force Fc, the gravitational force Fg = mg, and the net force Fnet; no two of which are the same force. The quandary is that they are sometimes equal to each other and you can get away with not distinguishing them separately. For example, in a frictionless free-fall problem the Fnet and force of gravity Fg = mg are equal to each other but nonetheless they are not identical and should have separate labels to specify which is which. As the problems get more complex, labeling every quantity you manipulate becomes indispensable. Memory retention experiments have shown that the maximum number of variables an average person can keep track of in memory is seven. My advice is to select symbols for all quantities given or requested. Write down your symbols on a sketch of the problem at the appropriate locations were they occur in this problem along with the values stated; like v1= 3.20 m/s or TA = 13.5oC. For the unknowns, you might write something like "x = ?" or just "x = " to indicate that the value of this quantity is one of the values what you are looking for in this problem.

SE&O - Separate Equations and Operations.

In order to save time and/or steps, one sometimes combines an equation and the operations needed to solve that equation into a single step. Often time, what results is a mathematically incorrect equation. For example, the following equation can not be correct, There is no way that 360 meters can equal to 12 seconds. The intention was to solve the equation, 360m = (30m/s)t , for the time t; which does equal to 12s when solved. The correct steps should be If you practice carrying out operations on an equation that makes the resulting equation incorrect, then eventually you will get into trouble. You will not be able to sort out any mistakes you may have made in writing down the equation from any mistakes you may have made while trying to solve the equation. It is hard (if not impossible) to discover any mistakes in an equation that is itself mathematical-ly incorrect be-cause of some operation you performed on the equation that might or might not have been correct when you first wrote it down. It is okay to perform operations, but make sure that at each step, the expression you generate is itself mathematically correct.

WEF - Write Down Equations First.

When solving a problem it is best to write down the equation you are using in sym-bolic form first, and then set about solving for the unknown requested. At the begin-ning of your solution, it is always helpful to express the principles of physics you are using as a mathematical equation (using the symbols you have selected to represent the given and unknowns). This technique is useful because it shows you - at a glance - what you have assumed are true about the question. Later you can re-read the ques-tion again to see if what you wrote down is consistent with what is explicitly stated in the problem. Note that if you can not get the answer in brackets, then adding more steps is indispensable since will help me pin point the location of any error.

UMS - Use More Steps.

If you add more intermediate steps to your solution you might be able to detect if you are making any errors. One advantage of using more steps is that you will be able to explicitly look back at your prior reasoning since it is written down. All I can deduce is that you made some error between the last term/expression/equation you wrote down, and this term/expression/equation.

ACME - Answer Correct, Method Erroneous.

The numerical value of your answer is correct. Unfortunately, the procedure you using to arrive at the answer is incorrect. Getting the correct answer is not the main objective of the homework. The primary intent is to enable you to construct/establish your own personal, conceptual model of the underlying physics involved. This personal understanding will allow you to solve similar problems. The method you used will only work in the special circumstances of this problem and will probably not work on even a closely related problem. (The trouble is that it sometimes works and sometime does not work.) There is much to be gained from figuring out the error in your reason-ing, and how to revise your personal understanding to fit this situation. In gen-eral I have found this type of error to be most creative and unique. Some examples that I have come across are:

AOK - Algebra OK to this Point.

I can find nothing wrong with your algebra/math up the point were I placed the "AOK", but the next step or answer is incorrect. It is most likely that your error occurred from ether:

AEC - Algebraic Errors Cancel Out.

The numerical value of your answer is correct. However, you have made two (or more) different algebraic errors that have by chance canceled each other out so that you obtained the correct answer by happenstance.

CC - Confusing Two Different Concepts.

You have mixed up one physical principle with a different principle such as:

CE - Confusing Two Different Events.

You are getting the value of some variable at two different times mixed up with each other. Try labeling the variable more carefully so that it clearly reflects the time of occurrence such as:

CUE - Conversion of Units Error.

Something has gone wrong in the method you are using for the conversion of the "units given" in the question and those needed, normally SI units. There is a list of conversion factors that may be helpful inside the back cover of the text book.

CQ - Confusing Two Different Quantities.

You have not clearly distinguished the difference between two quantities that are related but are not the same. Being related does not signify that two quantities are equivalent; they may be intimately connected, but they can not be interchanged with each other.

/= means not equal to

DPE - Decimal Point Error.

Your answer is basically correct except for the location of the decimal point. Its location is off because:

LX - Logic Error.

Spock (of Star Trek fame) would say:

HE - Heat Errors.

EX - Equation Incorrect.

There is something wrong with the equation you are using to solve this problem. There is a summary of the important equations at the end of each chapter.

ME - Magic Equation.

The equation you are using does give the correct answer, but you need to show how you arrived at this equation from the fundamental principles and equations in this chapter. Your method shows little understanding of the underlying physics involved. The only credit it deserves is for ingenuity in finding an equation that will give the correct answer.

MS - Magic Step.

There is no way that I can see that you could logically make this step. This step follows from something significant that you're missing. It is important to your personal, conceptual understanding to discern the rationale behind this step. You need to justify this step. I don't think you could have obtained the correct answer without using the answers in "{...}". If you had put down the steps that lead you to an answer, even if you know that this answer is incorrect, I could have located the origin of your misunderstanding. Getting the correct answer is not the ultimate goal of a homework question; understanding how to apply the principles of physics relevant to this question should be paramount goal if you want to appreciate the physics that applies to this question.

MOK - Method OK, Answer Incorrect.

The method/procedure you are using looks correct, but your answer is incorrect because the value you are using as a given (in this part of the problem) is incorrect:

PS - Psychic Synchronization.

The structure of your solution is too close to that of the other student designated. Unless you are psychically connected with this student, there is no way I can see how both of your solutions could be so much alike. Starting with the same principles, no two individuals would follow the same exact steps any more than any two people would sweep a floor identically. In this problem, you both have made the same type of "novel error" that called my attention to the similarities of both of your homework solutions. In addition to this most unique error, the architecture of the other steps you have taken to solve this homework problem are nearly identical. Studying and working together is encouraged, but this does not mean being in locked step. It has been my experience that no two students do things exactly the same way, even when they get the same answer. Exchanging ideas and information about the principles involved in physics problems does not mean that your own personal approach - down to last detail - will be identical to every other student's approach. It is my judgment that somebody is coping somebody else's work or, at the very least, giving too much detailed assistance. Who, I do not know? Thus I am giving you each half credit. If you want to discuss this, I will be glad to listen to your point of view. Come by and talk. Moreover, you are not allowed to set near each other on the next exam.

RE - Round Off Error.

You have not rounded your results off correctly. Look at both the fourth and fifth significant figure to see if the remainder after the third significant figure is greater than 1/2 of that location, i.e., to see if the 4 SF is greater than 5.

SCX - Special Case Does Not Apply.

The equation you are using to solve this problem pertains to a special case of this type of problem, but it does not apply to the specific conditions of this problem. It might help if you start with the more general form of the equations, and then transform them to into the particular equation you need to solve this homework problem.

SF - Significant Figure Problem.

For no good reason other than the need to agree on some standard degree of accuracy in this class, the answers in this class are required to be correct to three significant figures, 3 SF. This represents an accuracy of about 1%. Unless otherwise instructed, you need to express the answer to each question correctly to 3 SF. The givens in the problems will generally be written down explicitly to 3 SF. If not, assume the accuracy for values given in a question to be to 3 SF unless otherwise stated.

SXQ - Solved for the Wrong Quantity.

You have found a physical variable, but is not the unknown requested by the problem. The quantity you found may be correct, but it is not the answer to the question asked. I can not give you full credit even if your answer is correct. One technique that can help prevent this type of confusion is to reread/scan the question over again carefully after you have finished solving for some quantity and ask yourself "Is what I have found, what the question asked requested ?".

TX - Trigonometric Error.

There is an error in the way you are dealing with the vector quantities in this problem.

UX - Answer's Units are Incorrect.

The units indicated are incompatible with those expected. Unless otherwise requested, your answer's units should be one of the following SI units: > >
QUANTITY SI UNITS QUANTITY SI UNITS
Distance, Position m = meters Time, Period s = sec = seconds
Speed, Velocity m/s Acceleration m/s2
Mass kg = kilogram Force, Weight N = Newton=kg-m/s2
Work, Energy, Heat J = Joule = N-m 1 cal =4.186 J Power W = Watts = J/s
Momentum, Impulse N-s = kg-m/s2
Density kg/m3 Pressure Pa = Pascal = N/m2
Volume 1 m3 = 1000 liters Area m2
Angle rad = radians Angular velocity rad/s
Torque N-m Angular accel. rad/s2
Moment of Inertia kg-m2 Ang. Momentum, kg-m2/s
Charge C=Coul = Coulomb Current A = Amps = C/s
Electric Field N/C = V/m Electric Potential V = Volts = J/C
Resistance Omega = Ohms = V/A Capacitance F = Farad = C/V
Magnetic Field T=Tesla= 104Gauss Inductance H = Henry = V-s/A
Temperature K = Kelvin Entropy J/K
Frequency Hz = Hertz = 1/s

UP - Units Prefix Problem.

There is a discrepancy in your use of a prefix notation as an abbreviation for a power of ten.

UP2: Your answer is correct, but you can not use both a prefix and its equivalent power of ten at the same time. You can use one or the other, but not both together. For example, 0.00325 seconds could be written as 3.25 ms or as 3.25x10-3s but not as 3.25x10-3 ms. Note that 3.35x10-3 ms = 3.35x10-3 x 10-3 s = 3.35x10-6 s = 3.35 µs ? 0.00325 s.

UP3: One of the purposes of the prefix abbreviations is to be able to express the value of a quantity without having to use the power of ten notation. For example, a number like 3.77x10-3 s could be written simply as 3.77 ms. However to express this number as 3.77x10-6 ks or 3.77x10+3 µ s, both of which are correct, defeat the purpose for using prefixes altogether. If you are going to use power of ten notation, then 3.77x10-3 s is a preferable choice since it is in "pure" SI unit for time.

UP4: Warning, I can not tell if you are operating under the mistaken belief that a prefixed unit is equivalent to a "pure" SI unit. In particular, that you do not have to change a prefixed quantity to SI units before you substitute it into an equation, e.g., putting in milli-something does not always mean that the resulting answer will come out to be equal to milli-something else. Sometimes this will work if the equation is strictly linear, directly proportional, and you only one prefixed unit. Two examples were this will not work are:
- If t = 3.66 ms, then d = 1/2gt2 = 1/2(9.80 m/s2)(3.66 ms)2 /= 65.3 mm even though 1/2(9.8)(3.66)2 = 65.3. Here d =1/2(9.8 m/s2)(3.66x10-3m)2 = 65.3x10-6 m = 65.3 µm.
- If t = 3.66 ms, then v = gt = (9.80 m/s2)(3.66 ms) /= 35.9 m/ms. However, this answer is equal to 35.9 mm/s buy luck. Since the equation is linear function of time and distance, the 10-3 can be transferred from the seconds to the meters .