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Generally, how do you solve physics problems?

  1. Dec 10, 2006 #1
    Generally, how do you solve physics problems??

    This is for all the physics B problems in general. How do you guys solve the problems? Do you find equations and plug all the known values in? or do you keep all of the variables and solve for the one variable that you are missing without substituting any numbers??

    I'm curious to know because I've just come across a problem in the Princeton review and I couldn't do it at first. But then I looked at their solution and they solved for the unknown variable without substituting any numbers.

    What should I do?? In you experience, what technique worked out the best for you?

    Also, should you always include the units when you are solving for something? I find that putting units really takes up a lot of space and can get messy sometimes. However, if you leave out the units, sometimes you end up with the wrong answer because you don't match up all the units. (For ex. in a conservation of mechanical energy problem. You have an external friction force and you forget to convert it into Joules. Therefore your final kinetic velocity answer is wrong)

    What method(s) of solving Physics problems do you use?? This would definitely help me a lot!! Thanks for your input!
     
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  3. Dec 10, 2006 #2

    cristo

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    I would advise to always work through in algebra: solve the given equations for the unknown variable, then put the known values in at the last minute. This helps avoid numerical mistakes. Also, if you manipulate an equation correctly, but then mess up the substitution of values at the end, you are more likely to get partial marks. (Well, this is true for the UK exams I've done.. I don't know about US exams)

    With respect to units, I would never write them in, as this will just get messy, especially in longer equations when untis may get mistaken for algebraic symbols. However, before substituing the values in, always convert the values into the same units. For example, as you said above, convert all energies into joules (although, the frictional force would not have units of joules. I suspect this is a typo.)
     
  4. Dec 10, 2006 #3
    Hmm I agree with you about substituting known variables at the end and doing algebra with the variables only first. You brought up a good point, yeah I think my teacher said something about getting partial credit for doing the physics, not for plugging numbers in. So yeah I think your right about getting most credit for showing the correct work.

    About the conservation of mechanical energy. What I was saying was that the Friction force would have to be converted to Joules by taking the Work done by the friction force. W=-F*d Right? I think that is how you make all the units joules. I'm still iffy about whether or not you should include units. Sometimes I forget to convert certain units because I don't know what I need to convert or what I need to decompse. Units such as Newtons consists of kg and m/s^2 and sometimes you need to either break it down or combine units to achieve the variable you want to solve for.
     
  5. Dec 10, 2006 #4
    The best way is definately to solve for the variable and put everything into the calculator in one step. Sometimes, checking units right before a calculation is a good way to look for a mistake in your algebra
     
  6. Dec 10, 2006 #5

    PhanthomJay

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    It's a matter of choice , but I always find it easier to plug in as many numbers as you can first. For example, if you have
    E = 1/2mv^2 + mgh
    and you are asked to solve for v given the values of E = 1000J, m=10Kg, g=10m/s^2, and h =5m,
    if you plug in the numbers first, then
    1000 = 1/2(10)v^2 + (10)(10)5
    1000 = 5v^2 + 500
    500 = 5v^2
    100 = v^2
    v =10m/s
    But if you isolate v first, then
    E = 1/2mv^2 + mgh
    E - mgh = 1/2mv^2
    2(E - mgh) =mv^2
    2(E- mgh)/m = v^2
    v = (2(E -mgh)/m)^1/2
    v = (2(1000 - 10(10)(5))/10)^1/2
    v = (2(1000 -500)/10)^1/2
    v = (2(50))^1/2
    v = 100^1/2
    v = 10m/s
    Which do YOU find easier? And on units, well, they are VERY important, so you must be sure up front that your mass is in Kg, speed in m/s, Energy in Joules, height in meters, acc of gravity in m/sec^2. Otherwise, you'll really get mixed up if you plug the units in first.
     
  7. Dec 10, 2006 #6

    cristo

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    The above situation is a little more than "converting the units to Joules." If you are talking about the conservation of total energy, then the terms in the sum must all be energies. If you've set up the equation, and one of the terms is a force, then you've set your equations up wrong! You should'nt just use units to set the equations up, you should be familiar with the concepts behind them.

    What I meant about not using units, is that, say you have an equation, which you have solved for the unknown you want. Now, before plugging values in, you must convert them to the same units for the equation to make sense. e.g If you wanted to calculate the speed of an object which covered 100m in 1 minutes, then in order for your units to work out in the end, (as m/s) then you would need to convert the minute to seconds. (ok, this is a simple example, but I hope you understand what I'm getting at)
     
  8. Dec 10, 2006 #7

    chroot

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    It's not a matter of which method is easier. If you continue doing math on actual numerical values, shuffling them around in your calculator, you may well have round-off or other errors that will cause your answer to be approximate -- somewhat different from the actual, exact answer.

    - Warren
     
  9. Dec 10, 2006 #8
    Yeah I understand what you are saying. Thanks.
     
  10. Dec 10, 2006 #9
    So the best way would be to do what turdferguson said??
    "The best way is definately to solve for the variable and put everything into the calculator in one step."

    That way you can just come up with one good number in which you can approximate?
     
  11. Dec 10, 2006 #10

    chroot

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    If you can, you should always find an exact answer. For example, you should write down [itex]\sqrt{2}[/itex], not some approximate decimal expansion. The only way to find the exact answer is to use algebra. Plugging numerical values into your calculator, and then manipulating them numerically, is a great way to get an answer that's 10% different from what it should be, particularly if you start rounding intermediate values off as you go.

    - Warren
     
  12. Dec 10, 2006 #11

    I don't include units when I'm working with variables ( I keep track of them when dealing with long derivations of course), but I always put them in when I write the numbers down at the end. I think people who don't should be penalised even if they get the right units for the final answer.
     
  13. Dec 10, 2006 #12
    for units, I usually just put a parenthesis on the whole expression (with numbers), then put the units at the end (for example, if i have v=sqrt(2g*2 meter), i'll put v=(sqrt(2*9.8*2))meters). that way, the teacher can never take points off for my calculation and I don't have to deal with messy units.
     
  14. Dec 11, 2006 #13

    PhanthomJay

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    Okay! I'll bow to the majority. But I'm an old dog, and you can't teach me new tricks. It took me three times to get the correct answer trying to isolate the variable...too many parentheses and letters gave me an exactly wrong answer, two times! Plus, I am familiar with the fact that for example KE =1/2mv^2. If i'm told that v = (2(KE)/m)^1/2, you've long lost this old dog. :frown:
     
  15. Dec 11, 2006 #14
    lol... Thats why you need to eliminate all the unneccesary variables first. Therefore you would multiply both sides by 2 and divide both sides by v. I see what you mean though.. I'm still uncertain about all of this. I mean, some methods work better for different problems. Grrr...
     
  16. Dec 11, 2006 #15

    cristo

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    I think chroot pretty much answers your question. If you substitute rounded numbers in too early, then you bound to have some degree of inaccuracy in your final solution
     
  17. Dec 12, 2006 #16
    Rounding errors are a very minor inconvenience of working numerically. All respectable physics texts advocate and themselves do problems algebraically. The advantages are numerous. One of the most important is that you can verify your answer by imposing limiting conditions on the different variables. Unless a problem is something that HAS to be solved numerically (numerical integration for example), always work with variables until the very end. This also means that you don't have to write any units for variables carry units inside them. Of course what was said about getting partial marks is true.

    However when you write the final answer, don't just plug in the values in your calculator and write the answer. First show a step where you plug in all values including units into the derived expression, check that the units cancel out and multiply to give the correct final unit, and then plug in the values in the calculator.
     
  18. Dec 12, 2006 #17

    PhanthomJay

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    If you multiply by 2 and divide by v, you're not going anywhere in arriving at a correct solution. This is what i found many years ago when i taught the subject....the algebra knocks you down. Enough said.
     
  19. Dec 12, 2006 #18
    I prefer to work algebraically. This can be particularly useful if you're messing around looking for a solution and you find two different ways of expressing the same thing, then you can equate them and eliminate that thing in the process which might just help you out.

    With regards to units you should be aware of them, units really help you to actually understand things more intuitively. One trick I learned (the hard way) is that if you have inconsistent units, say a mix of SI units and imperial units you might not need to convert the imperial units over to SI if and only if you have a ratio of those units.

    For example if your asked for the ratio of two times, and you're given the times in units of days, converting the two times into seconds is pointless because the ratio will still be the same.
     
  20. Dec 12, 2006 #19

    chroot

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    Well, the bottom line is that if you're only interested in getting a passing grade in your introductory physics class -- and couldn't care less if you're prepared for any further physics classes, or have actually learned anything substantive -- then you may get by with just punching numbers into your calculator.

    If you intend on actually learning physics in any kind of depth, or intend on taking more advanced classes, then you literally cannot survive by solving things numerically on your calculator.

    - Warren
     
  21. Dec 12, 2006 #20
    oops. I didn't mean v... Well you can basically cancel out all the variables that have the same quantity on both sides of the equal signs. It would make it easier. For example, calculating the velocity of an object that slides down a frictionless ramp starting from rest.


    mgh=1/2mv^2

    You can cancel out the masses and get v=sq.rt.(2gh) etc.
     
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