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Math Help - MCAT Physics Math

  1. #1
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    MCAT Physics Math

    Please view attached file that shows part of the MCAT book’s calculation to pulley system question. I understand all the physics theory behind the question and answer, but I am lost on the math. 1) I would like to know what is the name of the math theory where you can just add two different physics equations together and 2) when I am doing physics questions how do I know when I can/should be able to add two different physics equations together? I used to be a strong physics and math student, but over time I forgot my high school theories . 3) My biggest problem in calculating physics problems is knowing when to apply certain math theories that I have learned from a different high school textbook and teacher. In my physics textbook there is a math review/foundation section in the back of the book. I have gone over the physics math review section and understand the entire basic math. But occasionally there will be math theories/understandings that creep up in long and complex physics calculations where I got the final answer wrong because I forgot how to apply a certain math theory and I am competent on the physics theories. I can review my old high school math notes, but there are many math theories that will not be used in MCAT physics, so I would be wasting my time reviewing high school math. Please advise what I should do to be stronger in MCAT physics math or if there is a website where I can practice more MCAT physics math, so I know what type of math theories apply towards specific physics questions or topics i.e. memorize certain math theories will be applied in certain MCAT physics calculations? Thank you for your help and advice.
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  2. #2
    A Plied Mathematician
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    In the situation you have there, you can add the two equations together, because all the terms have the same units: units of force. You can never add two physical quantities together unless they have the same units. If you have a situation like yours, however, where everything in sight has units of force, you can use substitution, elimination, Kramer's rule (assuming you have a linear system), etc., to solve a system of equations. It also depends on what you're trying to do.

    As for the MCAT math, I'm assuming that algebra-based physics is on the exam. In that case, I would study high school algebra, some geometry, and make sure you master your trigonometry. Trig is important, because in physics you're forever resolving vectors into different coordinate systems, which usually ends up being a trigonometric problem using sines, cosines and tangents.

    For the most part, what's really useful in physics is the ability to solve equations with lots of variables for a particular variable or parameter. You've got a long list of knowns, and probably a short list of unknowns: you'll have to be able to eliminate as many unknowns as possible in order to solve for your target variable (the quantity you want to know). You have to be able to look at a problem statement, draw a picture, and then start writing down correct equations that are relevant to that picture.
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