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So in class we constantly use multiple equations when solving a question, and sometimes we manipulate equations to help us solve. However, how do we know when we can manipulate them and combine them to solve our questions? De Broglie's Equation is the mixture of two different equations, so it seems like intermixing equations is common.
To combine equations, you should make sure that they have a variable in common such as wavelength or maybe frequency, so you can substitute. Also keep in mind about the units that are used by the equations and that the equations are used for a related topic.
Combining equations happens when there is a shared variable in the equations which can be replaced and manipulated to make a new equation. This often occurs because in order to solve the problem, there is a two step process using two different equations. The combining of equations changes the process into one step. The results are the same, except it can now all be calculated in one step.
You need to make sure to include units as you go through your problem and certain equations can be used to be plugged in for constants that are contained in your problem. Then at the end you must check to see that you have crossed out all undesired units so your final answer is in the desired units.
I have had trouble understanding this as well. I never seem to know when to use which equation and when to manipulate them. I think the only thing that could help is maybe doing many more examples and going to the peer learning sessions!
If the mixing of equations is confusing, then I don't think it is necessary to. You can use the base equations and just go through it systematically. I usually tend to do this, comparing what I have been given to what I need to get. Then, I will find what I'm missing in one equation and use another to solve for it as opposed to smashing them all together is one swoop.
If the question is asking for a value that isn't part of an equation, you can combine two of the equations with the help of a common factor to solve for the final variable. Like you said, this was done in the De Broglie's equation.
Combining equations will often be necessary as you normally will not have all the requirements for a certain equation given to you easily. Practicing combining equations will help you recognize when to combine.
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