Physics - equation abstraction help

[Hemorrage]

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Does anyone have any tips on how you "handle" questions that involve equation abstraction? By this i mean, if they say something along the lines of "If planet A is a radius 3x than planet B, whats the effect on the gravitational force". How do you handle this mathematically? I know this is an easy example but i find that i'm absolutely terrible at these kinds of questions. I typically end up making up numbers (which makes sense in the end but takes too long)

 

[milski]

Use whatever variable has changed with the factor of that change and plug in the formula that gives you the quantity that you care about.

For example, if a planet has the radius increase 3 times, what happens to its volume?
Volume=4/3pi*r^3
The new radius is 3r and the new volume is 4/3pi*(3r)^3=27*4/3pi*r^3=27Vprevious

 

[akim6890]

Often times they want a ratio of the two quantities you're comparing. A common one is resistance of a wire. They'll tell you wire A is twice as long as wire B but has a radius half as long as wire B. What is the ratio of resistance of wire A to wire B?

What I do is just write out the variables noted of the equation in terms of the quantity compared. In this case resistance is proportional to distance and inversely proportional to area with everything else constant, so I would write d1/A1 : d2/A2. Since they give you relative numbers you can just plug them in, so here I would write 2/1 : 1/4. Multiply both sides by 4 to get whole numbers and the ratio would be 8:1

 

[Shjanzey]

I have also noticed on many of these questions they want to test your ability to quickly analyze an equation and determine the possible outcome. They will often times mention a change to a particular physical property that will directly correspond to a variable in the given equation.

Then you have to examine the numerator or denominator to decide if the final value will be larger or smaller etc. To me these types of problems are purely an algebraic exercise.