AP Physics 1 - We Can Do This!

One of the most important skills you need to be successful in AP Physics 1 is the ability to quickly rearrange equations, set two or more equations equal to one another, and to solve for or even eliminate specific variables.  Weakness in this area is the primary reason that students complain that the class is so difficult  It isn't.  Their math skills just aren't robust enough and it makes the subject feel difficult.

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The good news is that you probably already have solid math skills, you just need practice with this particular topic.  :D

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Let's start with the easiest sort of manipulation.  The second law of motion is expressed by this equation:

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                              F = ma

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Where F is the force in newtons, m is the mass in kilograms, and a is the acceleration in m/s/s.  Just as a reminder, a newton is a derived unit.  Since 1 N = 1 kg x 1 m/s/s, you can see that a newton = kg m/s/s.

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To solve the equation to find the acceleration, you need to get m off that side.  Since that side is m times a, to get a to the other side, you simple divide both sides by m and are left with a new version of the equation:

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                           F/m = a

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A variation on this equation is the formula to find the gravitational force between two objects:

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Mass 1 is exerting a force on mass 2 and mass 2 is exerting a force on mass 1.  Newton's third law of motion states that:  for every action there is an equal and opposite reaction.  Mass 1 attracts mass 2 with the same force as mass 2 attracts mass 1.  This is not important to the topic of algebraic manipulation, but you might as well pick up a little physics as you go along!

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G is the gravitational constant 6.67 E-11 Nm^2/kg^2.  One issue with my choice of website management is that they do not allow for sub or superscripting.  Know that ^ means to superscript it.  When I type m1, I really mean m subscript 1.

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Let's say that you need to solve for m2.  You need to move G and r^2 to the other side.  Try it and then check you answer below:

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Fr^2/m1F = m2.

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Now, solve for r instead.

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r = square root of (Gm1m2/F)

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You can always solve problems using several steps, but as you progress, you may find it helpful to combine formulas into a single equation and just get it done with one fell swoop.  For example:

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Let's say that you have a ball and you'd like to know how fast it's going (v) just before it hits the floor and the only data you have for it is the height you've dropped it from.  For this event, you use the law of conservation of energy: energy cannot be created or destroyed, only converted from one form (potential gravitational) to another (kinetic).

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You could mass the ball, determine the Ug (potential energy), then set that equal to Uk (kinetic energy) and solve for velocity.  Or you could save yourself a lot of time and the need for a balance by starting with this:

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Ug = Uk

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mgh = .5mv^2 - I know I said not to use the carrot, but this website generator doesn't show formulas very well.  That's the x squared key.

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The masses will cancel nicely and you can solve for v = square root of 2gh.  That's so much simpler and cleaner!

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On the AP exam, you are expected to show how you get an answer.  Always start with a statement - in this case, conservation of energy, generate the equation, insert your data and then solve it with units and significant digits.

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Your assignment is the pdf that will pop up when you click on the blue button below.  Print it out and complete it.  There is no quiz on this topic.  There will be a test in the first week of school, however.  This is a critical skill.  If you are struggling, use youtube, Kahn academy or contact me on Remind.

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