I am trying to understand when the positive or negative of a specific value in an equation (work-energy and momentum-impulse) is to be evaluated based off the motion diagram and when it is not?
The ones in particular I am unsure about is work-energy and impulse-momentum:
PEi + KEi + W = PEf + KEf
pi + J = pf
The Attempt at a Solution
I know with kinematics, you must always evaluate the values compared to the motion diagram and assigned positive/negative directions. I know the same goes for forces when using dynamics. I am mainly trying to make sure I understand it right when it comes to the work-energy and impulse-momentum equations.
If I understand correctly, for PE, the g is always considered positive regardless of the motion diagram. For KE, I believe the same goes for the v value. Then for the W, I know the cosθ determines whether it will be positive or negative and the F and Δd are absolute values, making both positive (or 0 of course). So, if I understand correctly, the only thing that takes the positive/negative directions into consideration in work-energy is the cosθ, correct?
As far as momentum-impulse, again if I understand correctly, in these equations the direction of the force and velocity will change each of their respective signs, correct?
Our instructor has not been clear on this, threw both at us the same day, and then sometimes he uses the + or - from problems, sometimes he doesn't. After spending hours on my own trying problems, I think I have it figured out, but I would really appreciate someone confirming this for me.
Also, for future reference, how can you tell when an equation evaluates certain values based on the motion diagram +/- values and when it is evaluated as a magnitude (abs. value) instead?