In fact it’s about the what almost all of classical mechanics is. To understand this better we first need to know
a little mathematical background with vectors.
Vectors are quantities, numbers, or values that are measured generally with a magnitude and direction, most
quantities are scalar, as in they are only a measurement of magnitude. Speed is a scalar magnitude, and velocity
is a vector, for example if I were traveling in reverse in my car I would have a speed of lets say 10 mph however
this doesn’t tell you that I’m going backwards. Velocity on the other hand which is the speed and direction would in
this case be - 10mph, the negative sign just shows direction. (A slightly more complicated fact which I’m not going to go
into is that velocity is normally given with the magnitude and then an angle with direction referenced to something.
In the example above another way to say the velocity would be 10mph 180 degrees north of the positive direction
see exmp1)
So a complication arises from this, when adding or subtracting vectors, vectors are added or subtracted
or added the same when they are the same direction or opposite directions. For example lets say you are
traveling 5 miles per hour to the right and you slow down to 3 mph. The vector subtraction would be 5 to the
right + 2 to the left, so to account for the direction you get a + for right and – for left or (+5)+(-2) or 3.
Which is the same as adding or subtracting numbers. That’s great but what if they aren’t in the same or opposite
direction, then you have a problem.
To analyze the result you would use something called the tail to head method. You would draw an arrow for one
force and another arrow for the other force. You put the tail of one arrow to the head of the other. Then
you draw an arrow connecting these two from the head of the arrow to the tail of the other arrow. If the vectors
are at right angles something special happens. You can use trig(see trig exmp) to find out a lot of
information without actually having to draw the arrow and actually measure it.(see exmp2 and exmp 3)
(trig example) (exmp1) (exmp2)
Wait…what if the forces aren’t at right angles! Oh oh…what to do. Well think about if two forces can be
combined to form a result then maybe that result can be decomposed to give us the original vectors that created
it. If you were to split the screen into the y and x axis then start both forces in from the origin, then decompose
them you would have two forces
on the x axis and two forces on the y.