Newton!!!

For equilibrium:
assumptions:

-          no air resistance

-          no friction

-          a=0 ( ax=0 and ay=0 )

-          break down in to x and y components

-          T1x=T2x

-          set positive axis⊕

for inclined problems：

assumptions：

-          no air resistance

-          FN  perpendicular to the surface

-         ＋axis is the direction of the motion

-          break down in to x and y components

-          acceleration does not equal to zero

-          FN-Fgy=0

-          Fgx-f=ma

 

for pulley problems:

assumptions:

-          pulley is frictionless

-          rope is frictionless

-          no air resistance

-          + axis is the position of the

-          2 Free Body Diagrams

-          T1=T2

-          ay1 = ay2

-          break down in to x and y components acceleration

 

for train prblems,

we consider the trains as a whole, to solve for ax.

Assumptions:

- 3 FBD to find T

- no air resistance

- ay = 0

- cables weightless

- positive along acceleration

- acceleration is consistent