Newton's Problems

1: Equilibriums
Assumption:
-Positive axes
-∑F = 0 ( ∑Fx = 0 , ∑Fy = 0), a = 0
- no friction
- no air resistance
- rope is weightless

When calculating, divide all the force to x-axis and y-axis,
Fx = max        Fy = may
Fx = 0              Fy = 0

2: Inclines
a) object is at rest
Assumptions:
- postive is along the incline direction
- ∑F = 0, a = 0
- no air resistance
- FN is perpendicular to incline
                     ∑F = ma 
∑Fx = max                ∑F = may
∑Fx = 0                       ∑F = 0
Fgx - f = 0                 FN - Fgy = 0

b) object is moving
Assupmtions:
- positive is along the incline direction
- ∑Fy = 0 , ∑F is not equal to 0
- no air resistance
- FN is perpendicular to incline
use the same method of calculation as when object is at rest

3: Pulley
Assumptions:
- polley is frictionless
- rope is frictionless and weightless
- no air resistance
- 2 systems (2 FBDs)
- T1 = T2
- a of the system is the same (ay1 = ay2)

Note that ∑Fx = 0 for both objects
Do the calculation by dividing the foerces into x and y.
4: Trains
Assumptions:
- Use 3FBDs  to find T
- no air resistance
- ay = 0
- cables are weightless
- positive is in the direction of a
- a is consistant

Assume the whole system as an object to calculate the acceleration
Then use 3 FBDs to find tension amoung the masses