2D Particle Kinetics – Newton’s 2nd law
1.
Identify the motion and its characteristics.
2.
Draw FBD
.
3.
Set up proper coordinate system
based on motion
:
a.
xy
: horizontal or vertical motion
b.
xy
: parallel and perpendicular to an incline
c.
nt
: vertical circular motion
d.
n

y
: horizontal circular motion
4.
Apply Newton’s 2nd law in the components form
, that is, along the coordinate axes.
:
:
:
x
x
yy
nn
tt
F
ma
xy
F
ma
F
ma
nt
F
ma
F
ma
ny
F
ma
Σ=
⎧
−
⎨
⎩
⎧
−
⎨
⎩
⎧
−
⎨
⎩
5.
Additional information based on forces (friction force formula) and kinematics (acceleration).
Example
1. A 75 Kg man standing on a 15 Kg cart exerts a 150 N force on the rope to pull himself up the smooth ramp as
shown. If the angle of the incline is
θ
= 30˚, find the acceleration of the man. (
Ans
: 0.1 m/s
2
)
θ
2. The small sphere (mass
m
) is placed on the smooth inner surface of the spinning cone at a distance
L
from the
bottom as shown. If the sphere is observed to move with the cone without sliding along the surface, find the rotating
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 Spring '08
 TSChang
 Physics, Force, Friction, Mass, vertical circular motion, vertical circular loop

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