Force and Motion-II
Applying Newton’s Second Law
to More Complex Problems:
The Atwood Machine and the Inclined Plane.
Lecture 5
Thursday:29 January 2004
Applying Newton’s Second Law
(F=ma) to more complex problems.
Recall,


 F  ma,
in 2 dimensions :




 F  ma ,  F  ma
x
x
y
y
Motion in Two-Dimensions
• Motion in x direction is completely
independent of motion in y direction.
• Break problem into two parts. One
regarding x-motion, one regarding y-motion
• Each part is then handled just like motion in
1-Dim.
A Common Example:
Atwood’s machine
What do we know?
• Is tension the same for both masses?
• Is acceleration the same for both masses?
• Is the acceleration equal to g?
Atwood’s Machine
T  mg  ma
Mg  T  Ma
Add these to eliminate T .
Mg  mg  Ma  ma
( M  m) g  ( M  m)a
M  m

a
g
 M  m
Inclined Plane
Problem Solving Tip:
Rotate your coordinate system for the
inclined plane. Make one axis along the
direction of motion.
You can leave the coordinate system in
the “traditional” form for the hanging
weight.
N - m1g cos q  0
  m1g sin q = m1a
m2g  T = m2a
• Add the two equations involving T, in order to
eliminate T.
Inclined Plane
m2 g  m1 g sin q  m2 a  m1a
 m2  m1 sin q 
a
g

 m2  m1 
T  m2 g  m2 a
T  m1 g sin q  m1a