Force and Motion-IIApplying 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,

yyxxmm

m

aFaF

aF

,

:dimensions 2in

,

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

T

Mg mg Ma ma

M m g M m a

aM m

M mg

Add these to eliminate .

( ) ( )

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 m2g T = m2a m1g sin = m1a

• Add the two equations involving T, in order to eliminate T.

Inclined Plane

m g m g m a m a

am m

m mg

T m g m a

T m g m a

2 1 2 1

2 1

2 1

2 2

1 1

sin

sin

sin