Newtonâ€™s Laws and the Motion of Particles

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```					Newton’s Laws and the Motion
of Particles

Teacher Excellence Workshop
June 19, 2009
Introducing Forces
A force is a push or pull on an object.
When forces are unbalanced, they cause an
object to accelerate, or to change its
velocity by speeding up, slowing down, or
changing direction.
Draw the forces for a physics
book resting on a table

Force Diagram   Free Body Diagram

FT                FT

Physics Book
FG
FG
Newton’s 1st Law
(Law of Inertia)
If there is zero net force on a body, it
cannot accelerate, and therefore must
move at constant velocity. This means
If there is zero net force on a body, it
cannot accelerate, and therefore must
move at constant velocity. This means
   the body cannot turn.
   the body cannot speed up.
   The body cannot slow down.
Newton’s Second Law
A body accelerates when acted upon by a
net external force.The acceleration is
proportional to the net force and is in the
direction which the net force acts.
∑F = ma
   where ∑F is the net force measured in
Newtons (N)
   m is mass (kg)
   a is acceleration (m/s2)
Working 1st or 2nd Law Problems
1. Identify the system acted upon by forces
such that all parts of the system have the
same acceleration.
2.   Define a coordinate system.
3.   Identify forces by drawing a force or
free body diagram.
4.   Explicitly write SF=ma (or SF=0)
5.   Replace SF with the actual forces in your
free body diagram.
6.   Substitute numeric values, where
appropriate, and solve for unknowns.
Sample problem: In a grocery store, you push a 14.5-kg cart
with a force of 12.0 N. If the cart starts at rest, how far
does it move in 2.00 seconds?
Sample problem: In a grocery store, you push a 14.5-kg cart
with a force of 12.0 N. If the cart starts at rest, how far
does it move in 3.00 seconds?
Newton’s Third Law
For every action there exists an equal
and opposite reaction.
If A exerts a force F on B, then B
exerts a force of -F on A.
Newton’s Third Law must involve the
forces exerted by bodies on each
other.
Examples of
Newton’s
3rd Law

Copyright James Walker, “Physics”, 1st edition
Sample Problem: You rest an empty glass on a
table.
a) Identify the forces acting on the glass with
a free body diagram.

b) Are these forces equal and opposite?

c) Are these forces an action-reaction pair?
Why or why not?
Sample Problem: You rest an empty glass on a
table.
a) Identify the forces acting on the glass with
a free body diagram.

b) Are these forces equal and opposite?

c) Are these forces an action-reaction pair?
Why or why not?
Requirements for Newton’s
Laws

The 1st and 2nd laws require that ONE
system be analyzed and that ALL the
forces on the system be accounted
for.
The 3rd law requires that TWO
systems be analyzed and that the
forces of interaction between the
two be accounted for.
Sample Problem: A force of magnitude 7.50 N pushes three boxes as
shown. Find the acceleration of the system.

Copyright James Walker, “Physics”, 1st edition
Sample Problem: A force of magnitude 7.50 N pushes three boxes as
shown. Find the acceleration of the system.

Copyright James Walker, “Physics”, 1st edition
Sample Problem: A force of magnitude 7.50 N pushes three boxes as
shown. Find the force that box 2 exerts on box 3.

Copyright James Walker, “Physics”, 1st edition
Sample Problem: A force of magnitude 7.50 N pushes three boxes as
shown. Find the force that box 2 exerts on box 3.

Copyright James Walker, “Physics”, 1st edition
Newton’s 2nd Law in 2-D
The situation is more complicated
when forces act in more than one
dimension.
You must still identify all forces and
You then resolve your problem into an
x-problem and a y-problem
(remember projectile motion????).
Problem: A skier skis down a slope with an acceleration
of 3.50 m/s2. If friction can be ignored, what is the
angle of the slope with respect to the horizontal?
Problem: A skier skis down a slope with an acceleration
of 3.50 m/s2. If friction can be ignored, what is the
angle of the slope with respect to the horizontal?
Sample problem: An object acted on by three forces moves
with constant velocity. One force acting on the object is in the
+x direction and has a magnitude of 6.5 N; a second force has
a magnitude of 4.4 N and points in the -y direction. Find the
direction and magnitude of the third force acting on the
object.
Sample problem: An object acted on by three forces moves
with constant velocity. One force acting on the object is in the
positive x direction and has a magnitude of 6.5 N; a second
force has a magnitude of 4.4 N and points in the negative y
direction. Find the direction and magnitude of the third force
acting on the object.

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