Newton's Laws

AP Physics Rapid Learning Series - 06
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Newton’s Laws
Physics Rapid Learning Series
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© Rapid Learning Inc. All rights reserved.
Wayne Huang, Ph.D.
Keith Duda, M.Ed.
Peddi Prasad, Ph.D.
Gary Zhou, Ph.D.
Michelle Wedemeyer, Ph.D.
Sarah Hedges, Ph.D.
© Rapid Learning Inc. All rights reserved. - http://www.RapidLearningCenter.com 1

Learning Objectives
By completing this tutorial, you will:
„ Understand Newton’s
three laws of motion.
motion
„ Solve equilibrium
problems.
„ Explain the role of forces
like friction and air
resistance.
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„ Apply these laws to
dynamics problems.
Concept Map
Physics
Studies
Previous content
New content
Motion
Caused by
Velocity Forces
F
Constant
V l it
Slowed by
Friction
May be either
Static or Kinetic
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Adding many yields
Static Equilibrium Vectors
Net Force
described by

Newton’s Laws
These three basic laws, formulated by
Isaac Newton describe the forces acting
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Newton, on objects.
Newton’s First Law
Every object continues in its state of rest, or
uniform motion in a straight line,
unless it is acted upon by an outside force.
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BAM!

Inertia
This tendency to continue in a given state,
Newton’s 1st law is often called The Law of
Inertia.
The more mass an object has, the more inertia it has.
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Large amount of
inertia!
Small amount of
inertia!
Mass vs. Weight
Mass: The amount of matter in an object.
Unit: kg, g (kg is the SI unit)
Weight: The force upon an object due to gravity.
Unit: Newtons
Don’t confuse
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Don t mass & weight!
They might be
similar, but they are
not the same.

Mass Question
If you travel deep into space, does your mass
change?
No!
Your location doesn’t change
th t f tt t
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the amount of matter present
in your body. Even if you are
floating in space, you still
possess the same number of
atoms and molecules.
Weight Question
If you travel deep into space, does your weight
change?
Yes!
In space, there may be
less gravitational pull
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on you. Thus your
weight, a force, will be
less.

Force Units
Some are
familiar with the
English unit for
force the
However, the
typical metric
unit for force
force, i th N t
pound, lb.
is the Newton,
N.
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On earth, 1 kg of 1 N = 1 kg m/s2.
mass would
weigh 9.8 N.
Newton’s Second Law
Fnet = ma
net force,
N
mass, kg acceleration,
m/s2
The acceleration of an object is directly
proportional to the net force and inversely
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force, proportional to the mass.
It may also be seen as Fnet = ΣF. This
indicates that the net force is the sum of
all the forces acting on an object.

The Net Force
The net force is simply the resultant of all the
forces acting on an object.
C
B
D
E
G G G G G
A +B+C+D+E = F
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A
Fnet
It can be considered the leftover, or sum of all forces.
Paycheck Analogy
You may work 10 hours at $10 per hour, but your
pay at the end of the period is definitely not $100.
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After all taxes and deductions are accounted for,
what you actually get is your net pay. This is
similar to the net force.

Second Law Observations
A larger mass is more difficult to accelerate than a
smaller one! This is common sense!
Also, a larger force accelerates a mass
more than a smaller one!
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Second Law Example
If a 10 kg block rests on a frictionless surface,
how much will it accelerate if a 50 N force is
applied to it?
50 N 10 kg
a = ?
Fnet = ma
a = F t/ m
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Fnet/ a = 50 N /10 kg
a = 5 m/s2

Newton’s Third Law
For every force, there is an equal
and opposite force.
For every action, there is an
equal and opposite reaction.
Action Reaction
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Force Force
Newton’s Third Law Example
The exhaust gases from a rocket are forcefully
pushed downward out the rear of the nozzle.
An equal and opposite force is exerted
upwards on the rocket itself.
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The Normal Force
The chair supports, or pushes
up on you. This reaction force
is called the normal force.
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Your weight due to
gravity pulls you down.
The Normal Force Direction
This normal force is always perpendicular to the
surface.
If the surface is horizontal (flat), it is equal in
magnitude to the weight of the object.
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FN
W

Normal Force on an Incline
If there is an incline, the normal force is still
perpendicular to the surface, but it isn’t equal in
magnitude to the weight.
FN
W
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Equilibrium
Sometimes the forces acting on an object
balance out perfectly
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perfectly.

Equilibrium Definition
When all the forces on an object balance out, or
cancel out, the object has a net force of 0.
2
N
2 N 2 N Fnet = 0 N
2
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N
This condition is known as equilibrium.
Static Equilibrium
When an object is in equilibrium, and not
moving, this is called static equilibrium.
Person
hanging
motionless
Tension in rope
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Weight Fnet = 0 N

Static Equilibrium Example
Imagine a 50 N sign hanging from a cable and
a lightweight rod as shown below. What
(tension)/(force) is necessary in the cable to
hold the sign? Neglect the weight of the rod.
Newton’s Diner 60o
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Open
Force Diagram
It is often very useful to show a diagram that
describes all the forces acting in the problem.
60o
Vertical
component
of cable
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Open
Sign weight
Horizontal
component
of cable
Wall pushing
back on rod

Equilibrium Conditions
For the sign to remain hanging, all the forces on it
just balance.
The vertical
60o
Th h i t l
components
must balance.
The horizontal Open
components must
balance.
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Fnet = 0N
Calculating Tension - 1
To calculate the tension, look at the right triangle
formed. We will solve for the hypotenuse which
represents the cable tension.
O
60o
The vertical
component of the
tension must be 50 N
because that is the
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Open weight of the sign.

Calculating Tension - 2
cosθ = adj Hypotenuse
= tension in
hyp
hyp = adj
cable
60o cosθ
hyp = 50N
cos60
D
50N
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100N
hyp = 50N =
.5
adjacent = 50 N
equal to weight
of sign
Dynamic Equilibrium
An object can be moving and still be in
equilibrium.
It could be moving at a constant velocity.
There would be no net force or acceleration on
it. This is called dynamic equilibrium.
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Applied Force Fnet = 0 Resistance Force

Friction
Since it tries to slow all motion, one of
the most important forces to study is
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friction.
Direction of Friction
As previously mentioned, friction is a force that
always opposes motion.
friction
Air drag and air resistance are examples of friction
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between an object and the air.
friction

Types of Friction
There are two types of friction:
static (stationary) and kinetic (moving).
F = ma
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Static friction keeps
him from sliding off
the chair.
Kinetic friction slows
him as he slides.
Simple Friction Example
Imagine a man is pushing a 20 kg sled along a
floor at a constant velocity by applying a force of
40 N.
What is the weight of the sled?
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Fnet = ma weight = (20 kg)(9.8 m/s2) = 196N
Here we consider the pull from
gravity, not the horizontal
motion due to the man’s push.

Frictional Force on Sled
What is the force from friction on the sled?
Since it has a constant velocity, Fnet = 0. Friction
must also be 40N
friction
applied force = 40 N
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Fnet = 0 N, dynamic equilibrium
Coefficient of Friction
There is a way to mathematically describe the
amount of friction between any two given
surfaces.
μ = F
f
F
N
Force from
friction, N
Coefficient of
friction,
Greek letter
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mu
μ (mu) is a unit-less ratio.
Normal
force, N

Static and Kinetic Friction
Because the amount of friction depends on
whether the object is moving or still, there are
two possible μμ values:
μs= static coefficient of friction
μk = kinetic coefficient of friction
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The one you use depends on the situation!
Kinetic Friction Example
Previously, a man pushed a 20 kg sled at a
constant velocity with a force of 40N. What
is the coefficient of kinetic friction, μμk in this
case?
μ = F
f
k F
N
μ 40N k 2 =
( 20kg)(g)( 9.8m/s )
The normal
force is
equal in size
Since it moves
at a constant
velocity, the
frictional force
must t equal lth
the
pushing force.
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μ 40N k =
μk .20 =
196N
to the weight
No units for
μ

Dynamics Problems
The study of the forces acting on an
object is called dynamics These forces
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dynamics. produce motion!
Inclined Plane Example
Calculate the acceleration of this block sliding
down a frictionless incline.
3 kg The weight of the
object still points
directly down:
F = ma
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30 o
Fnet W = (3kg) (9.8 m/s2)
W=29.4 N down

Component Vectors on Inclined Plane
Notice how this weight vector could be broken into
two components.
These two
component
vectors, when
added tip to
tail give the
3 kg
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tail, weight as a
resultant:
W=29.4N
30 o
Perpendicular Force Component
3 kg F i th t
W=29.4N
F⊥ is the component
of weight that is
perpendicular to the
inclined surface.
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30 o
This component is responsible for pushing the object
into the surface. The reaction force to this one is the
normal force, FN.

Parallel Force Component
3 kg F⎟⎟ is the
W=29.4N
⎟⎟
component of the
weight that pushes
parallel to the
surface.
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30 o
F║
This component is responsible for pushing the
object along the incline.
Right Triangles
3 kg
W=29.4N
30 o
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F⎟⎟ , and F⊥ can be found relatively easily using simple
trigonometry. The triangle they form is a right
triangle. The weight is the hypotenuse.

Similar Triangles
3 kg
W=29.4N
30 o
30o
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The angle at the top of the triangle is the same as the
angle of the incline. The two form similar triangles.
This concept can be used for any inclined plane.
Calculation of Parallel Force
F
sinθ =
3 kg W
30o
F
29.4N
sin300 =
29.4
N F 14 7N
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=14.7N

Calculation of Acceleration
Finally, since we now have the force that is
pushing the object down the incline, we can
use Fnet= ma.
F║=Fnet=ma
14.7N=3kg(a)
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a=14.7N/3kg=4.9m/s2
Learning Summary
Friction
opposes
Newton’s 1st Law:
Inertia is the
property that
In either static
or dynamic
equilibrium,
ilib i
the net force
equals 0.
p p y
matter has to
resist changes in
its motion.
Newton’’s 3rd Law:
motion
μ = Ff / FN
Newton’’s 2nd Law:
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For every force
there is an equal
and opposite
reaction force.
Fnet=ma
Consider all the
forces acting on
an object.

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Newton’s Laws
Chemistry :: Biology :: Physics :: Math
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