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Chapter 3
Newton’s Laws
Classical Mechanics
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Describes the relationship between
the motion of objects in our
everyday world and the forces acting
on them
Conditions when Classical Mechanics
does not apply
• very tiny objects (< atomic sizes)
• objects moving near the speed of light
Forces
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Usually think of a force as a push or pull
Vector quantity
May be a contact force or a field force
• Contact forces result from physical contact
between two objects: pushing, pulling
• Field forces act between disconnected objects
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Also called “action at a distance”
Gravitational force: weight of object
Contact and Field Forces

F
Force as vector
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Magnitude + Direction
Components Fx, Fy
Fx  F cos 
Fy  F sin 
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Fy
tan  
Fx
F  F F
2
x
Units: Newton (N), pound(lb)
1lb=4.45N
2
y
Addition of Forces
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Graphical method
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Components method
Newton’s First Law
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An object moves with a velocity that
is constant in magnitude and
direction, unless acted on by a
nonzero net force
• The net force is defined as the vector
sum of all the external forces exerted on
the object
External and Internal Forces

External force
• Any force that results from the
interaction between the object and its
environment

Internal forces
• Forces that originate within the object
itself
• They cannot change the object’s velocity
Inertia

Is the property of a material to resist
changes in motion.
• Is the tendency of an object to continue
in its original motion
Mass
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A measure of the resistance of an
object to changes in its motion due
to a force
Scalar quantity
SI units: kg
Condition for Equilibrium
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Net force vanishes
No motion
F  F  F
1

F
F
2
 F3  ...  0
x
F1x  F2 x  F3 x  ...  0
y
F1 y  F2 y  F3 y  ...  0
Newton’s Second Law

The acceleration of an object is
directly proportional to the net force
acting on it and inversely
proportional to its mass.
F  ma
• F and a are both vectors
Units of Force

SI unit of force is a Newton (N)
kg m
1N  1 2
s

US Customary unit of force is a
pound (lb)
• 1 N = 0.225 lb
Sir Isaac Newton
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1642 – 1727
Formulated basic
concepts and laws
of mechanics
Universal
Gravitation
Calculus
Light and optics
Newton’s Third Law
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If object 1 and object 2 interact, the
force exerted by object 1 on object 2
is equal in magnitude but opposite in
direction to the force exerted by
object 2 on object 1.
•
F12  F21
• Equivalent to saying a single isolated
force cannot exist
Newton’s Third Law cont.

F12 may be called the
action force and F21
the reaction force
• Actually, either force
can be the action or
the reaction force

The action and
reaction forces act
on different objects
Weight vs Mass
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Weight is not mass but they are related
Weight is a force
Consider a Falling object
F  ma  F  mg
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Weight w=mg
Object on a table?
Weight
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The magnitude of the gravitational
force acting on an object of mass m
near the Earth’s surface is called the
weight w of the object
• w = m g is a special case of Newton’s
Second Law
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g is the acceleration due to gravity
g can also be found from the Law of
Universal Gravitation
More about weight
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Weight is not an inherent property of
an object
• mass is an inherent property
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Weight depends upon location
Using Second Law
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F=ma
Net Force
F   F  F1  F2  F3  ...

F
F
x
F1x  F2 x  F3 x  ...  max
y
F1 y  F2 y  F3 y  ...  may
Method
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Isolate object of interest
Draw picture, show all forces
Decide if the object is accelerating
Choose appropriate coordinate
system
find force components
Use F=ma
Example (prob. 23)
1200 kg car going 20 m/s collides
head on with a tree and stops in
2.0m.
• What is the average stopping force?
Example (Atwood’s Machine)
Two masses, 2.0 kg and 2.05 kg, …
0.5 m above ground.
Find acceleration and the time the
2.05 kg mass takes to reach the
ground.
Example
Force of 10 N gives a mass
acceleration of 1 m/s².
• How large a force is needed to
accelerate to 0.25 m/s²?
• If the mass is increased by a factor of
two, how large of a force will give an
acceleration of 2 m/s²?
Example
Two masses m1 (5kg) and m2 (10kg)
are connected by a rope on a table
top. Friction forces on m1 and m2
are 15N and 30N respectively. A
pulling force P acts on m2 at 45°
above horizontal and accelerates
the system with 0.2m/s² acc.
• Find tension in the rope
• Force P
Newton’s law of Gravitation
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Mutual force of attraction between
any two objects
Expressed by Newton’s Law of
Universal Gravitation:
m1 m2
Fg  G 2
r
Universal Gravitation, 2
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G is the constant of universal
gravitational
G = 6.673 x 10-11 N m² /kg²
This is an example of an inverse
square law
Universal Gravitation, 3
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The gravitational force exerted by a
uniform sphere on a particle outside
the sphere is the same as the force
exerted if the entire mass of the
sphere were concentrated on its
center
• This is called Gauss’ Law
Gravitation Constant
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Determined
experimentally
Henry Cavendish
• 1798
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The light beam and
mirror serve to
amplify the motion
Applications of Universal
Gravitation
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Weighing the Earth
mmE
w  Fg  G 2
RE
mmE
mg  G 2
RE
take g  9.8 m / s
mE
g G 2
RE
 mE  6 10 24 kg
gRE2
mE 
G
2
RE  6380 km
Applications of Universal
Gravitation
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Acceleration due to
gravity
g will vary with
altitude
ME
gG 2
r
Apparent Weight
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The weight of
object in an
accelerating frame.
Consider inside a
elevator
Why do we need 1st
law?
Example
An object weighing 500 N is uniformly
accelerated upward during a short
elevator ride. If the object’s apparent
weight was 625 N during the trip,
how long did the ride take to move
40 m upward?