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UNIT XX: DYNAMICS AND NEWTON’S LAWS
I. Definition of FORCE
•  DYNAMICS is the branch of mechanics concerned with the forces that cause motions of bodies
•  FORCE is a quantitative interaction between two (or more) objects. Forces push or pull.
•  A contact force occurs when two or more bodies touch
•  A “distance” force refers to phenomena like gravity or magnetism, where the
force is exerted “at a distance” or through space.
•  Force is a vector.
•  The application of a force causes a change in an object’s acceleration. Force and
acceleration are directly proportional.
•  Force is directly proportional to the mass of an object.
• Unbalanced forces CAUSE an object to accelerate (either speed up or slow down).
•  Balanced forces on an object mean acceleration = 0 m/s2
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II. Types of forces and their symbolism
Contact
Forces
Fric'onal
F
frict
Distance
Forces
Gravita'onal
Tension
F
tens
Normal
Fnorm
Air
Resistance
Fair
Applied
F
app
Spring
F
Fgrav
Electrical
Felectr or E
Magne'c
B
spring
Forces acting on an object are represented with vector arrows labeled with the
appropriate force symbol
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III. Illustrating 1-dimensional forces with Free Body Diagrams
•  A FREE BODY DIAGRAM is a drawing that illustrates the forces acting on an object
•  Free-body diagrams must show all the forces which exist for the object in the given situation.
•  A 1-dimensional force means that the force acts either vertically (up or down) or
horizontally (left or right)
Situation:
Box resting on a table
Fnorm
Fgrav
The normal force is a force that exists when two
objects are in contact. The box pushes down on
the table but the table exerts an upward force on
the box “Normal” means “perpendicular to”. The
normal force will be perpendicular to the surface
applying the force.
Gravitational force always points down. The
weight of an object quantifies the force due to
gravity.
THESE FORCES ARE BALANCED. ACCELERATION IS ZERO. NOTICE THE
VECTORS HAVE THE SAME LENGTH (MAGNITUDE) BUT WORK IN OPPOSING
DIRECTIONS.
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Situation:
Rain drop falling from the sky,
no air resistance
UNBALANCED
FORCE
Situation:
Rain drop falling from the sky,
with air resistance
UNBALANCED
FORCE
ACCELERATING
BODY
Fgrav
ACCELERATING
BODY
air resistance is
Fair a frictional force that
pushes against a
moving object.
Fgrav
Situation:
Box pushed to the right,
with friction
Fnorm
Ffrict
Fapp
Fgrav
The frictional force
works against the applied force
used to slide the box. If the
applied force exceeds the frictional
force, forces are unbalanced and
the box will accelerate. Later we will
distinguish between sliding and static
friction.
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Can a moving object have balanced forces?
YES, as long at the object is not accelerating (this is was one of Newton’s “breakthrough”
ideas, not intuitive, and we will discuss it more later). If the object IS accelerating, the
forces acting on it are unbalanced.
Situation:
Box was pushed to the right,
no friction or air resistance
Fnorm
Situation:
Rain drop falling from the sky,
with air resistance = gravity force
Fair
BALANCED
FORCE
MOVING YET
NON-ACCELERATING
BODY
Fgrav
The box was pushed from the left.
It is moving to the right. It will move
at constant velocity (zero acceleration)
until an unbalanced force changes
its acceleration.
Fgrav
A falling object eventually encounters
enough air resistance that its velocity
stops increasing. That’s terminal
velocity. At that point, the forces on
the moving body are balanced.
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Situation:
Picture hanging on a single wire
Ftens
Fgrav
Situation:
Picture hanging on 2 wires
Tension force is directed
along the length of a wire,
rope, etc. It pulls the
object it is attached to and the
object pulls back with equal
force. So the force on each
end of the wire is the same.
Ftens
Ftens
2 wires share
the tension
force equally.
Fgrav
2Ftens = Fgrav
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IV. NET FORCE
•  The net force is the vector sum of all the forces acting on an object.
Fnorm = 10N
Ftens = 20N
Ffrict = −5N
Fgrav = −20N
Fnet = Ftens + Fgrav = 20N + (−20N ) = 0N
Fapp = 25N
Fgrav = −10N
Fnet = Ftens + Fgrav + Ffrict + Fapp =
20N + (−20N ) + (−5N ) + 25N = +20N
REMEMBER, the signs just indicate the DIRECTION of the force vector
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V. Newton’s 1st LAW
A . INTRODUCTION
•  Here’s the usual way it is written:
Every
object
in
a
state
of
uniform
mo6on
tends
to
remain
in
that
state
of
mo6on
unless
an
external
force
is
applied
to
it.
•  Remember that a state of motion also includes no motion, or rest
•  The really big deal contained in this law is that a continuous force is NOT
necessary to KEEP an object moving. Once moving, an object keeps
moving until an unbalanced force acts to change its acceleration.
•  This law is sometimes called the Law of Inertia.
•  A force must overcome the inertia of an object to get it to accelerate.
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B. INERTIA
•  Inertia is the tendency of an object to resist a change in its acceleration.
•  Inertia is related to the amount of mass an object contains.
•  The higher the mass, the larger the inertia. More massive objects resist
changes in their state of motion.
•  How the mass is distributed in an object can affect its inertia.
•  Galileo is credited with developing the concept of inertia.
ONCE AN OBJECT’S INERTIA IS OVERCOME, IT WILL REMAIN
IN THE NEW STATE OF MOTION UNTIL ANOTHER FORCE ACTS
ON IT.
CONTINUOUS APPLICATION OF A FORCE IS NOT REQUIRED TO
KEEP AN OBJECT MOVING.
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VI. NEWTON’S 2nd LAW
A. DESCRIPTION
•  The usual way the 2nd Law is stated:


F = ma
the SI unit for F is the Newton, N
kgim
N= 2
s
•  The force is directly proportional to the object’s acceleration or mass.
•  The force and acceleration vectors point in the same direction
•  If sufficient force is applied in the + direction, the object accelerates in the + direction.
THIS LAW ALLOWS US TO CALCULATE HOW VELOCITES CHANGE WHEN
FORCES ARE APPLIED TO AN OBJECT
unbalanced force


F = ma
change in acceleration
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

F = ma
F is directly proportional to m and a
a is inversely proportional to m
for constant m,
for constant F,
LARGE F means LARGE a
LARGE m means SMALL a
SMALL F means SMALL a
SMALL m means LARGE a


 F
a=
m
for constant a,
LARGE F means LARGE m
SMALL F means SMALL m
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B. 2nd LAW and FREE FALL
Let’s apply the previous information to free fall (remember, motion due to the force
of gravity, ignoring air resistance)
acceleration due to gravity has the symbol g and is a CONSTANT equal to 9.8 m/s2


F = mg

 F
g=
m
If it’s true that g is a constant, then
we can see why objects, no matter what the
mass, hit the ground at the same time when
dropped together.
if m is LARGE, free fall F is correspondingly LARGE which
keeps g constant
if m is SMALL, free fall F is correspondingly SMALL which
keeps g constant
In other words, objects accelerate due to gravity at the same rate regardless of mass. Force
required to accelerate an object depends on its inertia (mass). More massive
objects require more force. In free fall, the RATIO of force to mass is constant
large mass object

F
=
m

F
m
small mass object
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

F = ma
Let’s make a substitution…
Recall…


Δv
F=m
Δt

 Δv
a=
Δt
This shows how force is related
to velocity
Lot’s of motion dynamics problems can be solved using Newton’s 2nd law.
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VII. NEWTON’S 3rd LAW
The 3rd LAW is usually stated like this:
For
every
ac6on
there
is
an
equal
and
opposite
reac6on.
•  Forces come in pairs. An object exerting a force on another object
experiences an equal force. The two forces are in opposite directions.
•  The MAGNITUDE of the force pair is the same. The directions are opposing.
Here’s an example of action-reaction force pairs:
air exiting an open balloon
air rushes down, pushing
against the atmosphere
balloon is pushed up
If the pin exerts the
same force on the ball,
why doesn’t
ball stop…or roll
backwards?
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