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Newton’s Laws
Mechanics - Study of Motion
Mechanics - the study of motion
Kinematics - How things move (time line for foundation of kinematics- early
1600's)
work done by Galileo,
i.
ii.
Why do all things accelerate at one rate?
How does the earth know to pull on more massive objects with
a proportionally larger force than it pulls on smaller masses?
work done by Kepler
i.
What is the force that emanates from the sun that is
responsible for holding planets in elliptical orbits?
Dynamics - Why things move as they do
work done by Isaac Newton,
i.
ii.
iii.
Work began in 1666
we will see in a later lecture how Newton unified these
two seemingly unrelated fields with one master stroke
His work led to the belief that all one had to do was to
understand the rules governing motion and the world
behaved as a machine – producing the same result for the
same given input
There are only THREE types of motion that we need to describe:
a. objects at rest
b. objects moving with constant velocity
c. objects that are accelerating
Inertia
Aristotelian View of Forces
a. The natural state of an object is to be at rest.
b. In order to get an object to move, one must apply a force. (Push a book, etc.)
c. However, once the force is taken away, the object once again comes to rest.
Galileo's ramp experiments
Regardless of the angle of ramp C the ball always seemed to rise to the same height
that it had on ramp B.
What would happen if he were to remove ramp C?
Clearly the implication would be that it would continue on with uniform motion
forever.
Galileo’s Definition of Inertia: the tendency of an object to resist a change in motion.
(the more massive an object, the greater its inertia)
Newton summarizes Aristotelian and Galilean physics by stating in his book Principia his
1st Law of Motion (what we have come to refer to as the Law of Inertia) :
Law Of Inertia
Newton's 1st Law - An object at rest, or in uniform straight line motion, will remain at rest, or
in uniform straight line motion, unless acted upon by a net external force.
Another way to state this law might be: If there are no net external forces acting on a body, then it will
continue in it's state of constant velocity (which may be zero).
This is easier to write mathematically.


if
F

0
, then
v

constan

n
n
n

1
which translates to: if we add up all of the forces acting on a body from 1 to
the nth force and get zero as the resultant, then the body is moving with
constant velocity.
Newton’s 2nd Law
Newton also explains what happens when the forces do not add up to be zero.
Newton's 2nd Law - A net force acting on a body produces on that body, an acceleration
that is directly related to the force impressed upon the body and inversely related to the
mass of the body.
An easier way to state it is:

 
if
F

F
,
then
F
m
a

n
n
et
n
et
n
n

1
The units of force are directly derived from this formula
units of force = kg m/s2.
This is sufficiently lengthy enough to warrant a short hand version. Thus a unit of force is called a
Newton (N) and was made in his honor. Thus, when keeping track of units:
N = kg m/s2
Since acceleration is a vector quantity, force is a vector quantity as well.
Caution - a common mistake in solving problems is forgetting to add up all of the forces before applying
the second part of Newton's 2nd Law.
Field versus Contact Forces
For our purposes we will define a force as a push
or a pull on an object.
We will categorize forces into two categories:
Contact forces – forces that result from the physical contact between two
objects
Field Forces – forces that arise from the interaction of an object located within a
field of influence of another object. E.g., an object in the gravitational field of the
earth, or the earth within the gravitational field of the sun, or an electron within
the electric field of a proton, or a piece of iron near a magnet, et cetera.
There are really only four quantified forces in all of nature:
Strong interaction
Weak interaction
Electromagnetic
Gravitation
3rd Law, Weight, and Normal Force
Newton's 3rd Law - For every action there is an equal but
opposite reaction


F


F
or mathematically stated:
ab
ba
It is an observation of Newton that forces naturally occur in
pairs
Example: Weight - the force with which
a gravitational body (such as the earth)
pulls on a body
r
r
Mathematically it is defined as: W  mg
Any body that has mass, has weight when
it is near to a gravitational body.
When a person (mass = 70 kg) is standing
on a floor, the force that he exerts on the

floor is his weight
3rd Law, Weight, and Normal Force
The floor, by Newton's 3rd Law, exerts an equal but opposite force of 686N to
prevent the person from falling through the floor.
This force that acts perpendicular to the floor is referred to as the Normal Force
and is another example of a Contact Force that we will encounter frequently.
It is referred to as the normal force, not
because it is always there, but because the
term normal is a mathematical term that
means perpendicular.
Not all surfaces are capable of exerting a force equal in magnitude to the
weight of object placed upon them. Thin ice is a good example, but almost any
surface can be destroyed, or broken, by placing a sufficiently large mass upon
it.
How does this Normal Force Arise?
What then, is the nature of this normal force that surfaces seem to exert? How does a wall
know to push back harder when I push with increasing force?
At the most basic level the object placed upon a surface is repelled by electromagnetism.
The outer most electrons that comprise the object are electrically repelled by the electrons
that comprise the surface.
The electrons offer a stronger and stronger repulsive force the closer and closer the object is
moved to the surface - just as two similar ends of magnets repel any effort to touch
them together.
We can break the electric bonds between the atoms that make up the surface if we exert a
large enough force.
Hence the more massive an object, the greater gravity tends to pull them onto a surface,
and the greater the surface tends to repel the object.
The object will be at rest on the surface (according to Newt's 1st Law) only if the surface is
capable of exerting an equal and opposite force to sustain it, otherwise the object
crashes through the surface.
Example
30N
What force does the 5kg block
exert on the 10 kg block?
Look at the two block system
as a single object…


F
a
netm
5kg
Focusing on the 10kg object…
(N2L)
30N
30
(10
5)a
F5on10



30NF5on10 Fnetma

30F5on10 10(2)

3010(2) F5on10

F5on10 10N
a30
/15
2m/s2
Focusing on the 5kg object…
F10on5


F
m
a
10
on
5

F
(5
)2
10
N
10
on
5
10kg
(N3L)
Free Body Diagrams
Free Body Diagrams
r
r
T1L T2L


r
FBL
r
FG
y


x
Free Body Diagrams
θ1
r
r
T1L T2L
θ2
θ1


r
FBL
θ2
r
FG
y


x
Train
C3
C2
C1
Three railroad cars are being pulled with a force of 12,000 N. Car 1
has a mass of 2000kg, car 2 has a mass of 3000 kg, and car 3 has a
mass of 5000kg. Neglecting friction, what is the acceleration of the
train and what is the force between car 2 and 3?
Solution
C3
C2
C1
Think of all three cars as a single object
whose mass is equivalent to the total
masses of the three cars. For now, look
at only the horizontal sense.
A free body diagram would indicate only
one force if we neglect frictional forces
F net
C3
C2
C1
A free body diagram of car 3 would
indicate only that car 2 is pulling on it
F23
Car 3 we already know is


accelerating at 1.2 m/s2 so it
F

m
a
net
must have a net force acting on
12
,000

(
2000

3000

5000
)
a it (provided by Car 2) of:
2
F23= 5000(1.2) = 6000N
a

12000
/10000

1
.2
m
/s
Tug of War
Two teams are comprised of equal strength players, each capable
of pulling with a force of 400 Newtons. Each team has 4
players each. Each person has a mass of 80 kgs.
In this case, the two forces exerted horizontally add up vectorally to be zero. Does that
mean the rope is not moving?
Examples cont.
An additional force is exerted by one of the players who becomes psyched. This person
now pulls with a force of 420N
Now there is a net force of 20 Newtons to the right. This net force is acting
upon a total mass of 640 kg (excluding the rope) which produces an
acceleration of:
r
r
Fnet  ma
r Frnet
a  m  20 N /640 kg
r
a  0.03 m/s 2
