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Chapter 4
Forces and Newton's Laws of Motion
Definition of Force
That which changes the velocity or direction of an
object.
Direct (contact)
Those forces which need to physically touch the object to
change its velocity or direction. Examples are friction,
tension in a rope, motion caused by a spring, etc.
Noncontact
Two types:
Those forces which do not have a visible hold on the
object. Examples are gravity, electric field, etc.
More Definitions...
Forces are Vectors
you label a force as you would a vector and need both
a magnitude and direction to fully describe them.
Mass
A scalar quantity which describes how much of the
object you have.
For instance, a car has more mass than a bicycle.
Isaac Newton
Born 1643 in
Lincolnshire England
Entered Cambridge
University to study
law but was attracted
to the teachings of
Galileo and Kepler.
Eventually he
produced the three
laws we are about to
learn.
Newton's First Law
An object at rest stays at rest unless acted upon by an
outside net force.
An object in motion stays in motion unless acted upon
an outside net force.
Net force is the vector sum of all forces acting on an
object!
Friction
Air Resistance
Engine
30 m/s
30 m/s
Engine = Friction + Air Resistance
Inertia vs. Mass
Inertia is the reason an object at rest stays at rest
or an object moving in a straight line continues to
move with the same velocity along that line
unless an external force causes it to do otherwise.
If you have two objects with different masses, the
one with more mass is said to have more inertia (a
greater tendency to not change its current speed or
direction).
This then leads us to intepret the measure of
inertia as the object's mass. Both inertia and mass
are measured in SI units of kgs.
Everyday Use of Inertia
The pedulum is a heavy weight
and is attached to the car but is
free to swing back and forth.
When the car rapidly slows
down, the pendulum's inertia
(tendency to not change it's
speed) causes it to continue
forward even though the car is
slowing.
This causes the locking bar to
stop the rotation of the ratchet
wheel and prevents the seatbelt
from being extended thus
holding the passenger close to
the seat.
A frame is the way you choose to view the problem.
Example: You are given a problem of a boat accelerating in some
direction on a lake. You could choose many different frames.
Inertial vs. Non-Inertial Frames
You could choose to view the water as the stationary object
and see the boat accelerating in some direction. This frame
includes the water, the boat, and anything in the boat. This
is an inertial frame since it is not accelerating, only objects
within it accelerate!
You could also choose to move along with the boat as it
accelerates. Now, the boat appears to be stationary and all
motion is relative to the boat. The frame includes only the
boat and anything in the boat. This is a non-inertial frame
since the frame itself is accelerating!
Newton's First Law and Non-Inertial
Frames
Newton's First Law (Law of Inertia) only applies
in inertial frames.
Good example from the book:
A passenger is riding in a car which begins to
accelerate. There are two frames of reference one can
easily identify.
You could reference all motion to the ground below the car.
The first law would apply here since the ground is not
accelerating!
You could reference all motion to the accelerating car. The
first law would not apply here since the car is accelerating.
Newton's Second Law of Motion
Simply stated:
F = ma
(only one force acting on the object = ma)
F = ma
SI unit for force is the Newton (I wonder why?)
definition:
1N = 1 kg m/s2
(sum of all forces acting on an object = ma)
Newton's Second Law
You may (and should) consider forces in the xdirection to be completely separate from forces in
the y-direction.
The 2nd law states: As long as a force is acting on
the object, there must be an acceleration (the
equality demands this). This means the velocity
must be changing as time changes.
Remember, a change in velocity does not only
mean a change in speed. It could also mean a
change in direction.
Free Body Diagrams
Engine
Friction
y
Friction Engine
x
These allow one to
draw all the forces in
one place and helps
simplify the problem.
If any force does not
lie on either the x or y
axis, it needs to be
broken into its
components.
y
Friction Engine
x
Comments on the Previous FBD
Fx = max ;
Fy = may
There is no acceleration
in the y direction since
there are no forces in this
direction (either positive
nor negative).
Since the force due to the
engine is larger than the
frictional force, the car
will accelerate in the +x
direction.
Simply states:
Newton's Third Law
If one object pushes on
another object, the object
being pushed, pushes back
with an equal but opposite
force.
The two objects do not
usually have the same mass,
so the less massive object
will have a larger
acceleration.
Forces on the First Person on One
Side of a Tug-of-War
Friction force
Normal force
Tension from the other team
Gravitational force
Tension from your team
Normal force = Gravitational Force (y direction)
The war starts with everyone stationary, therefore, vox = 0. After
the war starts, if the person does not start to move (∆vx = 0) then
there is no acceleration in the x direction and the 2nd law tells us
there is not a net force in the x direction.
This means the tension(+) = tension(-) + friction force.
Newton's Law of Gravitation
Magnitude:
F
G
m1 m 2
r
2
Direction: The line joining the two masses.
Moon: m2
+F
Earth: m1
-F
r
7.35 1022 kg
Mass of the Earth:
5.98 1024 kg
Mass of the Moon:
6.67 10-11 N m2 / kg2
r:
3.85 108 m
F:
1.98 1020 N
G:
Does the rotation of the moon about the earth
affect the position of the earth in space?
amoon = 1.98 1020 N / 7.35 1022 kg = 2.69 10-3 m/s2
#
"
aearth = 1.98 1020 N / 5.98 1024 kg = 3.31 10-5 m/s2
!
Newton's Law of Gravitation (2)
No, mass is universal. I have the same mass whether I
am on the earth, the moon, or simply floating in
space. Mass is the measure of how much of
something you have.
Weight is a quantity which depends upon where you
are and the force of acceleration there.
Example:
my mass is 80 kg
my weight on earth is then 784 N
my weight on the moon is 130 N
)
(
*
+
'
%
Isn't mass and weight the same thing?
&
$
Mass vs. Weight
This is the force provided by one object to
support another object.
Example: A book rests on a table and has a weight of 18 N (1.8
kg. 9.8 m/s2). Newton's third law says the table must push
back with an equal and opposite force since the book is not
accelerating up or down. This force provided by the table is
known as the normal force.
/
.
-
,
Normal Force
The word "normal" is a mathematical term which
is defined as the vector perpendicular to the
surface one is describing.
Examples of a Normal Force
N
mg
N
mg