Chapter 3
Newton’s Laws
THE MASS
Every object possesses inertia.
Inertia is the tendency of a body at rest to
remain at rest, and of a body in motion to
continue moving with unchanged velocity.
or
Inertia is the sluggishness of an object to
changes in its state of motion.
Mass - a measure of the inertia of an object
Demo - Inertia rocks
Demo – Hoop and chalk
THE STANDARD KILOGRAM
The standard kilogram is an object whose mass is
defined to be one kilogram.
Abbreviation is kg.
There is an English unit of mass. The slug.
A slug weighs 32.2 lb.
FORCE
In general force is the agency of change.
In mechanics forces cause accelerations.
It is a vector.
An external force is one whose source lies
outside of the system being considered.
THE NET EXTERNAL FORCE
The net external force acting on an object
causes the object to accelerate in the direction
of that force.
The combination of
forces that act on an
object is the net force.
(Only the net force is
shown in the figures on
this slide.)
The acceleration of an
object is directly
proportional to the net
force.
F
F
F
m
a
m
m
This symbol means
proportional to
aF
a
a
Consider the same net
force applied to
different mass
objects.
F
a
m
m
F
a
m
m
The acceleration is
inversely proportional
to the mass of the
object.
m
F
m
1
a
m
a
The acceleration is proportional to the force and
inversely proportional to the mass of the object.
THE NEWTON
The Newton (N) is the SI unit of force.
A resultant 1 N force will give a 1 kg mass an
acceleration of 1 m/s2.
The pound (lb) is the English (US customary) unit
of force.
A resultant 1 lb force will give a 1 sl mass an
acceleration of 1 ft/s2.
NEWTON’S FIRST LAW
An object at rest will remain at rest;
an object in motion will continue in motion with
constant velocity, except insofar as it is acted
upon by an external force.
“If you leave an object alone, it has constant
velocity.”
NEWTON’S SECOND LAW
Newton stated it in terms of momentum.
A less rigorous form of the second law will be
used here.
If the net external force acting on an object is
not zero, then the acceleration of the object is
directly proportional to the net external force
and inversely proportional to the mass of the
object.
F
a
m
or
F  ma
The force in each of these equations
represents the vector sum of all of the
forces acting on the object of mass m.
This vector equation can be written out as
three separate scalar equations.
F  ma
Fx  max
Fy  ma y
Fz  maz
NEWTON’S THIRD LAW
Forces represent interactions between one
piece of matter and another.
Therefore, forces come in pairs.
For each force exerted on one body, there
is an equal, but oppositely directed, force
on some other body interacting with it.
“You cannot touch without being touched.”
Paul Hewitt
This is often called the Law of Action and
Reaction.
THE LAW OF UNIVERSAL
GRAVITATION
m1
m2
r
m1m2
F 2
r
m1m2
F G 2
r
G  6.67 x10
11
N  m / kg
2
2
Gravity is the most dominant force in
nature.
Yet it is the weakest.
1 unit
2 units
4 units
3 units
Let’s look at the inverse-square
nature for the force of gravity.
THE WEIGHT
The weight of an object is the gravitational
force acting downward on the object.
Because the Earth is not a perfect uniform
sphere, and because it is spinning, the
weight measured by a scale (often called
the effective weight) will be very slightly
different from that defined here.
RELATIONSHIP BETWEEN
MASS AND WEIGHT
Look at the force of gravity on a freely
falling object.
We call that the weight of the object.
F  ma
W  mg
A 1 kg object would weigh 9.81 N
or 2.20 lb.
THE TENSILE FORCE
It is an applied force that tends to stretch
things.
It’s magnitude is called the tension.
THE FRICTION FORCE
It is a tangential force acting on an object
that opposes the sliding of that object on
an adjacent surface with which it is in
contact.
The friction force is parallel to the
surface and opposite to the direction of
motion or of impending motion.
Only when the applied force exceeds the
maximum static friction force will an
object begin to slide.
THE NORMAL FORCE
The normal force is a part of the contact
force between surfaces in contact.
The normal force is perpendicular to the
surfaces in contact.
The frictional force is parallel to the
surfaces in contact.
THE COEFFICIENT OF
KINETIC FRICTION
For surfaces in contact that are sliding
with respect to each other, the coefficient
of kinetic friction is the ratio of the
friction force to the normal force.
friction force F
k 

normal force N
THE COEFFICIENT OF
STATIC FRICTION
For surfaces in contact on the verge of
sliding with respect to each other the
coefficient of static friction is the ratio of
the maximum static friction force to the
normal force.
maximum static friction force Fs max

s 
N
normal force
FRICTION
Friction opposes the motion between surfaces
in contact with one another.
When there is a tendency for movement
between two surfaces and yet there is no
motion, the friction is static friction.
Static friction has an upper limit.
When there is motion between the two
surfaces, the friction is kinetic (sliding)
friction.
FFFFAFAA
A
A
F
F
F
On the verge
of slipping
Sliding
Maximum Static Friction
Friction, F
Kinetic (sliding) Friction
Applied Force, FA
DIMENSIONAL ANALYSIS:
Fundamental Dimensions
Length - L
Mass - m
Time - t
Derived dimensions are combinations of the
fundamental dimensions.
For example: length/time2
Remember that you can only add or subtract
things that are alike.
For example velocity plus velocity
x  vot  at
1
2
2
L
L 2
L t 2 t
t
t
MATHEMATICAL OPERATIONS
WITH UNITS:
When numbers are placed into equations, their
units must appear with them.
Units undergo the same mathematical
operation as the numbers do.
Conversion from one form of the unit to
another may be necessary.
For example meters to centimeters.
See examples in text, page 30.
Free Body Diagrams (FBD)
This is a diagram showing some object and the
forces applied to it.
It contains only forces and coordinate
information, nothing else.
There are only two kinds of forces to be
considered in mechanics:
Force of gravity
Contact forces
Example FBD
A car of mass m rests on a 300 incline.
FBD
N
F
y
q
q
mg
x
Newton’s Second Law
NSL
A car of mass m rests on a 300 incline.
FBD
NSL
N
Fx  max
F mg sin q  max
Fy  ma y
N mg cos q  ma y
What if friction is smaller?
F
q
q
mg
Newton’s Second Law
NSL
A car of mass m rests on a 300 incline.
FBD
NSL
N
Fx  max
F  mg sin q  max
Fy  ma y
N  mg cos q  ma y
F
q
q
oops
mg