Transcript Newton’s Laws of Motion

A Jar of Flies
A bunch of flies are in a capped jar. You place the jar on a scale.
The scale will register the most weight when the flies are
a) sitting on the bottom of the jar
b) flying around inside the jar
c) The weight of the jar is the same in both cases.
Excerpted from Thinking Physics by Lewis Caroll Epstein
Insight Press, 614 Vermont St., San Francisco, CA 94107-2636
www.appliedthought.com/InsightPress
The answer is: c.
When the flies take off or land there might be
a slight change in the weight of the jar, but if
they just fly around inside a capped jar the
weight of the jar is identical to the weight it
would have if they sat on the bottom. The
weight depends on the mass in the jar and
that does not change. But how is a fly's weight
transmitted to the bottom of the jar? By air
currents, specifically, the downdraft generated
by the fly's wings. But that downdraft of air
must also come up again. Does the air current
not exert the same force on the top of the
capped jar as on the bottom? No. The air
exerts more force on the bottom because it is
going faster when it hits the bottom. What
slows the air down before it hits the top?
Friction. Without air friction the fly could not
fly.
Newton’s Laws of Motion
Free-Body Diagrams
Normal, Tension and Friction Forces
Newton’s Law of Universal Gravitation
Weight
What is a force?
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Intuitively, we define force as a push or a pull.
Physical contact is necessary for this to occur.
Historically in physics, we also have non-contact
or so-called action-at-a-distance forces. These
are forces that act between objects with a
distance separating the objects. Examples are
gravity and electrical and magnetic forces.
Physicists, including Newton, have always been
uncomfortable with action-at-a-distance. The
mechanism of force is not clear.
The concept of an abstract field was classical
physics solution to the question of action-at-adistance.
Modern physics’ solution is the concept of particle
exchange (photons, mesons, gluons)
An Aside (theory?)
The goal of modern physics (theoretical and experimental) is to try to
develop a single theory for all forces observed in nature.
In the last 50 years the effort has been to reduce into a single theory
the four fundamental forces in nature -- electromagnetic force, strong
nuclear force, weak nuclear force and the gravitational force. The
“standard model” is the presently accepted theory for the strong
nuclear force (QCD, quarks) and the electroweak force. The effort
now is to combine gravity. The answer might by in the
multidimensional (10 or 11 dimensions?) superstring theory where
the fundamental particle is a string that mostly loop into itself except
in 3 long range dimensions we observe.
What is mass?
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A measure of the amount of matter in an object.
Mass that determines gravitational force is called
gravitational mass.
Mass that determines inertia or resistance to
change in motion is called inertial mass.
In classical physics, there is no fundamental
reason why gravitational mass should be the
same as inertial mass except for our choice of
definitions of units.
Most careful experiments show that they are
equal.
A postulate of special theory of relativity is the
equivalence of gravitational and inertial mass,
there is only one kind of mass.
SI unit of mass is the kilogram (kg).
Newton’s First Law
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An object continues in a state of rest or in a
state of motion at a constant speed along a
straight line, unless compelled to change that
state by a net force.
Question 1: The state of rest or motion can
only be measured with respect to a frame of
reference (and the coordinate system attached
to it). In what frame of reference is Newton’s
First Law valid or is it valid in all frames of
reference?
Question 2: Is force the same in all frames of
reference?
Inertial Reference Frames
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Newton’s Laws are valid in “inertial” frames of
reference.
An inertial frame is one that moves with constant
velocity relative to another inertial frame.
An inertial frame is one that is not accelerated
relative to another inertial frame.
An inertial frame is one where Newton’s Laws are
valid. “If an object, subject to no forces, does
not move in a reference frame, that frame is
inertial.”
Isaac Newton: An inertial frame is one attached
to the “fixed” or distant stars.
Question: Is Newton’s Law an experimental law
or simply a definition of force? This is a tough
question.
Earth is an approximate inertial
frame
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For motion that is localized and does not
cover distances comparable to the size of the
earth, the earth approximates an inertial
frame.
The earth is not really an inertial frame
because it is rotating about its axis and
revolving around the sun which is revolving
around the Milky Way, etc., etc., etc.
Rotating frames are accelerated.
Fictitious forces such as centrifugal and
Coriolis forces result from the non-inertial
nature of the earth as a reference frame.
Newton’s Second Law
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When a net force SF acts on an object of
mass m, the acceleration a that results is
directly proportional to the net force and has
a magnitude inversely proportional to the
mass. The acceleration direction is the same
as the direction of the net force.
SI Unit of Force: kg·m/s2 = newton (N)
SF
a
or
m
 F  ma
In the “Imperial” or British-Engineering System or simply the fps system,
force (weight) is a fundamental quantity defined by a standard object
which has a weight of 1 pound where g=32.174 ft/s2. A mass of 1 slug is
one that accelerates 1 ft/s2 when subjected to a 1 pound force.
Weight - Force on an object by the
earth
The proverbial apple falls with an acceleration g
downward because of the attraction of the earth.
This force of gravity is the weight of the object.
What is the weight in terms of m and g?
Neglecting air resistance, the only force on the falling
apple is the weight. Therefore, by Newton’s Second
Law
 F  mg  W
Newton’s Third Law
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Whenever one body exerts a
force on a second body, the
second body exerts an oppositely
directed force of equal
magnitude on the first body.
Note that the two forces are
acting on different bodies and do
not cancel each other out.
Newton’s Third Law is sometimes
called the Law of Action and
Reaction.
Example of Action and Reaction
In outer space there are no great forces
from other objects as an astronaut
pushes off a spacecraft. The only forces
acting are action and reaction forces
between the astronaut and the
spacecraft. The astronaut pushes on the
spacecraft; the spacecraft exerts an equal
magnitude but opposite direction force
on the astronaut. Thus there is only one
force on the spacecraft and only one
force on the astronaut. They move in
opposite directions due to these forces.
Universal Gravitation, Gravity
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Newton’s Law of Universal Gravitation
expresses the force of attraction between
any two masses in the universe.
A point mass, m1 exerts an attractive force
on a second point mass, m2 proportional to
the product of the masses and inversely
proportional to the square of the distance
between them. The force acts along the line
joining the two point masses.
The proportionality constant is called the
universal gravitational constant, G = 6.673 x
10-11 N-m2/kg2.
m1m2
F G 2
r
Weight
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Weight is the force of gravitational attraction
exerted by the earth on other bodies.
Weight is always downward (locally over a
small ‘flat’ area) or looking at a large scale,
towards the center of the earth.
If mE = earth’s mass, m is the mass of an
object on the earth’s surface and RE is the
radius of the earth
mE m
F  G 2  mg
RE
g G
mE
RE2
If we can indirectly “weigh” the earth by measuring its size.
Normal Force
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Normal force is the
reaction force exerted
by a surface on an
object due to the
force exerted by the
object on the surface.
It is called “normal”
force because it is
always normal or
perpendicular to the
surface.
W
Free-Body
Diagram
FN
Free-Body Diagram
Free-Body Diagram - a diagram of an isolated
object (all other objects removed) and all the
forces acting on the “free” object. It is
important that there be a complete accounting of
all forces including their directions. Forces
acting on other bodies are not included. We
apply Newton’s Laws on the Free Body.
Example: Apparent Weight in an
Accelerated Frame
Assume a is upward. In case
(a) a = 0.
a
(b) a is positive.
(c) a is negative.
(d) a = -g.
Apparent Weight - Solution
FBD - Person
Newton’s Second Law
(upwards is positive)
a
F
y
 m ay
FN  m g  m a
FN  m g  m a  ma  g 
FBD - Scale
FN
Weight of W
S
scale
Force exerted by
person (Newton’s
3rd Law)
(FN)F Normal force
exerted by
floor
Scale records the force
FN exerted by the
person standing on it.
What is the value of
FN for cases (a) to (d)?
Tension Force
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Reaction force in a string,
cord, rope, cable and
similar objects when
applied forces pull on it
tending to stretch the
string, cord, etc.
Think of a spring being
stretched; it will pull back
against the stretching
force. The resistance of
the spring to stretching is
the tension force.
Tension forces are
transmitted along the
length of the cord to the
opposite end and is always
“pulling back” in.
For massless rope, tension
is the same everywhere on
the rope whether it is
accelerated or not.
Force of Friction
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Friction is a force between
two surfaces in contact
directed parallel to the
surface.
Friction is due to attraction
between the atoms at the
points of contact.
Friction when surfaces are
not sliding is called static
friction.
Friction when the surfaces
are sliding relative to each
other is called kinetic
friction.
W
Static Friction
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Occurs between two surfaces
in contact that tend to slide
because of other forces
acting.
Is directed parallel to the
surface and opposite the
direction of possible motion.
Has a magnitude that can
vary from zero to a maximum
value. The actual magnitude
is what is necessary to
maintain equilibrium.
µS is a dimensionless quantity
called the coefficient of static
friction.
FN
f S   s FN
f SMAX   s FN
Kinetic Friction
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Force of friction between sliding surfaces.
Has a constant magnitude that does not
depend on the velocity of sliding.
Has a magnitude less than the maximum static
friction force.
f k  k FN
k is a dimensionless quantity called the coefficient of
kinetic friction. Its value is less than s
Both static and kinetic friction do not depend on the total surface
area but only on the coefficient and the normal force. You would
think that friction should depend on area. Actually it does but the
critical area is the area of microscopic contact sites. The
dependence on the normal force and coefficient is a macroscopic
description of this dependence.
Relevant Sample Problems to
be done in the next lecture Applications of Newton’s Laws