Transcript ppt

Mechanics Road Map
Kinematics
How things move
Dynamics
Why things move
Classical
Mechanics
Mechanics
Quantum
Mechanics
Infant stage
Wave vs particle
Quantum tunnelling
Schrödinger's cat
What the *#&! Is
going on with
those electrons!!!
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Dynamics
Why do things move?
The answer is simply “forces”.
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Introduction to Forces
Forces cause things to move.
Forces can push or pull
Forces do not need contact in order to exist.
The unit for force is a Newton ( N ) and can be thought of as
the amount of force that is needed to accelerate 1 kg of mass
at 1 m/s2
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Fundamental Forces
All forces can be derived from a single, or combination of
what are known as the four fundamental forces.
From strongest to weakest they are:
Strong Nuclear
Holds atomic nuclei together
Strong
Electromagnetic
Holds electrons within an atom
Weak Nuclear &
Electromagnetic
Contact forces such as touch, or noncontact forces such as a magnet.
Gravity
Causes objects to fall
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“DO NOT COPY TABLE”
(Table can be found on pg 128 of text)
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Forces can change an object’s inertia.
Inertia: Inertia is the natural tendency of an object to remain in
its current state of motion. The amount of an object’s inertia is
directly related to its mass.
Mass: The quantity of matter an object contains.
(A.K.A. The amount of stuff in an object)
Gravitational influence: the property of matter that determines the
strength of the gravitational force. This is what causes weight to
exist and will be discussed in grater detail in grade 12.
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“DO NOT COPY TABLE”
(Table can be found on pg 127 of text)
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DO
Table cloth Demo
Section Review Pg 129 #’s 1-4
(pdf 22)
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Units of Measurement
“DO NOT COPY TABLE”
Length
Speed
Standard
Metric
Foot
Mile
Meter
Kilometre
Mile per Hour
Kilometre per Hour
Volume
Gallon
Litre
Temperature
Fahrenheit
Celsius
Weight
Force
Pound
Pound
Newton
Mass
Slug
Newton
Kilogram
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Mass vs Weight
Despite common misconception Mass and weight are two totally
different quantities.
Mass is the amount of stuff in an object
Weight is the gravitational force exerted on an object by Earth’s
(or any other planets) gravitational field, and can be found with
the following formula. Where g, on Earth at sea level is always
equal to -9.8 m/s2
W  mg
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Example
Try calculating your own weight, in Newton’s, keeping in
mind that mass is measured in kilograms not pounds. However
here on Earth at sea level 1 kg of mass has 2.2 lbs of weight.
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Example
Find the weight of a 2.26 kg bag of sugar.
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The value of g is –9.81 m/s2 “on earth, at sea level”, but what
about when your not at sea level or, not even on earth for that
matter?
As it turns out the farther away from the center of the earth, you
are, the smaller the value of g.
For example g would be smaller on top of a mountain and bigger at
the bottom of the deepest ocean.
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“DO NOT COPY TABLE”
(Table can be found on pg 132 of text)
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Likewise the value of (g) on other planets is different as well,
this concept will be looked at in depth in grade 12.
The two main quantities involved, are the mass and radius of
the planet.
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Example:
Calculate the weight of a 4 kg spherical chicken on the surface
of the moon.
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Example:
If Mr. Harper has a weight of 1256 N, on earth, find his mass.
What would his mass and weight be on the moon?
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Mass and Weight Facts
Mass is an exception to the rule for base units, the base unit for
mass is kilograms (kg) not grams (g)
In this course weight will always be measured in Newton’s
Weight is always directed radially downwards towards the center of
the earth
Weight has both magnitude and direction therefor it is a vector
Weight is always present even during free-fall
Weight will change slightly with altitude
Weight is different on each planet
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DO
Pg 137 #’s 1 – 4 (pdf 23)
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Friction
Friction is the force that opposes the motion between two surfaces
that are in contact.
(Makes things hard to move)
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On the microscopic scale
all surfaces are rough.
When two surfaces are
in contact with each
other the high points on
one surface temporarily
bond or lock with the
high points of the other
surface.
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There are two types of friction.
Static friction is when there is no relative motion between the
two objects.
“Such as a square pig sitting motionless on the floor.”
Kinetic (sliding) friction is when there is relative motion
between the two objects.
“Such as when you manage to start to push that
same square pig across the floor.”
**Kinetic friction is “always” a lesser value then static friction.**
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Friction depends on two things
1. The nature of the surfaces in contact, every different pair of
surfaces will act differently with respect to friction.
Every surface has a different amount of “grippeness”. This
grippeness can be measured, and then for every pair of surfaces
an associated value is given.
This grippeness value is called the coefficient of friction.
The symbol for the coefficient of friction is Mu (μ), which can
only be determined experimentally.
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“DO NOT COPY TABLE”
(Table can be found on pg 140 of text)
Note how the
grippy surfaces
have higher
coefficients of
friction that the
slippery
surfaces.
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The second thing that the force of friction depends on is:
2. The magnitude of the force pushing the two surfaces
together. This force is called the normal force (fn) and for
simple cases where an object lying on a level surface, it is
equal to the weight of that object.
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Normal Force
Many people seem to struggle with the concept of “normal force”
perhaps it is because the normal force is not an obvious force, take
for example the following
A 2 kg book is sitting on a shelf.
W
If the only force acting on the book is that of weight, then the
book should fall down because there is no other force present to
counter act that of gravity.
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If there is only weight present then an object will always fall
W
W
W
W
W
W
W
W
W
If the object is not falling then there must be a second force
balancing the weight.
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This second force is known as the “normal force”, and in the
case of an object sitting on a surface it is always directly
opposite the weight..
The normal force is always perpendicular to the surfaces in
contact. This is the origin of its name “normal force” it is
normal to the surface.
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The normal force is not always equal to the weight of an object;
it is the force pressing the surfaces together.
In this case the normal force is equal to the applied force from
the hand, which is pushing the surfaces together.
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The force of friction depends on both the coefficient of
friction and the normal force. It can be found using the
following formula
f f  fn 
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Using Normal Force to Calculate Friction
Find the force of friction in between Calvin’s toboggan and
the snow if the coefficient of friction between wood and snow
is 0.30, and the normal force for the toboggan is 400 N.
ff = 120 N in the opposite direction
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Example:
In the winter, people will often place square pigs in the back of
their trucks to increase the amount of friction between the tires
and the road. Find the increase in the frictional force that would
result by placing a 200 kg square pig in the back of a truck.
1400 N
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Example:
A horizontal force of 85 N is required to pull Mr. Harper on a
sled at constant speed over dry snow to overcome the force of
friction. If Mr. Harper and the sled have a combined mass of
52 kg. Calculate the coefficient of kinetic friction between the
sled and the snow.
μ = 0.17
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Example
A smooth wood block is placed on a smooth wooden tabletop.
You find that you must exert a force of 14.0 N to keep the 40.0 N
block moving at a constant velocity.
a) what is the coefficient of sliding friction for the block
and table?
μ = 0.350
b) if a 20.0 N brick is placed on the block, what force would
be required to keep the block and brick moving at a constant
velocity?
fa = 21.0 N
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Free Body Diagrams
FBD’s are often used to
summarize all the forces
acting on an object
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DO
Pg 144 # 5-8 (pdf #23)
Pg 147&148 #1-15 (omit #9)
(pdf #23)
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Net Force
We often have questions dealing with more than one force at the
same time. To deal with this we need to define what is meant by
net force.
The net force (F) is simply all of the forces added together,
keeping in mind at forces are vectors and they have associated
directions.
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For example, if a force was applied in the negative direction
it would have a negative (-) sign.
F  f 1  f 2  f 3  .......
Upper case (F) is used to denote Net force from all other forces
which are always lower case (f).
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Example:
Three people are pushing on a square pig. The first pushes
to the right with force of 40 N, the second pushes to the left
with a force of 75 N, the third also pushes to the left with a
force of 15 N. If the pig has a mass of 25 kg, find the net
force acting on the pig.
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Example:
Mr. Harper is trying to lift is pet pig Peter in to the back of his
truck in an attempt to increase the amount of friction between the
truck tires and the road. He very quickly realizes that he is to much
of a wimp to be able to do it by him self so he recruits some of his
physics students to give him a lift. If Mr. Harper is able to lift 529
N and Mark can lift 641 N and Sally can lift 734 N:
a) Draw a FBD of the forces involved.
b) What is Peter’s mass?
194 kg
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DO
Dynamics Extra Pr Work Sheet
Friction lab
**Extra problems if students want to do.**
End of chapter Review Pg 149 -151
#’s 1 - 35
Omit #’s 3, 7, 10, 13, 18, 20, 21, 25, 29,
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Newton’s Laws
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Newton’s three laws of motion
Newton’s first law of motion: an object at rest or in uniform
motion will remain at rest or in uniform motion unless acted on by
an external force.
(AKA) an object at rest stays at rest
Remember the table cloth demo?
Here Newton is simply restating the definition of
inertia from Chapter 4.
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Newton’s second law of motion:
The acceleration of the body is directly proportional to the net
force on it and inversely proportional to its mass.
(AKA) F = ma
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Discuss conceptual problem Pg 161
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Newton’s third law of motion:
When one object exerts a force on second object, the second
exerts a force on the first that is equal in magnitude but opposite
in direction.
(AKA) action/reaction forces
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Example:
What force is required to accelerate a 1500 kg race car at 3.0
m/s2?
f = 4500 N
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Example:
A 2.0 x102 g spherical Chicken is accelerated upwards at 2.3
m/s2. What is the value of the applied force?
2.4 N
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DO
Practice Problems Pg 163 #’s 1-3
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Example:
An artillery shell has a mass of 55 kg. The shell is fired from
a gun, leaving the barrel with a velocity of 770 m/s. The gun
barrel is 1.5 m long. Assume that the force, and thus the
acceleration, of the shell is constant while the shell is in the
gun barrel. What is the force on the shell while it is in the
gun barrel?
f = 1.1 x 107 N
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Example:
A TV produces light when fast-moving electrons collide with
phosphor molecules on the surface of the screen. Electrons of
mass 9.1 x 10-31 kg are accelerated from rest in the electron “gun”
at the back of the vacuum tube. Find the velocity of the electron
when it exits the gun after experiencing an electric force of 5.8 x
10-15 N over a distance of 3.5 mm.
6.7 x 106 m/s
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Example:
A curler exerts an average force of 9.50 N on 20.0 kg stone.
( Assume that the ice is frictionless.) The stone started from
rest and was in contact with the girl’s hand for 1.86
seconds.
a) Determine the average acceleration of the stone.
0.475 m/s2
b) Determine the velocity of the stone when the curler
released it.
0.884 m/s
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DO
Practice Problems, Pg 168 #’s 4-8
Practice Problems, Pg 170 #’s 9,10
Section Review, Pg 176 #’s 1-7 omit # 5
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Example:
A 55 kg person is standing on a scale in an elevator. If the scale
is calibrating newtons, what is the reading on the scale when the
elevator is not moving? If the elevator begins to accelerate
upwards at 0.75m/s2, what will be the reading on the scale?
540 N & 580 N
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Example:
A spherical pig in a square chicken are riding in a vacuum
sealed elevator. The combined mass of the elevator and its
occupants is 700 kg. Calculate the magnitude and direction
of the elevators acceleration if the tension in the supporting
cable is 7500 N.
0.904 m/s2
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Example:
A spring scale hangs from the ceiling of an elevator. It
supports a package that weighs 25 N.
a) what upward force does the scale exert when the elevator is
not moving ?
25 N up
b) what force most the scale exert when the elevator and object
accelerate upward at 1.5 m/s2?
29 N up
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DO
Practice Problems Pg 186 #’s 21 - 23
Section Review Pg 194 #’s 1-7 omit # 4
**Extra problems if students want to do.**
End of Chapter Review
Pg 206 #’s 1, 2, 3, 5, 6, 10, 16, 23, 28, 29, 30, 32
(note: No Momentum Questions)
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