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8/10/2019 Lec22 Physical Quantities
http://slidepdf.com/reader/full/lec22-physical-quantities 1/22
Announcements The book “A Tour of the Subatomic Zoo” is at the SU Bookstore,
not the Orange bookstore. (The SU Bookstore is the one in Schine)
Frontiers of Science Lecture this Thursday at 7:30,
Grant Auditorium. (Benefit of the doubt credits!)
“The Elegant Universe”
Brian Greene, Columbia University
Lectures will be posted in the morning, so feel free to bring a
printed copy with you to class. Sometimes they will be availablethe night before.
FYI, When printing the PDF file for a lecture, you can print multipleslides to a sheet using the Printer Properties dialog box.
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Introduction to PhysicalQuantities
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Scalars
Scalar quantities are those which are described solely by their
magnitude
Some examples are:
Mass e.g. 14 [kg], 36 [lbs], …
Time e.g. 10 seconds, 40 minutes, …
Volume e.g. 1000 cm3, 4 litres, 12 gallons
Temperature e.g 14o
F , 25o
C, … Voltage e.g. 9 Volts, etc
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Vectors
Vector quantities are those which need to be described by BOTHmagnitude and direction
Some of the most common examples which we will encounter are:
Velocity e.g. 100 [mi/hr] NORTH
Acceleration e.g. 10 [m/sec2] at 35o with respect to EAST
Force e.g. 980 [Newtons] straight down (270o)
Momentum e.g. 200 [kg m/sec] at 90o.
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Distance The separation between two locations.
Distance can be measured in many types of units. We will mostly use:
MKS Units
millimeters [m]
centimeters [cm]
meters [m]kilometers [km],
etc
You should be comfortable with converting from [cm] to [m], [mm] to [km], and so on.
We may use the symbolic notation d to mean a change in the
position.
The symbol should be read as “the change in”
FYI : 1 [km] = 0.6 [mi]
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Time
In physics, we are most often less interested in absolute time than
changes in time, or a time interval.
Time can be expressed in several units as well:
seconds [sec]
minutes [min]
hours [hr]
daysyears
etc…
Example 1: How much time does it take for the earth to make onerevolution?
Example 2: How long did it take for you to drive to the store today?
We usually refer to a time interval as : t
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VelocityVelocity is a measure of the rate of change of the distance with
respect to time.
v = d / t
It will usually be measured in [m/sec].
What does 5 [m/sec] mean? It means if an object passes by us at 5 [m/sec], it will advance its
position by 5 [m] every second. So after 2 [sec], it will have
advanced 10 [m], and 20 [m] in 4 [sec] and so on.
If a train moves at 50 [meters/sec], how far will it go in 50 seconds ?
a) 100 miles b) 2.5 [km] c) 250 [m] d) 2500 miles
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Acceleration (I)
Acceleration is the rate of change of velocity with respect to time
a = v / t [a] = [m/sec] / [sec] = [m/sec2]
What does a = 5 [m/sec2] mean?
If an object starts at rest, its velocity increases by 5 [m/sec]
every second.
Time (sec) Acceleration Velocity
0 5 m/sec2 0 m/sec
1 5 m/sec2 5 m/sec
2 5 m/sec2 10 m/sec
3 5 m/sec2 15 m/sec
4 5 m/sec2 20 m/sec
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Acceleration (II)
Acceleration can be negative also! We call this deceleration.
If the acceleration is in the same direction as the velocity,
the object has positive acceleration (it speeds up).
If the acceleration is in the opposite direction as the velocity,
the object has negative acceleration or deceleration (it slows down).
Deceleration: Animated GIF of car decelerating
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What is a Force ?Force is simply:
A PUSH A PULLor
Forces have both magnitude
and direction
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Force and Acceleration Experimentally, we find that if we apply a force
to an object, it accelerates.
We also find that the acceleration (a) is directly
proportional to the applied force (F ) and inversely
proportional to the mass (m) . That is:
a = F / m
This is Newton’s Law, and it is often written:
F = ma
This means:
Increasing the force increases the acceleration;
decreasing the force results in a lower acceleration.
I saac Newton
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Force (I) A force is generally a result of an interaction between two (or more)
objects (Try and think of a scenario where a force is applied with onlyone object involved)?
Can you think of some examples of forces?
Gravitational
Electric
Magnetic
Friction
Wind drag
Van der Waals forces
Hydrogen bonds
Forces in a compressed or stretched spring
+…
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Forces (II) Since two or more objects must be involved, a force intimately
tied to the notion of an interaction .
Interactions are now believed to occur through the exchange of
“force carriers”. This is a very important point, and we’ll come
back to it later…
So far, we know only of four types of fundamental forces in
nature:
Gravity, Electromagnetic, Weak, and Strong
We will come back to each of these
All other forces in nature are understood to be the residual effects
of these fundamental forces
Particle Exchange and Force (use Explorer)
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Momentum (I)What is momentum?
Momentum is simply the product of the mass and the velocity.Denoting momentum as p , it is simply:
The units of momentum are [kg][m/sec] == [kg m/sec]
Momentum is a very important subject in physics because it is
what we call a conserved quantity . What does this mean?
We will come back to the idea of conserved quantities in physics.
They play a very important role in understanding the world around us!
p = m*vmv
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Momentum (Example I)
If a 500 [kg] car is traveling west at 20 [m/sec], what is
its momentum?A) -1x104 [kg m/sec]
B) -1x103 [kg m/sec]
C) 25 [kg m/sec]
D) 1x105 [kg m/sec]
p = mv
= (500 [kg])(-20 [m/sec])
= -10,000 [kg m/sec]
= -1x10
4
[kg m/sec]
-20 [m/sec] 500 [kg]
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Momentum (Example II)
If a 5000 [kg] truck is travelling east at 10 [m/sec], what is its
momentum?A) -5x104 [kg m/sec]
B) 5x104 [kg m/sec]
C) 500 [kg m/sec]
D) 1x104
[kg m/sec]
10 [m/sec]5000 [kg]
p = m*v
= (5000 [kg])(10 [m/sec])
= 50,000 [kg m/sec]
= 5x104 [kg m/sec]
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Momentum (Example III)If the car and the truck collide, what is the total momentum of the
car and truck just before impact?
A) 6x104 [kg m/sec]
B) -4x104 [kg m/sec]
C) 4x104 [kg m/sec]
D) 0 [kg m/sec]
Since their momenta are aligned in the same direction, we can
just add them:
PTOTAL = -1x104
[kg m/sec] + 5x104
[kg m/sec] = 4x104
[kg m/sec]
10 [m/sec]
5000 [kg]
-20 [m/sec]
500 [kg]
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Energy
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Energy
What do you mean mass is a form of energy?
We’ll get to this later….
The thing about energy is that it cannot be created ordestroyed, it can only be transformed from one form into
another
Yes, like momentum it is a “conserved” quantity. We will learn that conserved quantities are a powerful tool in
“predicting the future”!
8/10/2019 Lec22 Physical Quantities
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Summary I
In nature, there are two types of quantities, scalars and vectors
Scalars have only magnitude, whereas vectors have both
magnitude and direction.
The vectors we learned about are distance, velocity, acceleration,
force, and momentum
The scalars we learned about are time, and Energy.
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Summary II
Forces are the result of interactions between two or moreobjects.
If the net force on an object is not zero, it will accelerate. That
is it will either speed up, slow down, or change direction.
Energy and momentum are conserved quantities. This has
far-reaching consequences for predicting whether certain “events”
or “processes” can occur.
There are many forms of energy. The topic of energy will
be discussed in greater detail in next lecture.