Date post: | 06-Mar-2018 |
Category: |
Documents |
Upload: | vuongkhuong |
View: | 218 times |
Download: | 4 times |
ISP209s10 Lecture 3 -1-
Today
• Announcements:
– HW#2 and extra credit #1 is due Wednesday1/27 by 8:00 am
– Pls. register your clickers on LONCAPA
• Loose ends from last class
• Law of Inertia (Newton’s 1st Law)
• What is Force? Introduction
ISP209s10 Lecture 3 -2-
A pictorial way to calculate rates of change
• Draw a line tangent
to the curve at the time
you want. The line can
be any length.
• Mark two points on
the line and record the
values.
• Calculate the slope of
the tangent line
sm
tt
ddspeedm 59.0
5.23.9
26
12
12 =!
!=
!
!==
ISP209s10 Lecture 3 -3-
Speed versus distance plot
Example: Motion of a car as a function of time.
We can get this graph from this one by repeating the previous
calculation for several different times and plotting the points
ISP209s10 Lecture 3 -4-
Homework Problem Traveling Car
1st sketch the
speed vs. time
graph
Next, use the
speed graph to
sketch the
acceleration vs.
time graph
ISP209s10 Lecture 3 -5-
Adding and Subtracting 2 Vectors
• Imagine two vectors (A and B)represent two walks, one in one
direction and the other in another direction.
• A negative sign means "go the opposite direction the arrow
shows".
• The resultant vector (C) points from your original starting point
to where you ended up at the end of the second walk.
ISP209s10 Lecture 3 -6-
Adding and Subtracting 2 Vectors
Example 1:
ISP209s10 Lecture 3 -7-
Adding and Subtracting 2 Vectors
Example 2:
ISP209s10 Lecture 3 -8-
History of our effort to understand motion
• Aristotle(384 BC – 322 BC)– Natural motions: items seek their natural locations
– Violent motions like moving across the room require an agent
• Galileo (1564-1642)– Tried to deduce the laws of motion from experiments
– Introduced the concept of inertia. (Inertia is not a well definedconcept.)
• Isaac Newton (1643-1727)– Formulated laws that govern planetary motion and most** motion
we see in our daily lives
– Invented Calculus along the way
– Many view Newton (along w/Einstein) as the “greatest” ever
** Except for the very small (Quantum Mechanics) and fast (Special Relativity)
ISP209s10 Lecture 3 -9-
• Aristotle distinguished three kinds of motion
• Natural motion: falling objects and liquids, rising
air and flames
• Violent motion: needing a constant push or pull to
continue
• Celestial motion: motion of the moon, planets, sun,
and stars
Aristotle’s “Common Sense” Theory of Motion
ISP209s10 Lecture 3 -10-
Now, throw a ball across the room. Once it leaves your
hand, what keeps it moving? Aristotle says there must
be a constant force to keep it in motion.
Sounds like common sense, no?
Problems with Aristotle’s Theory
We saw last lecture that our “common sense” or
intuition can be totally wrong…
ISP209s10 Lecture 3 -11-
Galileo’s thought experiment: Let a ball roll down an incline; it
will speed up. Let it roll up the incline; it will slow down. In
between, on a perfectly flat surface with no friction, the ball will
keep rolling at a constant speed forever.
Galileo’s Thought Experiment
ISP209s10 Lecture 3 -12-
Galileo’s method:
• Experimentation, to test a specific hypothesis
-E.g., Aristotle’s theory of falling objects
• Idealization, to eliminate side effects that may mislead
-E.g., air resistance and friction
• Consider only one question at a time
- E.g. speed of falling objects of different masses
• Quantitative methods: precise measurement
- E.g., timing the fall of different objects from a tower
Galileo and the Scientific Method
ISP209s10 Lecture 3 -13-
• Imagine we could turn off air resistance, friction, and
gravity. How would things move?
• Descartes had the answer (which Newton took as his first
principle of motion):
The Law of Inertia: A body that is subject to no external
influences (also called external forces) will stay at rest if
it was at rest to begin with and will keep moving if it was
moving to begin with; in the latter case, its motion will be
in a straight line at an unchanging speed.
The Law of Inertia
ISP209s10 Lecture 3 -14-
• For example, if you are driving a car on an icy
road – a VERY icy road – and try to stop or turn,
you will find that your car continues to go in a
straight line, as there is little friction.
• You can also watch videos of astronauts – they
will float in a straight line with constant speed
(unless something pushes/pulls them)
The Law of Inertia
ISP209s10 Lecture 3 -15-
• The law of inertia tells us that an undisturbed
object will keep moving with a constant velocity.
• If an object’s velocity is changing, it is
accelerating. Acceleration is the rate of change of
velocity:
acceleration = (change in velocity)/time
Acceleration and the Law of Inertia
ISP209s10 Lecture 3 -16-
• Falling objects accelerate as they fall.
• How do we know this? Hold your book above
the floor and let it drop.
• What is its speed right when you let it go?
(Don’t throw it!) What is its speed when it hits
the floor?
Falling
ISP209s10 Lecture 3 -17-
• This diagram shows an object
falling.
•Note that both its distance and its
velocity are increasing.
•From one second to the next, the
distance traveled increases, but the
change in velocity is the same.
Falling
ISP209s10 Lecture 3 -18-
• We see that the speed is proportional to the time –
10 m/s at 1 s, 20 m/s at 2 s, and so forth.
• What about the distance? Clearly it is not
proportional to the time.
• However, if we look at the pattern of how the
distance changes from second to second, we can see
that the distance is proportional to the square of the
time.
Falling
ISP209s10 Lecture 3 -19-
• The object in the diagram is changing its speed
at a rate of 10 m/s per second. Therefore, its
acceleration is 10 m/s2.
• This is (approximately) the acceleration due to
gravity anywhere on the Earth.
• It does NOT depend on the mass, size, or shape
of the object. Aristotle was wrong.
Falling
Click HERE for a demonstration using a coin and featherISP209s10 Lecture 3 -20-
What is a Force?
• A force is a push or pull.
• Force is a vector, it has a magnitude and a direction.
• A better definition is given by Newton’s Three Laws ofForce (my versions)
– If the net force on an object is zero the object will notaccelerate.
– The amount of acceleration depends on the mass of the object
and the amount of the applied force: F = ma .
– For every force, there is an equal and opposite force.
• Improved definition: Force is the rate of change ofmomentum.
ISP209s10 Lecture 3 -21-
How much force?
Neglecting friction from the air, a 80.0 kg professor
falls off a bench and accelerates toward the ground at
9.81 m/s2.
What is the magnitude of the force of gravity on the
professor?
F = mass x acceleration = 80.0 kg x 9.81 m/s2 = 785.
N
ISP209s10 Lecture 3 -22-
• Undisturbed objects will continue moving in a straight
line with constant speed (Law of Inertia, aka Newton’s
1st Law )
• any change in speed or direction (I.e., acceleration)
must require a force.
• Force is an action, such as a push or pull, rather than
a thing. A force is exerted on one object by another.
Force: Why Things Accelerate
ISP209s10 Lecture 3 -23-
Is it possible to have a force without acceleration?
Only if there are two forces that cancel each other out.
Force: Why Things Accelerate
ISP209s10 Lecture 3 -24-
• If you kick a football, when does it accelerate? If
you watch carefully, you will see that the ball only
accelerates while your foot is in contact with it.
• Other forces: friction, air resistance – these both
act to slow moving objects
• Gravity: force exerted by the Earth (due to its very
large mass)
Force: Why Things Accelerate
A bit different then the previous examples.
Nothing is “touching” an apple to make it
fall. Gravity acts at a distance across space.
ISP209s10 Lecture 3 -25-
Through experimentation, we see that the acceleration is
proportional to the force:
a ! F
Connecting Force and Acceleration
ISP209s10 Lecture 3 -26-
• Inertia is not the same as weight
• Imagine being in outer space. Nothing has
weight, but objects still have inertia – they will
resist a pull or push.
• Mass is the quantitative measure of inertia. In
the metric system, mass is measured in kilograms.
Connecting Force and Acceleration
ISP209s10 Lecture 3 -27-
Through experimentation, we see that the same force
produces a smaller acceleration of a greater mass.
Acceleration is inversely proportional to mass:
a ! 1/m.
Connecting Force and Acceleration
ISP209s10 Lecture 3 -28-
So, we have found that acceleration is proportional
to force and inversely proportional to mass:
a ! F/m
One newton (N) is defined as the force it takes to
accelerate 1 kg at 1 m/s2; using these units, we can
write:
a = F/m
Connecting Force and Acceleration
ISP209s10 Lecture 3 -29-
What is a force on a deeper level?
• These laws let us recognize a force, but whatcauses a force?
– Modern view is related to Quantum Field Theory.
– Forces are the result of an exchange of “virtual”particles that pop in and out of existence from“thin air”.
• To understand field theory, we have to talkabout energy and quantum mechanics (later inthe term).