Download Set 4: Newton Changes Everything

Set - 4
Explaining
Motion
What is the difference between
speed and velocity?
A.
B.
C.
D.
The two are the same.
Velocity relates to
instantaneous speed, but not to
average speed.
Velocity is the speed and the
direction the object is traveling.
Velocity relates to invisible
objects like atoms, while speed
relates to visible objects like
cars.
What is the difference between
average speed and instantaneous
speed?
A.
B.
C.
D.
Average speed is the speed of an average runner
and instantaneous speed is the speed of a very
fast runner.
Instantaneous speed is the average speed of a
very small portion of the trip.
Average speed is calculated over many trips, but
instantaneous speed is calculated during one trip.
They're the same thing.
Why do we care about
motion?


Because we all move in various ways.
Our cars move and they move us. Our
friends move.
Music is sound and sound moves
through the air. We need these
concepts to really understand what
music is and how it works.
The next slide gives an example
of why we need this stuff to
understand music.

The Ear




Responds to Pressure
A force on the membrane
A movement inside the ear
Translation into the brain
Music !
If you drop a piano out of a 20
story building



How long will it take
to hit the ground?
How fast will it be
moving?
After it hits the
ground .. how
difficult will it be to
play it?
This chapter


Mostly physics
Needed for understanding of many
concepts in music.
Introduction—“Explaining Motion”

In physics, to explain something means to create a
model that can predict the outcome of experiments.

Motions appear to be reproducible; that is, if we start out
with the same conditions and do the same thing to an
object, we get the same resulting motion.
The same motion occurs regardless of:
 when the experiment is done, and
 where the experiment is done.

This reproducibility is a necessary condition for
attempting to search for a set of rules that nature obeys.
Rules of nature might be difficult to find, but they do not
change.
Translation



Under identical and repetitive
conditions, the same outcome will
always occur.
Physical motion is PREDICTABLE
based upon certain laws of motion.
There are three of them that are
referred to as NEWTON’S LAWS.
Do Objects Tend to Rest?

Give your book a brief push across a table.


If you epeat this book-pushing experiment on a
surface covered with ice.



Although the book starts in a straight line at some particular
speed, it quickly slows and stops.
The book would travel a much greater distance before
coming to rest.
The ice is slicker than the desktop. Different surfaces
interact with the book with different strengths.
What would happen to the book if the surface were
perfectly slick?

The book would not slow down at all; it would continue in a
straight line at a constant speed forever.
Galileo
The man … Galileo of Pisa


Born in Pisa (1564)
Thought the Church had become
“sterile” and began to “translate” it nto
“modern” music.


His work began the development that
culminated in ITALIAN OPERA!
Smart Dude!
Galileo

Enrolled in medicine but switched to
Mathematics.


At the age of 25, he was appointed Chair
of Mathematics at Padula.
In 1610 Developed the telescope

Observed



Mountains on the moon
Moons of Jupiter
Phases of Venus
Galileo


From his OBSERVATIONS, he favored
the Copernican world view that the
Earth orbited around the sun rather than
the other way around.
This created big conflicts with the
church. Eventually, he was confined to
his home where he died in 1642.
Galileo’s Thought Experiment


Galileo noted that a ball rolling down a slope speeds up.
Conversely, if the ball rolls up the slope, it naturally slows down.
 The ball experiences an interaction on the falling slope that
speeds it up and an interaction on the rising slope that slows
it down.
Now, Galileo asked himself, what would happen to the ball if it
were placed on a level surface? Nothing. Because the surface
does not slope, the ball would neither speed up nor slow down;
the ball would continue its motion forever.
FOREVER ???
The importance of TIME in
Galileo’s Experiments
The red dots represent the positions after
equal time intervals.
Pendulum
What can we say about this motion?
Acceleration …. WHY??
The Tower??




Aristotle claimed that a
heavier object will hit the
ground sooner than a light
object dropped at the same
time.
Galileo did the experiment
and proved Aristotle wrong.
There is no evidence to
prove that Galileo actually
did this experiment.
But he may have!
What he would have found
had he done the experiment:



The longer the object fell, the faster it
went.
The weight (to be more carefully defined
shortly) of the object didn’t matter.
The size of the object MAY have
mattered.
Timing…
More importantly



For every second a falling object falls
(vertically), its speed increases by about
10 meters per second (or 32 ft/sec).
This only works if air resistance can be
neglected.
The object is said to be UNIFORMLY
ACCELERATING.
The “acceleration” of gravity:g
g  10 (meters per second) per second
g  32 (feet per second) per second
Galileo’s
BIG Contribution
OBSERVE
MODEL
Change Something
Acceleration

If an object starts with a velocity v0 and
ends with a velocity vf after a time t, then
the average acceleration is said to be
final velocity - initial velocity
average accelerati on 
time

Units: velocity/time = (m/sec)sec or m/s2
Some algebra …
a
v f  v0
t
v f  v0  at
v f  v0  at
An object is thrown into the air with a velocity of
20 m/s. How long will it take to get to the top of
the trajectory? How long back to the thrower?
No Surprise: Instantaneous
Acceleration
v
ainstantaneous 
t
AGAIN:
Acceleration of gravity

~10


2
m/s
Actually 9.8 m/sec2
32 ft/sec2
An object is THROWN vertically down
from the top of a building with an initial
speed of 20 meters per second. 2
seconds later it will have a speed of
A.
B.
C.
D.
30 m/s
40 m/s
50 m/s
60 m/s
A woman throws a ball straight up into the air at
a speed of 30 m/s. After how many seconds
will the ball return to her hands?

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3
4
5
6
None of these
Look at the graph:
Vf
v
Area = v x t
= distance traveled
V0
t
Time t
Distance = v0t + (1/2) at2
Reaction Time Experiment

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2 People
One holds the meter stick
The second has hand at the bottom
When the first person releases the
meter stick, the second catches it as
fast as possible.
From the distance, we can calculate
reaction time.
Reaction Time
DROP THE RULER
Distance = v0t + (1/2) at2
Start from rest so
Distance = (1/2) at2
D = (1/2) gt2
2D
t
g
LET’S DO IT AGAIN!
REACTION TIME
From before
v f  v0
a
t
v f  v0  at
v f  v0  at
Falling objects : a  -g
The Modern Explanation

Galileo was the first to suggest that
constant-speed, straight-line motion
was just as natural as at-rest motion.

Natural motion is one in which the speed and
direction are constant.
An interaction with an external agent is required to
cause an object to change its velocity.
 Objects at rest tend to remain at rest. Objects in
motion tend to remain in motion.
This property of remaining at rest or continuing
to move in a straight line at a constant speed is
known as inertia.


Note

This resistance to changes in motion
was later quantified by Sir Isaac Newton
This is the next topic
The Modern Explanation

There is more to inertia than getting things
moving. If something is already moving, it is
difficult to slow it down or speed it up.


An example is drying your wet hands by shaking
them. When you stop your hands abruptly, the
water continues to move and leaves your hands.
In a similar way, seat belts counteract your body’s
inertial tendency to continue forward at a constant
speed when the car suddenly stops.
The Modern Explanation

All objects do not have the same inertia.



Imagine trying to stop a baseball and a
cannonball, each of which is moving at 150
kilometers per hour (about the speed a majorleague pitcher throws a baseball).
The cannonball has more inertia and, as you can
guess, requires a much larger effort to stop it.
Conversely, if you were the pitcher trying to throw
them, you would find it much harder to get the
cannonball moving.
Fun Trick with Inertia
Newton and Galileo’s Legacy


Although Galileo did not fully
explain motion, he did take the
first important step and, by
doing so, radically changed the
way we view the motion of
objects.
His work profoundly influenced Isaac
Newton, the originator of our presentday rules of motion.
Sir Isaac Newton



Born in 1642
One of the GREATS
of physics (on a par
with Einstein!)
Strange dude …
rumor is that he died
a virgin.
Newton

Born in England and he was supposed
to return and look after the family farm.


At age 17 he returned from boarding
school he proved to be a total failure at
farming.
Went to Trinity College, paying his way
by waiting on tables and cleaning rooms
for faculty and wealthy students.

Many students do this today as well.
Newton



In1667 he published a treatise on infinite
series.
Developed a reflecting telescope and was
elected membership in the Royal Society.
Decided that Christianity had deviated from
the original teachings of Christ and refused to
take the college’s holy orders.

He was excused .. The only person ever to have
received this allowance.
More Newton

In 1686 he published his Principia .. Which
established the laws of motion in a mathematical
way.


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
He developed the calculus while Leibnitz developed a
different approach. For years they fought over who was the
real inventor!
He showed that white light was a mixture of all of the
colors of the rainbow.
He developed the math to show that the planets and
comets rotated around the sun in elliptical orbits.
He died in 1727.
Newton’s First Law
Newton’s first law of motion. It is also
referred to as the law of inertia:
-The velocity of an object remains
constant unless it is acted upon by
an external force.
 For the velocity of an object to remain
constant, its speed and its direction
must both remain constant.

Newton’s First Law

Remember:


Velocity can be ZERO
Therefore Newton’s first law also says that:
an object at REST (not moving) will stay at
rest.
Newton’s First Law: Force??

The first law incorporates Galileo’s idea
of inertia and introduces a new concept,
force.


.
A book sliding across the table slows down
and stops because there is a force
(called friction) that opposes the motion.
Similarly, a falling rock speeds up because
there is a force (called gravity) acting on
it.
What Are Forces?


Casually speaking, a force is a push or a pull.
We don’t actually see forces. We see objects
behave in a certain way, and we infer that a
force is present.
 The direction of the force is
as important as its size, in
the way they make objects
behave.
Therefore, we treat forces as vectors.
What’s Up??
No force UP!
Superman’s
WEIGHT
A guy is pulling his girlfriend
on a sled at constant velocity.
Let’s discuss the FORCES that are acting.
Question #1: What object are we
talking about? The Guy? The Girl?


We must apply our
ideas to only ONE
object at a time, or
an appropriate
combination of
objects that are
functioning as a
single body.
The (Girl + Sled) since they
move together!
Something NEW: The force the earth pushes up with!
We call it the NORMAL FORCE
The Pull
Friction
Weight of the girl AND the sled
Normal?
The two are equal but opposite
in direction.
W
N
Gravity
N=W
FREE BODY DIAGRAM of the (Girl +
Sled) since they move together!
EQUAL
components
Balanced & Unbalanced Forces

Remember that Newton’s first law refers to the
unbalanced force.

In many situations there is more than one force on
an object.
There is an unbalanced force only if the sum of the forces is not zero.
When two forces of equal size
act along a straight line but in
opposite directions, they
cancel each other.
Balanced & Unbalanced Forces



When we observe an object with no
acceleration, we infer that there is no
unbalanced force on that object.
If you see a car moving at a constant speed
on a level, straight highway, you infer that the
frictional forces balance the driving forces.
What is the net force acting on an airplane in
level flight flying at 500 mph due east?

Because the speed and direction are constant,
there is no acceleration, and the net force must be
zero.
Adding Vectors


Mathematicians have developed rules
for combining vector quantities such as
displacements, velocities, accelerations,
or forces.
In this chapter you will learn to combine
vectors using a graphical method and
the scale shown in the next slide.
Vector Shorthand



In texts, vectors are represented by
boldface symbols (such as F).
When writing by hand about vectors, you
use an arrow over the symbol (such as F ).
The magnitude of the vector quantity is
represented by an italic symbol. Therefore,
a force is written as F, and its magnitude is
written as F.
Drawing Vectors Accurately
We can represent any vector
by an arrow; its length represents the
magnitude of the quantity, and its direction
represents the direction of the quantity.
To complete this representation, we assign
a convenient scale to our drawings. Here,
one centimeter on paper represents 20
meters on the ground.
Tail-to-Tip Vector Addition

When you are given “a list of directions,” each
succeeding arrow is drawn beginning at the head
of the previous arrow.

The arrow drawn from the tail of the first arrow to the
head of the last arrow represents the vector sum.
 You can determine the direction and magnitude of this
last vector, the sum, with a ruler and a protractor.
In this way the three forces
acting on the ball (a) can be
added to find the net force (b).
Note that you don’t have to start
with F1. The order in which the
forces are added doesn’t matter;
you could choose F2 or F3. Try it!
Adding Vectors
F2
SUM
F1
F2
F3
The Same Diagram
F3
F1
Vectors we have used:





Position (Not too often in this class)
Velocity
Acceleration
Force
Any others???
Summary: Newtons FIRST
Law

Objects in motion tend to remain in
motion unless acted upon by an
external force.

Objects at rest tend to remain at rest
unless acted upon by an external force
Do objects at rest have a
velocity??
Newton’s Second Law

The acceleration of an object is
proportional to the net force acting on it.


Twice the force produces twice the
acceleration.
The direction of the acceleration is always in
the direction of the net force.
Two springs pulling side by
side exert twice the force of one
spring pulled by the same amount.
Thus, they produce twice the
acceleration.
Newton’s Second Law

Mass and acceleration are inversely
proportional.

Inversely indicates that the changes in the
two values are opposite each other.
If the mass is increased by a certain
multiple, the acceleration produced by
the force is reduced by the same
multiple.
Newton’s Second Law


Newton put the two preceding ideas
together into his second law of motion.
“The net force on an object is equal to
its mass times its acceleration and
points in the direction of the
acceleration.”
Conceptual Question on the 2nd Law

A crate falls from a helicopter and lands on a
very deep snowdrift. The snow slows the
crate and eventually brings it to a stop.
During the time that the crate is moving
downward through the snow, is the
magnitude of the upward force exerted on the
crate by the snow greater than, equal to, or
less than the magnitude of the gravitational
force acting downward on the crate?
Answer to the Conceptual Question

Because the crate is moving downward, its
velocity is pointing down. Because the crate
is losing speed, its acceleration must be
pointing in the opposite direction—that is, up.
The net force always points in the same
direction as the acceleration. Therefore, the
force acting upward on the crate must be
larger than the force acting downward. Thus,
the snow exerts the greater force.
Defining Units of Mass and Force


In the previous chapter, we have defined a measure
for acceleration, but not as yet for mass and force.
Historically, a certain amount of matter was chosen
as a mass standard.



The mass of a liter of water has a mass of 1 kilogram.
The force needed to accelerate a 1-kilogram mass at 1
(meter per second) per second is called 1 newton (N),
in honor of Isaac Newton.
In using any rule of nature, we must use a consistent
set of units.
Newton’s Second Law - UNITS
F=ma
Newtons
Kilograms
Meters/second2
Everything in this course is
pretty much based on F=ma
Meters/second2



Can be written as
(meter/second)/second
Consider an object accelerating at 10
(meters/second)/second
Every second its velocity increases by
10 m/s.
Example


At t=0 (what does this mean???), an
object is moving at 15 m/s and is
accelerating at 10 m/s2.
What is its velocity as a function of
time??
The results
Time (seconds)
0
1
2
3
4
5
6
7
Velocity
15
25
35
45
55
65
75
85
The Graph
Velocity vs Time
Velocity (m/s)
100
80
60
40
20
0
0
2
4
time (seconds)
6
8
Numerical Question on the 2nd Law

What is the net force needed to accelerate a
5-kg object at 3 m/s2?

When accelerations are measured in (meters per
second) per second, as they are here, the masses
must be in kilograms and the forces in newtons.
A newton can be written as kg · m/s2.
Applying the second law, we have


Mass ≠ Weight

Mass is often confused with weight.


Our weight depends on where we are.



They are proportional to each other.
We compress the spring in a bathroom scale because Earth
is attracting us.
If we were on the Moon, our weight would be less because
the Moon’s gravitational force on us would be less.
Our mass, however, is not dependent on our location
in the Universe. It is a constant property that depends
only on how much there is of us.
Consequence:
Does the 2nd Law Apply in Space?

Being weightless does not mean that you are
massless.


Imagine a huge truck in outer space “hanging” from a spring
scale. Although the scale would read zero, if you tried to kick
the truck, you would find that it resisted moving.
Weight can be expressed in newtons to clear up
misunderstandings.
A 1-kilogram mass near Earth’s surface has a weight of 9.8
newtons, or about 2.2 pounds. Therefore, a “pound” of
butter has a weight of 4.5 newtons and a mass a little less
than ½ kilogram.
Weight as a Force

Let’s represent the acceleration due to gravity
by the symbol g, where we’ve used a vector
to indicate both the size and direction. If we
then replace the net force Fnet by the weight
W, we obtain:
General equation
of the 2nd Law
Re-stated in
gravitational terms
How Much Do You “Weigh”?

(Remember, mass cannot be expressed in newtons;
weight can.)
 Calculate the weight of a child with a mass of 25 kg.
 Obtain the mass of a dog that has a weight of 150 N.
Introducing Free-Body Diagrams

Imagine that you are pulling your little sister on a sled
and that the sled is speeding up. There are many
forces acting on the sled.





The rope is exerting a tension on the sled, pulling it forward.
Earth is pulling down on the sled with a gravitational force.
The snow is pushing up on the sled with a force commonly
called a normal force.
(Normal means perpendicular, and this force acts
perpendicular to the surface between the sled and the
snow.)
Your sister is pushing down on the sled with a normal force,
and the snow is resisting your efforts with a frictional force
that acts parallel to the surface of the snow.
Introducing Free-Body Diagrams

Which of these forces
do we use in
Newton’s second
law?
Fnet = ma
Actor
Direction
Rope
Forward
Earth
Downward
Sister
Downward
Snow
Backward
Snow
Upward
 Fnet , the net force, is the vector sum of all the forces
acting on the sled. It is important, therefore, to
correctly identify all the forces acting on an object
when analyzing its motion.
 We identify the forces by drawing a freebody diagram.
Free Fall Revisited—Fnet

Objects falling on Earth don’t fall in a
vacuum but through air. Thus, in realistic
situations, a falling object has two forces
acting on it simultaneously:



the weight acting downward,
and the air resistance acting upward.
And the greater the speed, the greater
the air resistance.
Free Fall Revisited—Terminal
Speed

With these facts in mind, consider the downward motion of a
falling rock.



As the rock speeds up, however, its weight remains constant
while the air resistance increases.



Thus, the net force and the acceleration decrease.
The rock continues to speed up but at a decreasing rate.
Eventually, the rock reaches a speed for which the air
resistance equals the weight.


Initially, it falls at a low speed, and the air resistance is small.
Because there is a net force, the rock accelerates, thus increasing
its speed.
Fnet = 0. The rock stops accelerating.
This maximum speed is called the terminal speed of the object.
Terminal Speeds

The terminal speeds of different objects are not
necessarily equal. Factors include:






The shape of the falling object,
Its size,
Its weight, and
Resistive properties of the medium.
An object will continue to accelerate until the terminal
force is the same size as its weight.
The maximum speed of a skydiver near sea level is
190 mph—no matter how high up they were when
they started!

If they fall spread-eagled, this value is decreased.
Forces Discouraging Movement—
Static Friction

The static frictional force seems
a bit mysterious. Because it is
equal to the force you exert:



The frictional force is small if
you push with a small force (a).
If you push with a large force,
the frictional force is large (b).
It ceases to exist when the
applied force is removed.
Forces Discouraging Movement—
Kinetic Friction


If your applied force exceeds the maximum
static frictional force, the crate accelerates in
the direction of your applied force.
Although the crate is now sliding, there is still
a frictional force (c).

The value of this kinetic friction is
less than the maximum value of the
static frictional force. Unlike air
resistance, kinetic friction has a
constant value, independent of the
speed of the object.
Test Static vs. Kinetic Friction


With a simple wooden block and a long rubber band, you can
verify the behavior of static and kinetic friction.
Connect the rubber band to the block with a thumbtack, and
slowly pull on the block.


If the block does not move, the static force is equal but opposite
in direction to the force of the rubber band.


The stretch of the band provides a visual indication of the force you
are applying.
Continue to increase your pull. What happens?
Repeat the experiment, with the block sliding across the table at
a constant speed.

How does the stretch of the rubber band now compare with its
maximum stretch in the static situation?
Newton’s Third Law

There is no way to push something
without being pushed yourself.



For every force there is always an equal
and opposite force.
If an object exerts a force on a second
object, the second object exerts an
equal force back on the first object.
Forces always occur in pairs. And these
forces never act on the same body.
I dropped it and the world stood still

Consider a ball with a weight of 10 newtons falling
freely toward Earth’s surface.
Earth exerts a force Web on the ball. According to
Newton’s third law, the ball exerts an equal and
opposite force Wbe on Earth.
Web = Wbe = 10 N.
Earth’s mass is so large that its acceleration toward
the ball is minuscule. Earth does accelerate—every
time we drop something—but we don’t notice it.
Another Example

When you fire a rifle, it recoils.


Third Law: Rifle pushes bullet, bullet pushes rifle.
But why doesn’t the rifle accelerate as much
as the bullet?


The force of the bullet on the rifle is the same size
but produces a small acceleration because the
mass of the rifle is large.
The force of the rifle on the bullet produces a large
acceleration because the mass of the bullet is
small!
Without the 3rd Law, You Cannot Walk


In walking you must have a force exerted on you in the direction
of your acceleration. And yet the force you produce is clearly in
the opposite direction.
As you start to walk, you exert a force against the floor (down
and backward); the floor therefore exerts a force back, causing
you to go forward (and up a little).
 If you want a clearer demonstration of this, try walking in a
rowboat.
As the man walks to the left, he
exerts a force on the boat that causes
the boat to move to the right.
Without the 3rd Law, You Cannot Stand
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Without the third law, paradoxical events
would occur in the Newtonian world view.
 A person stands on a floor. Because
the person is not accelerating, the net
force must be zero.
Q: What is the force that balances the
gravitational force?
A: Earth exerts a force Wep on the person, which causes the
person to exert a force Npf on the floor. By Newton’s third law,
the floor exerts an equal and opposite force Nfp on the person.
Although Wep and Nfp are equal and opposite, they are not an
action–reaction pair; they both act on the person.