Transcript Chapter 4 - AstroStop

Chapter 4
Newton's Second Law
of Motion
1.
FORCE CAUSES ACCE LERATION
The combination of
forces that act on an
object is the net
force.
(Only the net force is
shown in the figures
on this slide.)
The acceleration of an
object is directly
proportional to the net
force.
F
F
F
m
m
a
a
m
This symbol means
proportional to


a F
a
2. FRICTION
Friction opposes the motion between
surfaces in contact with one another.
When there is a tendency for
movement between two surfaces and
yet there is no motion, the friction is
static friction.
Static friction has an upper limit.
When there is motion between the two
surfaces, the friction is sliding
(kinetic) friction.
F
F
F
FA
A
A
F
FF
F
A
A
On the verge
of slipping
Sliding
Maximum Static Friction
Friction, F
Sliding (Kinetic) Friction
Applied Force, FA
Static and kinetic friction
 (In stopping a car, shoot for
static friction.)
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3. MASS AND WEIGHT
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Every object possesses inertia (mass).
Inertia is the sluggishness of an
object to changes in its state of
motion.
Mass - a measure of the inertia of an
object
(Units - kg and slug)
A slug weighs 32 lb.
 Inertia deals with how hard it is
to start and stop an object.
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Weight - force that earth exerts on an
object
(Units - N and lb)
A Newton is approximately the
weight of a small apple.
Slide - Newton’s apple
1 kg weighs 2.2 lb.
Mass and size are often confused.
Galileo introduced inertia.
Newton grasped its significance.
4. MASS RESISTS ACCE LERATION
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The acceleration of an object not
only depends on the force applied
to an object but it also depends on
the mass of the object.
Consider the same
net force applied to
different mass
objects.
F
F
a
m
m
a
m
m
The acceleration is
inversely
proportional to the
mass of the object.
F
m
m
a 1
m
a
5. NEWTON’S SECOND LAW OF MOTION

 F
a
m
or
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F  ma
The force in each of these equations
represents the vector sum of all of
the forces acting on the object of
mass m.
Units of force - N and lb
If the net force is parallel to the velocity, then
the speed of the object increases.
If the net force is anti-parallel to the velocity,
then the speed of the object decreases.
If the net force is perpendicular to the
velocity, the direction of the velocity changes.
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Acceleration is always in the
direction of the net force.
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F  ma
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Force is usually thought
of as a push or pull.
Examples - gravitational
electrical
"Force is anything that
can accelerate an object.”
Net Force

“Net” means the total force acting on
an object. It is the vector summation
of all the forces acting on the object.
Net Force


F  ma
Video - Scale in Elevator
Force only changes the state of
motion.
 Zero acceleration does not imply
zero velocity.
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Demo - Spool and string
 Story - Wicked king & beautiful
princess
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THE WICKED KING AND THE
BEAUTIFUL PRINCESS
Once upon a time there was a terribly wicked King
who had a daughter who was very beautiful. This
daughter was in love with a handsome prince who didn’t
take Physics 101, and before long the prince and the
princess had become inseparable. The King, however,
was wicked and did not believe in happiness and so he had
his daughter locked up in a prison at the top of a tall tower.
The prince learned of this
and was determined to rescue the
one he loved, so he started out for
the tower where the unhappy
princess sat imprisoned.
When he arrived at the base
of the tower the prince looked up
and noticed that there was a
wooden beam protruding from
the top of the structure. He
immediately contrived a method
to use this to reach his princess.
He attached a sturdy basket to
one end of a very long rope and to
the other end he tied a stone.
Then with a mighty heave he
threw the stone across the top of
the beam so that the rope was
looped across the beam. The
prince had thus constructed a
simple pulley. He then stepped
into the basket, and since the
pulley had a mechanical advantage
of two, he proceeded to hoist
himself up.
In due time the prince
reached the top and was
rewarded with a long embrace
by the King’s daughter. The
prince could not return the
embrace, nor could he begin
his work to release the
princess, since letting go of
the rope would cause the
basket to fall. So he began
searching for a way to fix the
rope to the tower wall.
Luck seemed to be
smiling on the young man
because close by he
discovered a metal hook
imbedded in the stone wall.
The prince tugged on the
hook with one hand (the
other hand holding the rope
tightly), and finding it
secure, he proceeded to tie
the rope to the hook.
But the instant he did that, the supporting beam broke
and the basket, together with the poor prince, came
crashing to the ground.
What had happened was this. The King, who was
very wicked, also happened to have had Physics 101 (no
connection between the two), and he had originally
designed the beam to support the weight of the prince and
the weight of the basket, but no more.
During the time the unsuspecting prince was hoisting
himself up, the total load on the beam was simply his
weight plus the weight of the basket.
But as soon as one end of the rope was hooked onto
the tower, the situation changed drastically. Now the
weight of the prince plus the weight of the basket all
exerted a force on one end of the rope while the tower, via
the hook, pulled down on the other end with an equal and
opposite force. The total force on the beam was now twice
the original weight. The beam broke. Why?
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Demo – Block and tackle
6. WHEN ACCE LERATION IS g – FREE FALL
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Only force of gravity is acting on
object
All objects accelerate the same.
a = g or F/m = g .
The weight of an object of mass m
is the force that the earth exerts on
the object.
W = mg .
One kilogram weighs 9.8 Newtons.
One slug weighs 32 pounds.
7.
WHEN ACCE LERATION IS LESS
THAN g – NONFREE FALL
Consider the net force acting on
the object.
 The force due to air resistance
depends on the size and speed
of the object.
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Terminal Velocity
Net Force
Acceleration = g
mg
F
0<Acceleration < g
Velocity = 0
but motion is about to begin
v increasing downward
mg
F
0<Acceleration << g
mg
v still increasing downward
just not as rapidly as before
F
Acceleration = 0
mg
Terminal velocity
Example: Mouse in a mine shaft
 Light and heavy parachutists
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Chapter 4 Review Questions
Which is a better way to get a
feeling for the inertia of an
object?
(a) hold it in your hand
(b) shake it back and forth
Which of the following represents a situation
when the acceleration of an object is not in
the same direction as the net force acting on
the object.
(a) a bowling ball swinging by a cord attached
to the ceiling
(b) a car speeding up along a straight line on
the highway
(c) a book sliding to a stop on the top of a
table
(d) All of the above
(e) None of the above
What is the magnitude of the
acceleration of a 2 kg object when
the net force on the object is
10 N?
(a) 10 m /s2
(b) 20 m /s2
(c) 5 m /s2
If an object weighs 10 lb, what must
the air resistance force be if the
object is falling and has reached
terminal velocity?
(a) 10 lb
(b) 32 lb
(c) there is no way of telling without
knowing what the value of the
terminal velocity is