I. Aristotle on Motion
A. Aristotle (4th century BC– first to suggest
force causes motion.
1. Divided motion into two types
a. Natural Motion– said to
be either straight up or down.
Objects would seek their
natural resting place (boulder
fall to ground, smoke rise)
b. Violent Motion -was “imposed” motion. Result of
forces that pushed or pulled. (this motion had an
external force) 2. Objects in natural resting
places could not move by
themselves. (had to be pushed
or pulled)
B. Before 16th century though Earth must be in its
natural resting place (a force large enough to move it
was unthinkable)
II. Copernicus and the Moving Earth
A. Nicolaus Copernicus (1473-1543)- said
Earth and other planets move around sun.
1. Worked on his idea in secret to
escape persecution
III. Galileo on Motion
A. Foremost scientist of the late-Renaissance
Italy
1. supported Copernicus–
heliocentric theory (planets rotate
around sun)
2. Resulted in house arrest for his
thinking
Contact vs. Long Range Force
Contact Force- acts on an object by
touching it.
Long-range Force- is
exerted without contact (e.g.
magnetic forces, gravity
2. Friction– name given to the force that acts
between materials that touch as they move past
each other
Galileo on Motion
• Galileo stated that if friction were entirely
absent, a ball moving horizontally would
move forever.
• No push or pull would be required to
keep it moving once it is set in motion.
Galileo tested his idea by rolling balls along
plane surfaces tilted at different angles.
• A ball rolling down an inclined plane
speeds up.
• A ball rolling up an inclined plane—in a
direction opposed by gravity—slows
down.
• A ball rolling on a smooth horizontal
plane has almost constant velocity.
Galileo on Motion
• Downward, the ball moves with Earth’s
gravity.
• Upward, the ball moves against gravity.
• On a level plane, it does not move with or
against gravity.
•Galileo stated that if friction were entirely
absent, a ball moving horizontally would
move forever.
•No push or pull would be required to keep it
moving once it is set in motion.
Galileo on Motion
• The ball rolling down the incline rolls up the
opposite incline and reaches its initial height.
• The ball rolls a greater distance to reach its
initial height.
• The ball rolling down the incline rolls up the
opposite incline and reaches its initial height.
• The ball rolls a greater distance to reach its
initial height.
• If there is no friction, the ball will never stop.
3. Galileo argued that only when friction is present–
as it usually is– a force needed to keep an object
moving.
4. He stated– every material object resists
change to its state of motion– called ineretia
5. Led the way for Isaac Newton
IV. Newton’s Law of Inertia
A. Isaac Newton (1642-1727)- born same
year that Galileo died
B. Developed famous laws of motion (replaced
Aristotelian ideas that dominated for previous
2000 years)
1. Newton’s First Law of Motion– usually referred
to as the law of inertia
Every object continues in a state of rest, or of
motion in a straight line at constant speed,
unless it is compelled to change that state by
forces exerted upon it.
a. Restatement of Galileo’s ideas
b. Simply put– things tend to keep doing what
they're already doing
V. Mass-A Measure of Inertia
A. Mass is Not Volume– entirely different
concepts
1. Volume-a measure of space (units
like cubic meters, liters, etc.)
2. Mass -measured in kilograms
B. Mass is Not Weight
1. Often confused with weight
2. Mass– measurement of amount of material
in an object and depends on number of and
kind of atoms that compose it
3. Weight– a measure of the gravitational
force acting on the object
a. One Kilogram Weighs 9.8
Newtons
1). Newton (N)-SI unit of mass
Which would be harder
to shake? A stone in its
weightless state in
space or in its weighted
state on Earth?
Mass—A Measure of Inertia
1. Two thousand years ago, people thought that Earth did not
move. One major reason for thinking this was that
a. no force was large enough to move the Earth.
b. Earth’s motion would be unnatural.
c. Earth was near the center of the universe.
d. Earth moved in a perfect circle.
Assessment Questions
1. Two thousand years ago, people thought that Earth did not
move. One major reason for thinking this was that
a. no force was large enough to move the Earth.
b. Earth’s motion would be unnatural.
c. Earth was near the center of the universe.
d. Earth moved in a perfect circle.
Answer: A
Assessment Questions
2. According to Aristotle and his followers over centuries, Earth was at
the center of the universe. The first European to effectively challenge
that notion was
a. Copernicus.
b. Galileo.
c. Newton.
d. Einstein.
Assessment Questions
2. According to Aristotle and his followers over centuries, Earth was at
the center of the universe. The first European to effectively challenge
that notion was
a. Copernicus.
b. Galileo.
c. Newton.
d. Einstein.
Answer: A
Assessment Questions
3. Galileo’s conclusions about motion helped advance science because
they were based on
a. experiments rather than philosophical discussions.
b. philosophical discussions rather than experiments.
c. nonmathematical thinking.
d. Aristotle’s theories of motion.
Assessment Questions
3. Galileo’s conclusions about motion helped advance science because
they were based on
a. experiments rather than philosophical discussions.
b. philosophical discussions rather than experiments.
c. nonmathematical thinking.
d. Aristotle’s theories of motion.
Answer: A
Assessment Questions
4. If gravity between the sun and Earth suddenly vanished, Earth would
continue moving in a(n)
a. curved path.
b. straight-line path.
c. outward spiral path.
d. inward spiral path.
Assessment Questions
4. If gravity between the sun and Earth suddenly vanished, Earth would
continue moving in a(n)
a. curved path.
b. straight-line path.
c. outward spiral path.
d. inward spiral path.
Answer: B
Assessment Questions
5. To say that 1 kg of matter weighs 10 N is to say that 1 kg of matter
a. will weigh 10 N everywhere.
b. has ten times less volume than 10 kg of matter.
c. has ten times more inertia than 10 kg of matter.
d. is attracted to Earth with 10 N of force.
Assessment Questions
5. To say that 1 kg of matter weighs 10 N is to say that 1 kg of matter
a. will weigh 10 N everywhere.
b. has ten times less volume than 10 kg of matter.
c. has ten times more inertia than 10 kg of matter.
d. is attracted to Earth with 10 N of force.
Answer: D
Assessment Questions
6. The Earth moves about 30 km/s relative to the sun. But when you
jump upward in front of a wall, the wall doesn’t slam into you at 30
km/s. A good explanation for why it doesn’t is that
a. the sun’s influence on you is negligible.
b. the air in the room is also moving.
c. both you and the wall are moving at the same speed, before,
during, and after your jump.
d. the inertia of you and the wall is negligible compared with that of
the sun.
Assessment Questions
6. The Earth moves about 30 km/s relative to the sun. But when you
jump upward in front of a wall, the wall doesn’t slam into you at 30
km/s. A good explanation for why it doesn’t is that
a. the sun’s influence on you is negligible.
b. the air in the room is also moving.
c. both you and the wall are moving at the same speed, before,
during, and after your jump.
d. the inertia of you and the wall is negligible compared with that of
the sun.
Answer: C
Assessment Questions
I. Force Causes Acceleration
A. Force causes acceleration
1. Acceleration depends on net force
2. Objects acceleration is directly
proportional to the net force acting on it.
acceleration α net force
(the symbol α stands for “is directly proportional to.”)
II. Mass Resists Acceleration
A. Acceleration depends on mass
1. acceleration produced is inversely
proportional to the mass.
2. Inversely– means that the two values
change in opposite directions
massonaccelerati
1
III. Newton’s Second Law
A. Newton’s Second Law states:
The acceleration produced by a net force on an
object is directly proportional to the magnitude of
the net force, is in the same direction as the net
force, and is inversely proportional to the mass of
the object
In equation form:
acceleration α mass
net force
1.Using units of newtons (N) for force, kilograms
for mass (kg), and meters per second squared
(m/s2) for acceleration, we get the new equation
2. If we let a = acceleration, F = force, and m =
mass:
acceleration = mass
net force
m
Fa
think!
If a car can accelerate at 2 m/s2, what acceleration can it
attain if it is towing another car of equal mass?
Newton’s Second Law
think!
If a car can accelerate at 2 m/s2, what acceleration can it
attain if it is towing another car of equal mass?
Answer: The same force on twice the mass produces half
the acceleration, or 1 m/s2.
Newton’s Second Law
do the math!
A car has a mass of 1000 kg. What is the acceleration
produced by a force of 2000 N?
Newton’s Second Law
do the math!
A car has a mass of 1000 kg. What is the acceleration
produced by a force of 2000 N?
5.3 Newton’s Second Law
do the math!
If the force is 4000 N, what is the acceleration?
Doubling the force on the same mass simply doubles the
acceleration.
Newton’s Second Law
do the math!
How much force, or thrust, must a 30,000-kg
jet plane develop to achieve an acceleration of
1.5 m/s2?
Newton’s Second Law
do the math!
How much force, or thrust, must a 30,000-
kg jet plane develop to achieve an
acceleration of 1.5 m/s2?
Arrange Newton’s second law to read:
force = mass × acceleration
F = ma
= (30,000 kg)(1.5 m/s2)
= 45,000 kg•m/s2
= 45,000 N
Newton’s Second Law
IV. Friction
A. Friction is a force
1. Acts on materials that are in contact
with each other
2. friction acts in opposite direction to
oppose motion
3. friction mainly due to irregularities in the
two surfaces.
B. Friction not restricted to solids sliding over one
another
1. Occurs in liquids and gases
a. both called fluids
b. Friction of liquids appreciable even at
low speeds.
3. When friction is present, an object may move
with a constant velocity even when outside force is
applied to it.
a. In such case, friction force balances applied
force
b. Can diagram using a free-body diagram
think!
Two forces act on a book resting on a
table: its weight and the support force
from the table. Does a force of friction
act as well?
Friction
think!
Two forces act on a book resting on a table:
its weight and the support force from the
table. Does a force of friction act as well?
Answer: No, not unless the book tends to
slide or does slide across the table. Friction
forces occur only when an object tends to
slide or is sliding.
Friction
V. Applying force– Pressure
A. Pressure– amount of force per unit area
B. In equation form:
(Pressure is measured in Newton’s per square
meter, or pascals)
A
FP
pressure = area of application
force
think!
In attempting to do the bed-of-nails
demonstration, would it be wise to begin
with a few nails and work upward to
more nails?
Applying Force-Pressure
think!
In attempting to do the bed-of-nails demonstration, would it
be wise to begin with a few nails and work upward to more
nails?
Answer: No, no, no! There would be one
less physics teacher if the
demonstration were performed with
fewer nails. The resulting greater
pressure would cause harm.
Applying Force-Pressure
VI. Free Fall Explained
A. Galileo showed falling objects accelerate
equally, regardless of their masses
1. strictly true if air resistance is negligible
2. approximately true when air resistance
is very small
B. Aristotle believed that an
object weighing tens times
as much would fall ten times
faster (disproved by Galileo
and others
Galileo’s famous
demonstration at Leaning
Tower of Pisa)
C. Use equation for weight (force of gravity):
or
Rearrange and get
(when mass is also
considered, the acceleration
of any object is the same)
mgFg maFg
m
Fa
g
VII. Falling and Air Resistance
A. Air resistance decreases the net forces
acting on a falling object
1. When air resistance equals downward
force on falling object (force of gravity–
also called weight) then net force is zero
and no further acceleration occurs.
2. terminal speed– when acceleration terminates
3. When consider direction (which is down for falling
objects) we call this maximum speed terminal
velocity
Fg
Fdrag
think!
Which experiences a greater air
resistance force, a falling piece of paper
or a falling elephant?
Falling and Air Resistance
think!
Which experiences a greater air resistance force, a falling
piece of paper or a falling elephant?
Answer: The elephant! It has a greater frontal
area and falls faster than a piece of paper—
both of which mean the elephant pushes
more air molecules out of the way. The effect
of the air resistance force on each, however,
is another story!
Falling and Air Resistance
think!
If a heavy person and a light person
open their parachutes together at the
same altitude and each wears the same
size parachute, who will reach the
ground first?
Falling and Air Resistance
think!
If a heavy person and a light person open their parachutes
together at the same altitude and each wears the same size
parachute, who will reach the ground first?
Answer: The heavy person will reach
the ground first. Like a feather, the light
person reaches terminal speed sooner,
while the heavy person continues to
accelerate until a greater terminal speed
is reached.
Falling and Air Resistance
1. An object will accelerate when
a. SF = 0.
b. it is unbalanced.
c. it is pushed or pulled with a net
force.
d. its mass increases.
Assessment Questions
1. An object will accelerate when a. SF = 0.
b. it is unbalanced.
c. it is pushed or pulled with a net force. d. its mass increases.
Answer: C
Assessment Questions
2. When a net force acts on an object, its
acceleration depends on the object’s
a. initial speed.
b. mass.
c. volume.
d. weight.
Assessment Questions
2. When a net force acts on an object, its
acceleration depends on the object’s a. initial speed.
b. mass. c. volume.
d. weight.
Answer: B
Assessment Questions
3. A cart is pushed and undergoes a certain
acceleration. Consider how the acceleration
would compare if it were pushed with twice
the net force while its mass increased by
four. Then its acceleration would be
a. one quarter.
b. half.
c. twice.
d. the same.
Assessment Questions
3. A cart is pushed and undergoes a certain
acceleration. Consider how the acceleration
would compare if it were pushed with twice
the net force while its mass increased by
four. Then its acceleration would be a. one quarter.
b. half. c. twice.
d. the same.
Answer: B
Assessment Questions
4. Friction is a force like any other force and
affects motion. Friction occurs in
a. solids sliding over one another.
b. fluids.
c. air.
d. all of these
Assessment Questions
4. Friction is a force like any other force and
affects motion. Friction occurs in a. solids sliding over one another.
b. fluids.
c. air.
d. all of these
Answer: D
Assessment Questions
5. When you stand on one foot instead of
two, the pressure you exert on the ground
is
a. half.
b. the same.
c. twice.
d. quadruple.
Assessment Questions
5. When you stand on one foot instead of
two, the pressure you exert on the ground
is a. half.
b. the same.
c. twice.
d. quadruple.
Answer: C
Assessment Questions
6. The reason a 20-kg rock falls no faster than
a 10-kg rock in free fall is that
a. air resistance is negligible.
b. the force of gravity on both is the same.
c. their speeds are the same.
d. the force/mass ratio is the same.
Assessment Questions
6. The reason a 20-kg rock falls no faster than
a 10-kg rock in free fall is that
a. air resistance is negligible.
b. the force of gravity on both is the same.
c. their speeds are the same.
d. the force/mass ratio is the same.
Answer: D
Assessment Questions
7. Kevin and Suzanne go sky diving. Kevin is
heavier than Suzanne, but both use the
same size parachute. Kevin has a greater
terminal speed compared with Suzanne
because
a. he has to fall faster for air resistance to
match his weight.
b. gravity acts on him more.
c. he has greater air resistance.
d. he has weaker terminal velocity.
Assessment Questions
7. Kevin and Suzanne go sky diving. Kevin is
heavier than Suzanne, but both use the
same size parachute. Kevin has a greater
terminal speed compared with Suzanne
because
a. he has to fall faster for air resistance to
match his weight. b. gravity acts on him more.
c. he has greater air resistance.
d. he has weaker terminal velocity.
Answer: A
Assessment Questions
Newton's Second Law
• The acceleration of an object is equal
to the force you apply divided by the
mass of the object.
Newton's Second Law
• If an object
has more
mass it
accelerates
at a lower
rate
because
mass has
inertia.
Calculate acceleration
• A cart rolls down a
ramp.
• The cart has a mass of
500 grams (0.5 kg).
• Using a spring scale,
you measure a net
force of 2 newtons
pulling the car down.
• Calculate the
acceleration of the
cart.
Calculate acceleration
• Three people are pulling on a wagon applying forces
of 100 N,150 N, and 200 N.
• The wagon has a mass of 25 kilograms.
• Determine the acceleration and the direction the
wagon moves.
Calculate force
• An airplane needs to
accelerate at 5 m/sec2 to
reach take-off speed before
reaching the end of the
runway.
• The mass of the airplane is
5,000 kilograms.
• How much force is needed
from the engine?
Calculate force
• A tennis ball contacts the racquet
for much less than one second.
• High-speed photographs show that
the speed of the ball changes from -
30 to +30 m/sec in 0.006 seconds.
• If the mass of the ball is 0.2 kg, how
much force is applied by the
racquet?
Equilibrium
• The condition of zero acceleration is
called equilibrium.
• In equilibrium, all forces cancel out
leaving zero net force.
• Objects that are standing still are in
equilibrium because their acceleration is
zero.
• Objects that are moving at constant
speed and direction are also in
equilibrium.
• A static problem usually means there is
no motion.
Equilibrium Rule
For any object or system of
objects in equilibrium the sum
of the forces acting equals zero
ΣF = 0
Tension force acts upwards
Weight acts downwards
Calculate force
• A woman is holding
two dogs on a leash.
• If each dog pulls with
a force of 80 newtons,
how much force does
the woman have to
exert to keep the dogs
from moving?
The Second Law:
Force, Mass, and Acceleration
Key Question:
• What is the relationship between force,
mass, and acceleration?
How about an easy one…
A single force of 40 N acts upon a 5-kg
block. What is the magnitude of the
acceleration of the block?
(Don’t forget the units!)
Consider this…
After returning home from the beach, Samantha
hangs her wet 0.20-kg bathing suit in the
center of the 6.0-m-long clothesline to dry.
This causes the clothesline to sag 4.0 cm. What
is the tension in the clothesline?
Solution First, convert cm to m. 4.0 cm = 0.040 m
Because the bathing suit is hung in the center of the clothesline, the tension in each side of the line is the same. You must find the downward force on the clothesline, which is simply the weight of the bathing suit.
Given: m = 0.20 kg Unknown: w = ?
g = 10.0 m/s/s Original equation: w=mg
Solve: w = mg = (0.20kg)(10.0m/s/s) = 2.0 N
Consider this…
Butch, the 72.0-kg star quarterback of
Belmont High School’s football team,
collides with Joe, a stationary left tackle,
and is brought to a stop with an
acceleration of -20.0 m/s/s. (a) what
force does Joe exert on Butch? (b) what
force does Butch exert of Joe?
Solution (a) The force depends upon the rate at which Butch’s
mass is brought to rest.
Given: m = 72.0 kg Unknown: F = ?
g = -20.0 m/s/s Original equation: F =ma
Solve: F = ma = (72.0 kg)(-20.0 m/s/s) = -1440 N
The – sign in the answer implies that the direction of
the force is opposite that of Butch’s original
direction of motion.
(b) Newton’s 3rd law states that for every action there
is an equal and opposite reaction. Therefore, if Joe
exerts a force of -1440 N on Butch, Butch will exert
the same 1440 N force back on Joe, but in the
opposite direction.
Try this one…
A 30.0-g arrow is shot by William Tell
through an 8.00-cm thick apple sitting on
top of his son’s head. If the arrow enters
the apple at 30.0 m/s and emerges at 25.0
m/s in the same direction, with what force
has the apple resisted the apple?
Solution: First, convert g to kg and cm to m.
30.0 g = 0.0300 kg 8.00 cm = 0.0800 m
Next, find the acceleration of the arrow before finding the force.
Given: Vo = 30.0 m/s Unknown: a = ?
Vf = 25.0 m/s Original equation:
Solve: (25.0 m/s/s) – (30.0 m/s/s) = 625 m^/s^ - 900 m^/s^
2(0.0800 m) 0.160 m
= -1720 m/s^
The – sign before the answer implies that the apple was causing the arrow to slow down.
Now solve for the force exerted by the apple.
Given: m = 0.0300 kg Unknown: F = ?
a = -1720 m/s^ Original formula: F = ma
Solve: F = ma = (0.0300 kg) (-1720 m/s^)
= -51.6 N
This is the force that the apple exerts on the arrow. It
is negative direction is opposite of the arrow’s
direction of motion.
Chapter 6: Newton’s Third Law or Motion
Action and Reaction
I. Forces and Interactions (6.1)
A. Force is part of a mutual action– an
interaction
1. Acts between one thing and another
2. Each exert a force on the other object
II. Newton’s Third Law (6.2)
A. Third law states:
Whenever one object exerts a force on a second
object, the second object exerts an equal and
opposite force on the first object
1. One force called action force and the other is
called the reaction force
a. It doesn’t matter which we call action or
reaction force
b. They are “partners” in single interaction
c. Neither force exist without the other
d. They are equal in strength and opposite in
direction
(“To every action there is always an equal opposing
reaction”)
B. Without the action force there cannot be
reaction force
1. Thus no resulting forward motion
2. Forces include contact and long-range
forces
III. Identifying Action and Reaction (6.3)
A. Identifying action and reaction pair
1. Can be difficult to identify sometimes
a. Start by identifying the interaction (e.g. Object A
interacts with object B)
1). Action: Object A exerts a force on
object B
2). Reaction: Object B exerts a force on
object A
IV. Action and Reaction on Different Masses (6.4)
A. Interaction between falling boulder and the
Earth
1. Forces are equal in strength and
opposite in direction
a. Boulder falls to Earth
b. Earth falls to boulder
2. Forces between Earth and boulder are equal, but
masses not
a. Newton’s second law states that
acceleration is not only proportional to net
force, but also inversely proportional to
mass.
b. Earth’s large mass– infinitesimally small
acceleration
B. Cannon example
1. Interaction between cannon and
cannon ball is exactly equal in magnitude
and opposite in direction
2. Must consider Newton’s Second law
m
Fa
V. Defining Systems (6.5)
A. If action and reaction forces are internal to
a system, they cancel each other and
produce no acceleration of the system
B. Action and reaction
forces do not cancel each
other when either is
external to the system
being considered.
2. Horse system (horse moves forward by interaction
with the ground– horse pushes backwards on the
ground and the ground pushes forward on the
horse
3. Horse-cart system (when consider only internal
forces , forces that act and react within the
system, they cancel. There must be interaction
with ground to produce acceleration)
B. Stalled car example– you cannot move car
forward by sitting in car and pushing on the
dashboard. Must interact with the ground-
make ground push car.
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