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• Mass and
Weight
• Friction Force
• Periodic
Motion
6.3 Interaction Forces
• Contact v.
Long Range
• Force
Diagrams
• F = ma (2nd
Law)
• Combining
Forces
• Measurement
• 1st Law—
Inertia
6.2 Using Newton’s Laws
6.1 Forces and Motion
Layout of Chapter 6
• Identifying
them
• Newton’s 3rd
Law
• Fundamental
Forces
• Ropes and
Strings
6.1
FORCE AND MOTION
4.1 The Concepts of Force and Mass
A force is a push or a pull.
Contact forces arise from physical
contact .
Action-at-a-distance or longrange forces do not
require contact and include gravity
and electrical forces.
Mathematically, the net force is
written as

F

where the Greek letter sigma
denotes the vector sum.
Newton’s Second Law
When a net external force acts on an object
of mass m, the acceleration that results is
directly proportional to the net force and has
a magnitude that is inversely proportional to
the mass. The direction of the acceleration is
the same as the direction of the net force.

a


F
m



F  ma
How do we
MEASURE FORCE? IN A NEWTON, OF COURSE
SI Unit for Force
 m  kg  m
kg   2   2
s
s 
This combination of units is called a newton (N).
How do we
DIAGRAM FORCE ON AN OBJECT
Arrows are used to represent forces. The length of the arrow
is proportional to the magnitude of the force.
15 N
5N
The net force on an object is the vector sum of all
forces acting on that object.
The SI unit of force is the Newton (N).
Individual Forces
4N
10 N
Net Force
6N
Individual Forces
Net Force
5N
64
3N
4N
What does unbalanced really mean?
• In pursuit of an answer, consider a physics book at rest
on a table top. There are two forces acting upon the
book. One force – the Earth's gravitational pull – exerts
a downward force. The second force – the push of the
table on the book (sometimes referred to as a normal
force) – pushes upward on the book.
Balancing Act
• Since these two forces are of equal magnitude and in
opposite directions, they balance each other. The book is
said to be at equilibrium. There is no unbalanced force
acting upon the book and thus the book maintains its state
of motion. When all the forces acting upon an object
balance each other, the object will be at equilibrium; it will
not accelerate. (Note: diagrams such as the one above are
known as free-body diagrams and will be discussed in detail
in Lesson 2.)
Another Pictorial Example
Object in motion
Balanced or Not?
• To determine if the forces acting upon an object are balanced or
unbalanced, an analysis must first be conducted to determine which
forces are acting upon the object and in what direction. If two
individual forces acting on an object are of equal magnitude and
opposite direction, then these forces are said to be balanced. An
object is said to be "acted upon by an unbalanced force" only when
there is an individual force acting on the object which is not
balanced by another force of equal magnitude and in the opposite
direction . Such analyses are discussed in Lesson 2 of this unit and
applied in Lesson 3.
Check your Understanding
• Copy this down for information used in further examples.
• Luke Autbeloe drops a 5.0 kg box of shingles (weight
approximately 50.0 N) off the barn house roof into a
haystack below. Upon hitting the haystack, the box of
shingles encounters an upward restraining force of 50.0 N .
Use this description to answer the following questions.
Example 1
• 1. Which one of the following velocity-time graphs best
describes the motion of the shingles? Support your
answer with sound reasoning.
Answer 1
• Graph B
• The shingles experience negative acceleration until they hit
the haystack. At that point the forces are balanced, so
velocity becomes constant
Example 2
• 2. Which one of the following ticker tapes best describes
the motion of the falling shingles from the time they are
dropped to the time they hit the ground? The arrows on
the diagram represent the point at which the shingles hit
the haystack. Support your answer with sound reasoning.
Answer to #2
• Tape A is correct.
• It shows the negative acceleration and constant
velocity.
Example 3 (has many parts)
• 3. Several of Luke's friends were watching the
motion of the falling shingles. Being "physics types",
they began discussing the motion and made the
following comments. Indicate whether each of the
comments is correct or incorrect. Support your
answers.
• A) A. Once the shingles hit the haystack, the forces
are balanced and the shingles will stop.
Correct or Incorrect?
• Incorrect.
• They stop accelerating but do not stop moving.
Part B
• B. Upon hitting the haystack, the shingles will
accelerate upwards because the haystack applies an
upward force.
Answer to B
• Incorrect
• The balanced forces on the shingles will keep velocity
constant.
Example C
• C. Upon hitting the haystack, the shingles will bounce
upwards due to the upward force.
Answer to C
• Incorrect
• Forces are balanced
Example 4
• 4. If the forces acting upon an object are balanced,
then the object
• A. must not be moving.
• B. must be moving with a constant velocity.
• C. must not be accelerating.
• D. none of the above.
Answer to #4
• A is possible but is not necessarily true at all times
• B an object with balanced forces cannot be
accelerating
• C It could be at rest and staying at rest or could be
in motion with constant velocity but not accelerating
making C the correct answer
A free-body-diagram is a diagram that
represents the object and the forces that
act on it.
The net force in this case is:
275 N + 395 N – 560 N = +110 N
and is directed along the + x axis of the coordinate system.
If the mass of the car is 1850 kg then, by
Newton’s second law, the acceleration is
F  110 N

a

 0.059 m s
m
1850 kg
2
4.4 The Vector Nature of Newton’s Second Law
4.4 The Vector Nature of Newton’s Second Law
The net force on the raft can be calculated
in the following way:
Force

P

A
x component
y component
+17 N
0N
+(15 N) cos67
+(15 N) sin67
+23 N
+14 N
ax
F


ay
F


x
m
y
m
 23 N
2

 0.018 m s
1300 kg
 14 N
2

 0.011 m s
1300 kg
Newton’s First Law
An object continues in a state of rest
or in a state of motion at a constant
speed along a straight line, unless
compelled to change that state by a
net force.
The net force is the vector sum of all
of the forces acting on an object.
Ladder of Inertia
Inertia In Motion
Looking into
NEWTON’S 1ST LAW, OTHER FORCES, AND
MISCONCEPTIONS OF FORCE
Force
Sub
Definition
Direction
Friction
Fric or
f
The contact force that acts to oppose Parallel to the surface and opposite
sliding motion between two surfaces the direction of sliding
Normal
N
The contact force exerted by a
surface on an object.
Spring
Sp
A restoring force, that is, the push or Opposite the displacement of the
pull a spring exerts on an object
object at the end of the spring
Tension
T
The pull exerted by a string, rope, or Away from the object and parallel to
cable when attached to a body and
the string, rope, or cable at the point
pulled taut
of attachment
Thrust
thrust
A general term for the forces that
move objects such as rockets,
planes, cars, and people
In the same direction as the
acceleration of the object barring
any resistive forces
Weight
grav or
g
A long range force due to
gravitational attraction between two
objects, generally Earth and an
object
Straight down toward the center of
the earth
Perpendicular to and away from the
surface
Misconceptions about Forces
WRONG
1.
2.
3.
4.
5.
When a ball has been thrown, the
force of the hand that threw it
remains on it.
A force is needed to keep an object
moving.
Inertia is a force.
Air does not exert a force
The quantity ma is a force.
Right
1.
2.
3.
4.
5.
No, it is a contact force; therefore,
once the contact is broken, the
force is no longer exerted.
It will continue moving with no
change in velocity or direction.
Inertia is a property of matter.
Air exerts a huge, usually balanced
force.
F = ma
4.1 The Concepts of Force and Mass
Mass is a measure of the amount
of “stuff” contained in an object.
Weight is actually a force and
can be found by using Newton’s
2nd Law
W = mg
Weightless and Apparent Weight
Apparent Weight
• The force exerted on the scale
measuring your weight at any point
• If there is additional force pushing
down (i.e. you are in an elevator
accelerating upward), your
apparent weight is greater than
your mass.
• If there is less force pushing down
on the scale (i.e. the elevator is now
accelerating downward) then you
have a weight less than your mass.
Weightless
• Specific circumstance of
acceleration = g
• Condition of free fall
• Your weight is zero but you
are not without mass
Looking into
FRICTION
In nature there are two general types of
forces, fundamental and non-fundamental.
Fundamental Forces
1. Gravitational force
2. Strong Nuclear force
3. Electroweak force
Examples of non-fundamental forces:
friction
tension in a rope
normal or support forces
A force that opposes motion between two surfaces
FRICTION
Friction
Eliminating Friction
Static Friction
The force that resists the initiation of
sliding motion between two surfaces
that are in contact and at rest
Kinetic Friction
The force that opposes
the movement of two
surfaces that are in
contact and are sliding
over each other
Ways to reduce harmful friction
• Lubricants (grease, oil, water)
• Replace sliding friction with rolling friction
• Make the surface smoother (sanding)
Ways to increase helpful friction
• Make surfaces rougher
• Increase the force pushing the surfaces together
How cars move
• Car’s wheels push against the road
• Road pushes back
• Without friction between the tires and roadway, there would
be no net force and no movement
Air Drag and Terminal Velocity
• Air or fluids cause friction that is dependent on
speed
• As speed increases, so does the friction
• An object’s shape and density also affect the friction
as well as the nature of the fluid itself.
• Terminal velocity is reached when the drag force
equals the force of gravity
Don’t try this at home!
• A common physics demonstration relies on this principle that
the more massive the object, the more it tends to resist
changes in its state of motion. The demonstration goes as
follows: several massive books are placed upon the physics
teacher's head. A wooden board is placed on top of the books
and a hammer is used to drive a nail into the board. Due to the
large mass of the books, the force of the hammer is
sufficiently resisted (inertia). This is demonstrated by the fact
that the blow of the hammer is not felt by the teacher. A
common variation of this demonstration involves smashing a
brick over the teacher's hand using a swift blow of the
hammer. The massive brick resists the force and the hand is
not hurt at all. (CAUTION: Do not try these demonstrations at
home!)
For you to try
• 1. Imagine a place in the cosmos far from all
gravitational and frictional influences. Suppose an
astronaut in that place throws a rock. The rock will:
• a) gradually stop.
• b) continue in motion in the same direction at
constant speed.
Try this one:
• 2. An 2-kg object is moving horizontally with a speed
of 4 m/s. How much net force is required to keep the
object moving with the same speed and in the same
direction?
And this one:
• 3. Mac and Tosh are arguing in the cafeteria. Mac
says that if he throws his jello with a greater speed it
will have a greater inertia. Tosh argues that inertia
does not depend upon speed, but rather upon mass.
With whom do you agree? Why?
Example 4
• 4. If you were in a weightless environment in space,
would it require a force to set an object in motion?
Example 5
• 5. Mr. Wegley spends most Sunday afternoons at
rest on the sofa, watching pro football games and
consuming large quantities of food. What effect (if
any) does this practice have upon his inertia?
Explain.
Example 6
• 6. Ben Tooclose is being chased through the woods
by a bull moose which he was attempting to
photograph. The enormous mass of the bull moose is
extremely intimidating. Yet, if Ben makes a zigzag
pattern through the woods, he will be able to use the
large mass of the moose to his own advantage.
Explain this in terms of inertia and Newton's first law
of motion.
Example 7
• 7. Two bricks are resting on the edge of a lab table. Shirley
Sheshort stands on her toes and spots the two bricks. She
acquires an intense desire to know which of the two bricks is
more massive. Since Shirley is vertically challenged, she is
unable to reach high enough and lift the bricks; she can,
however, reach high enough to give each brick a push.
Discuss how the process of pushing the bricks will allow
Shirley to determine which of the two bricks is more
massive. What difference will Shirley observe and how can
this observation lead to the necessary conclusion?
Another Look at Inertia
• As you learned in the previous unit, an object which is
not changing its velocity is said to have an
acceleration of 0 m/s2. Thus, an alternate definition
of inertia would be:
• Inertia is the tendency of an object to resist
accelerations.
•
Example
• 1. Several physics teachers are taking some time
off to play a little putt-putt golf. The 15th hole at
the Hole-In-One Putt-Putt Golf Course has a large
metal rim which putters must use to guide their
ball towards the hole. Mr. Schmidgall guides his
golf ball around the metal rim. When the ball leaves
the rim, which path (1, 2, or 3) will the golf ball
follow?
Answer
• 2 because it will go in an inertial direction which is a
straight path
Pictorial Review
Pictorial Representation
Example 1
• An applied force of 50 N is used to accelerate an object to the right across a
frictional surface. The object encounters 10 N of friction. Use the diagram to
determine the normal force, the net force, the mass, and the acceleration of
the object. (Neglect air resistance.)
Answer 1
•
•
•
•
•
•
•
•
•
Since there is no VERTICAL acceleration, there is no net vertical force so
Fnorm = F grav = 80 N
The mass can be calculated using F = mg or 80 N = m (10 m/s2) = 8 kg
Fnet is the sum of all forces
Fnorm – Fgrav = 0 N
50 N right – 10 N Left = 40 N right
Fnet = m a
40 N = (8 kg) a
a = 5 m/s2
Example 2
• An applied force of 20 N is used to accelerate an object to the
right across a frictional surface. The object encounters 10 N of
friction. Use the diagram to determine the normal force, the net
force, the coefficient of friction (µ) between the object and the
surface, the mass, and the acceleration of the object. (Neglect air
resistance.)
Answer 2
•
•
•
•
•
•
•
•
•
Again, no vertical acceleration so Fgrav = Fnorm = 100 N
Mass can be found by W = mg or F = mg
100 N = m (10 m/s2) = 10 kg
m = Ffric/ Fnorm = 10 N /100 N = 0. 1
Fnet is the sum of all forces
100 N up – 100 N down = 0 N
20 N right – 10 N left = 10 N right
Fnet = m x a  (10 N) = 10 kg x a
a = 1 m/s2
Example 3
• A 5-kg object is sliding to the right and encountering a friction
force which slows it down. The coefficient of friction (µ) between
the object and the surface is 0.1. Determine the force of gravity,
the normal force, the force of friction, the net force, and the
acceleration. (Neglect air resistance.)
Answer 3
• Since there is no vertical acceleration, there is no vertical
force, so Fgrav = Fnorm = 50 N
• Ffric = m Fnorm  Ffric = 0.1 (50 N) = 5 N
• Fnet is the sum of all unbalanced forces.
• 50 N up – 50 N down = 0 N
• 5 N left is unbalanced = 5 N left
• Fnet = m x a  5N = 5 kg x a
• A = 1 m/s2
Word of Caution
• Avoid forcing a problem into the form of a previously solved
problem. Problems in physics will seldom look the same. Instead of
solving problems by rote or by mimicry, utilize your conceptual
understanding of Newton's laws to work towards the solution. Use
your understanding of weight and mass to find the m or the Fgrav in
a problem. Use your conceptual understanding of net force (vector
sum of all the forces) to find the value of Fnet or the value of an
individual force. Do not divorce the solving of physics problems
from your understanding of physics concepts. If you are unable to
solve physics problems like the ones above, it is unlikely that you
are having a math difficulty; rather it is more likely that you are
having a physics difficulty.
Looking at
PERIODIC MOTION
Simple Harmonic Motion
• If the force that restores the object to its equilibrium
position is directly proportional to the displacement of
the object, the motion is called simple harmonic
motion
• Period = time needed to repeat one complete cycle of
motion (T)
• Amplitude = maximum distance the object moves from
equilibrium
The pendulum
• A pendulum is an example of simple harmonic motion
• T = 2 x  x (1/g)
Resonance
• Small forces applied at regular intervals to a vibrating
or oscillating object resulting in a greater amplitude
• The time interval between applications of force is
equal to the period of the oscillation.
• Examples: rocking a car to get out of snow bank or
rhythmically jumping on a trampoline or pushing a
swing to get higher
Recap
• A force is a push or a pull upon an object which results
from its interaction with another object. Forces result from
interactions! As discussed in the last lesson, some forces
result from contact interactions (normal, frictional,
tensional, and applied forces are examples of contact
forces) and other forces result from action-at-a-distance
interactions (gravitational, electrical, and magnetic forces
are examples of action-at-a-distance forces).
Moving on…
• According to Newton, whenever objects A and B interact with each
other, they exert forces upon each other. When you sit in your chair,
your body exerts a downward force on the chair and the chair
exerts an upward force on your body. There are two forces
resulting from this interaction — a force on the chair and a force on
your body. These two forces are called action and reaction forces
and are the subject of Newton's third law of motion. Formally stated,
Newton's third law is:
• "For every action, there is an equal and opposite reaction."
But what does it mean?
• The statement means that in every interaction, there is a
pair of forces acting on the two interacting objects. The
size of the force on the first object equals the size of the
force on the second object. The direction of the force on
the first object is opposite to the direction of the force on
the second object. Forces always come in pairs – equal and
opposite action-reaction force pairs.
Implications
• A variety of action-reaction force pairs are evident in nature. Consider the
propulsion of a fish through the water. A fish uses its fins to push water
backwards. But a push on the water will only serve to accelerate the water. In
turn, the water reacts by pushing the fish forwards, propelling the fish through
the water. The size of the force on the water equals the size of the force on the
fish; the direction of the force on the water (backwards) is opposite to the
direction of the force on the fish (forwards). For every action, there is an equal
(in size) and opposite (in direction) reaction force. Action-reaction force pairs
make it possible for fishes to swim.
What makes birds fly?
• Consider the flying motion of birds. A bird flies by use of its wings.
The wings of a bird push air downwards. In turn, the air reacts by
pushing the bird upwards. The size of the force on the air equals the
size of the force on the bird; the direction of the force on the air
(downwards) is opposite to the direction of the force on the bird
(upwards). For every action, there is an equal (in size) and opposite
(in direction) reaction. Action-reaction force pairs make it possible
for birds to fly.
Motion in everyday
• Consider the motion of your automobile on your way to school. An automobile is
equipped with wheels that spin backwards. As the wheels spin backwards, they
push the road backwards. In turn, the road reacts by pushing the wheels
forward. The size of the force on the road equals the size of the force on the
wheels (or automobile); the direction of the force on the road (backwards) is
opposite to the direction of the force on the wheels (forwards). For every
action, there is an equal (in size) and opposite (in direction) reaction. Actionreaction force pairs make it possible for automobiles to move.
Example 1
• 1. While driving, Anna Litical observed a bug striking the
windshield of her car. Obviously, a case of Newton's third
law of motion. The bug hit the windshield and the windshield
hit the bug. Which of the two forces is greater: the force on
the bug or the force on the windshield?
Answer 1
• For every action there is an EQUAL reaction. The fact that
the bug splatters only means that with its smaller mass, it
is less able to withstand the larger acceleration resulting
from the interaction.
• The forces are EQUAL in size.
Example 2
• 2. Rockets are unable to accelerate in space because ...
A) there is no air in space for the rockets to push off of.
B) there is no gravity is in space.
C) there is no air resistance in space.
D)... nonsense! Rockets do accelerate in space.
Answer 2
• It is a common misconception that rockets do not
accelerate in space. Rockets do accelerate in space.
Rockets are able to accelerate due to the fact that they
burn fuel and push the exhaust in a direction opposite to
the direction they wish to accelerate
• Answer is D
Example 3
• 3. A gun recoils when it is fired. The recoil is the result of
action-reaction force pairs. As the gases from the
gunpowder explosion expand, the gun pushes the bullet
forwards and the bullet pushes the gun backwards. The
acceleration of the recoiling gun is ...
a) greater than the acceleration of the bullet.
b) smaller than the acceleration of the bullet.
c) the same size as the acceleration of the bullet
Answer 3
• The force on the gun equals the force on the bullet.
However, acceleration depends on both force and mass.
The bullet has a great acceleration due to the fact that it
has a smaller mass. Remember acceleration and mass are
inversely proportional.
• The correct answer is B
Example 4
• 4. In the top picture, a physics student is pulling upon a rope which is attached
to a wall. In the bottom picture, the physics student is pulling upon a rope which
is held by the Strongman. In each case, the force scale reads 500 Newtons. The
physics student is pulling
a) with more force when the rope is attached to the wall.
b) with more force when the rope is attached to the Strongman.
c) the same force in each case.
Answer 4
• The rope transmits the force from the physics student to the
wall (or Strongman) and vice versa. Since the force of the
student pulling on the wall and the wall pulling on the student
are action-reaction force pairs, they must have equal
magnitudes. Inanimate objects such as walls can have push
and pull.
• The correct answer is C. The student is pulling with 500 N in
both cases.
Force Pairs
• According to Newton's third law, for every action force there is an
equal (in size) and opposite (in direction) reaction force. Forces
always come in pairs — known as "action-reaction force pairs."
Identifying and describing action-reaction force pairs is a simple
matter of identifying the two interacting objects and making two
statements describing who is pushing on whom and in which
direction. For example, consider the interaction between a baseball
bat and a baseball.
Label the diagram Which
is action and reaction
pairs?
• The baseball forces the bat to the right (an action); the bat
forces the ball to the left (the reaction). Note that the nouns
in the sentence describing the action force switch places
when describing the reaction force.
Athlete pushes bar upward
• Bar pushes athlete downward.
Bowling ball pushes pin rightwards.
• Pin pushes bowling ball leftward.
Compressed air pushes balloon wall outwards.
• Balloon wall pushes compressed air inward.