Download Chapter 2 Lecture Forces (Start)

Chapter 2 Lecture
Newtonian
Mechanics
Prepared by
Dedra Demaree,
Georgetown University
© 2014 Pearson Education, Inc.
Newtonian Mechanics
• Why do seat belts and air bags save lives?
• If you stand on a bathroom scale in a moving
elevator, does its reading change?
• Can a parachutist survive a fall if the parachute
does not open?
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Be sure you know how to:
• Draw a motion diagram for a moving object
(Section 1.2)
• Determine the direction of acceleration using a
motion diagram (Section 1.6)
• Add vectors graphically and by components for
one-dimensional motion (Section 1.2 and
Appendix B)
• Last chapter: learned to describe motion
• This chapter: learn why an object has a
particular acceleration
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2.1 Describing and representing
interactions
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Describing and representing interactions
• Objects can interact directly, when they touch
each other—for example, in a push or a pull.
• Objects can interact at a distance—for example,
when a magnet attracts or repels another
magnet without touching it.
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Choosing a system to describe interactions
• We choose one particular object for analysis;
this object is called the system.
• All objects not part of the system can interact
with it (touch it, pull it, and push it) and are in the
system's environment.
• Interactions between the system object and
objects in the environment are called external
interactions.
• External interactions can affect the motion of the
system.
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Using a system when sketching a process
• Make a light boundary (a closed dashed line)
around the system object to emphasize the
system choice.
• Any parts of an object that are inside the system
can have internal interactions.
• We will model an object such as a car as pointlike and ignore internal interactions.
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Choosing a system to describe interactions
(Cont'd)
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Representing interactions
• Make a light boundary (a closed dashed line) around the
system object to emphasize the system choice.
• Draw an arrow to represent interactions between the
system and the environment, such as the arrow in the
figure showing the hands pushing upward on each ball.
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Force
• Force is a vector quantity that characterizes how hard
(magnitude) and in which direction an external object
pushes or pulls on the system object.
• The symbol for force has subscripts identifying the
external object that exerts the force and the system
object on which the force is exerted.
• The SI unit for force is the newton (N).
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What Do Forces Do?
• As the block starts to move, in order to keep the
pulling force constant you must move your hand in
just the right way to keep the length of the rubber
band—and thus the force—constant.
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Force Body Diagrams (FBD)
• Used with the point-like model
– The system object is represented by a dot.
• Arrows used to represent the forces
– Length of the arrow relates to the strength of
the force.
– Direction the arrow points relates to the
direction in which the force is exerted on the
system object.
• Includes forces exerted on the system object
• Shows the forces at a single instant
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Free Body Diagrams
A free body diagram is a drawing that is used in
order to show all the forces acting on an object.
Drawing free body diagrams can help when trying to
solve for unknown forces or determining the
acceleration of the object.
Drawing force body diagrams (FBD)
1.
2.
3.
4.
Sketch the situation.
Circle the system.
Identify external interactions.
Place a dot at the side of the sketch
representing the system object.
5. Draw force arrows to represent the external
interactions.
6. Label the forces with a subscript containing two
elements.
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Constructing force diagrams
• Example: a rock sinking into sand
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Free Body Diagrams
1. Draw and label a dot to represent
the box. See, you don't even have to
be able to draw a stick figure to do free
body diagrams.
2. Draw an arrow from the dot
pointing in the direction of one of the
forces that is acting on that object.
Label that arrow with the name of the
force.
3. Repeat for every force that is acting
on the object. Try to draw each of the
arrows to roughly the same scale,
bigger forces getting bigger arrows.
Fg
FN
Fapplied
Fg
Free Body Diagrams
4. Once you have finished your free
body diagram, recheck it to make
sure that you have drawn and
labeled an arrow for every force.
This is no time to forget a force.
5. Draw a separate arrow next to
your free body diagram indicating
the likely direction of the
acceleration of the object. This will
help you use your free body
diagram effectively.
6. Repeat this process for every
object in your sketch.
a
FN
Fapplied
Fg
Remember - the acceleration
found does NOT tell you
which way the object is
moving - it only tells you how
the velocity is changing!
Types of Forces
Short Catalog of Forces
Forces
• Commonly imagined as a push or pull on some
object
• Vector quantity
• May be a contact force or a field force
– Contact forces result from physical contact between
two objects
– Field forces act between disconnected objects
Fundamental Forces
• Types
–
–
–
–
Strong nuclear force
Electromagnetic force
Weak nuclear force
Gravity
• Characteristics
– All field forces
– Listed in order of decreasing strength
– Only gravity and electromagnetic in mechanics
Section 4.1
Weight
• The gravitational pull of
the earth on an object on
or near the surface of the
earth is called weight.
• The agent for the weight
forces is the entire earth.
• An object’s weight
vector always points
vertically downward, no
matter how the object is
moving.
Weight and Mass
Mass is measured in kilograms and weight is
measured in Newtons because it is a force.
Labled: Weight or W or Fg 𝑜𝑟 𝑚𝑔
Does the value of the mass or the weight of an object
change depending on where it is?
Spring Force
• Springs come in in many forms. When deflected,
they push or pull with a spring force.
Normal Force
• The force exerted on
an object that is
pressing against a
surface is in a
direction
perpendicular to the
surface.
• The normal force is
the force exerted by a
surface (the agent)
against an object that
is pressing against
the surface.
Microscopic Model
Springy Atomic Model for Solids
- Consider a solid object to be made of atoms
- Connected by bonds that are like springs.
- We can now understand how the table knows how much
to push back. When the an object (in this case a book)
is placed on the table it only feels its weight so it starts
to accelerate downward. This deforms the table
bringing upward spring forces into play. The table
deforms until the forces are enough to cancel the
weight.
Normal Force
• The normal force is responsible for the
“solidness” of solids.
• The symbol for the normal force is n . I will also
write as Fn
• Perpendicular touching forces are called normal
forces.
• Normal forces are not always vertical.
Tension Force
• When a string or rope or wire pulls on an object, it
exerts a contact force that we call the tension
force.
• The direction of the tension force is always in
the direction of the string or rope.
Ropes provide tension (a pull)
In physics we often use a “massless” rope with opposing
tensions of equal magnitude
Friction
• Friction, like the normal force, is exerted by a
surface.
• The frictional force is always parallel to the
surface.
• Kinetic friction, denoted by f k , acts as an object
slides across a surface. Kinetic friction is a force
that always “opposes the motion.”
• Static friction, denoted by f s , is the force that
keeps an object “stuck” on a surface and
prevents its motion relative to the surface. Static
friction points in the direction necessary to
prevent motion.
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Friction
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Drag
• The force of a fluid (like
air or water) on a moving
object is called drag.
• Like kinetic friction, drag
points opposite the
direction of motion.
• You can neglect air
resistance in all
problems unless a
problem explicitly asks
you to include it.
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Thrust
• Thrust is a force that occurs when a jet or rocket
engine expels gas molecules at high speed.
• Thrust is a force opposite the direction in
which the exhaust gas is expelled.
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Electric and Magnetic Forces
• Electricity and magnetism, like gravity, exert
long-range forces.
• The forces of electricity and magnetism act on
charged particles.
• These forces—and the forces inside the
nucleus—won’t be important for the dynamics
problems we consider in the next several
chapters.
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2.2 Adding and Measuring Forces
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Adding forces graphically
• Draw the vectors head to tail.
• Draw the vector that goes from the tail of the first
vector to the head of the second vector.
– This is the sum vector, also called the
resultant vector.
– In this case this vector is the net force (it is
not a new force, but rather the combined
effect of all the forces being exerted on the
object).
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Adding forces graphically (Cont'd)
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Example: Lifting a suitcase
• The upward force you exert on
the suitcase is larger than the
downward force Earth exerts on
the suitcase.
• The net effect is a 50-N force
pointed straight up.
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Adding forces graphically (Cont'd)
• If several object in the environment exert
forces on the system object.
– Use vector addition to find the sum Σ of the
forces exerted on the object
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Draw FBD for these exercise
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Measuring force magnitudes
• Force is a vector quantity with both magnitude
and direction.
• One method to measure an unknown force is to
calibrate a spring in terms of some standard
force.
• This calibrated spring can then be used to
measure other forces.
• A spring scale is the simplest instrument to
measure forces.
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Measuring force magnitudes (Cont'd)
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Physics language: Force
• Force is a physical quantity characterizing an
interaction between two objects.
– Always identify the two interacting objects.
– Force includes both the magnitude and the
direction of the interaction.
• The word "force" in physics is more precisely
defined than how we use it in everyday life.
• The definition of "force" in physics has also been
refined through history.
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Draw FBD…do not forget about the Normal
Force
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2.3 Conceptual Relationship between
force and motion
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Conceptual Relationship between force and
motion
• Question: Is there a relationship between the
forces that are exerted on an object and the way
the object moves?
• Lets take a look
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Patterns observed in the experiments
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Observational experiments for a bowling
ball rolling on a very hard, smooth surface
• In all experiments, the vertical forces add to zero
and cancel.
– We consider only forces exerted in the
horizontal direction.
• In the first experiment, the sum of the forces
exerted on the ball is zero.
– The ball's velocity remains constant.
• When the ruler pushes the ball, the velocity
change arrow points in the same direction as the
sum of the forces.
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Adding and Measuring Forces
Each of the experiments the ∆𝑣 arrow for the systems object
and the sum of the forces Σ𝐹 that external objects exert on
that object are in same direction
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Testing the relationship between the sum of
forces and the motion of the system object
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Testing the relationship between the sum of
forces and the motion of the system object
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Relating forces and motion
• What have we learned so far
– Δ𝑣 always points in the same direction of the
sum of forces Σ𝐹 exerted on it
– We know from chapter 1 that the 𝑎 points in
the same direction as the Δ𝑣.
– Thus we can say the ∆𝑣 arrow for the
systems object and the sum of the forces Σ𝐹
that external objects exert on that object are
in same direction
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Relating forces and motion
Or:
1. if the Σ𝐹 is 0. the object continues with no change
in velocity (is the velocity 0 or constant?)
2. If Δ𝑣 point in the same direction of the Σ𝐹 the
object speeds up (accelerates)
3. If Δ𝑣 point in the opposite direction of the Σ𝐹
objects slows down (or accelerates in the opposite
direction of the motion)
2.4 Reasoning without mathematical
equations
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Think about the options you
have for Δ𝑣 = _____
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Reasoning without mathematical equations
• Motion and force diagrams and the rule relating
motion and force can be used to reason
qualitatively about physical processes:
– To determine the relative magnitudes of
forces if you have information about motion
– To estimate velocity changes if you have
information about forces
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2.5 Inertial reference frame and Newtons
First Law
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Inertial reference frame
• Here the saying goes again: Again,
Description of motion depends om the observers
reference frame.
• So far in this chapter we have only talked about
the observer standing on the Earth’s surface
• Determined that forces when all the sum of all
Σ𝐹=0 the object moves at constant velocity or is
stopped.
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Inertial reference frame
• An inertial reference frame is one in which an
observer:
– Sees that the velocity of the system object
does not change if no other objects exert
forces on it or
– Sees no change in the velocity if the sum of
all forces exerted on the system object is zero
• In non-inertial reference frames, the velocity of
the system object can change even though the
sum of forces exerted on it is zero.
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Inertial reference frame
• A passenger in a car or train that is speeding up
or slowing down with respect to Earth is an
observer in a non-inertial reference frame.
– When you are in a car that stops abruptly,
your body jerks forward, yet nothing is
pushing you forward.
• Observers in non-inertial reference frames
cannot explain the changes in velocity of objects
by considering the forces exerted on them by
other objects.
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Newton's First Law of Motion
• For an observer in an inertial reference frame,
the object continues moving at constant velocity
(including remaining at rest):
– When no other objects exert forces on an
system object or
– When the forces exerted on the object add to
zero
• Inertia is the phenomenon in which an object
continues to move at constant velocity when the
sum of the forces exerted on it by other objects
is zero.
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Inertia
• Is the tendency of an object to continue in its
original motion
– In the absence of a force
• Thought experiment
– Hit a golf ball
– Hit a bowling ball with the same force
– The golf ball will travel farther
– Both resist changes in their motion
– Think of mass as the unit of inertia….
2.6 Newtons 2nd Law
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Newtons 2nd Law
• So far we have learned about the relationship
between Σ𝐹and Δ𝑣
• Δ𝑣 and 𝑎 are related because they point in the
same direction
• Now we need to figure out an equation so we
can determine the 𝑎 of an object knowing Σ𝐹 the
exerted on it.
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Newton's Second Law Of Motion
• Observation experiments help us construct the
following relationship between the sum of forces
on a system object and the system object's
motion:
• The symbol α means "is proportional to." For
example, if the sum of the forces doubles, then
the acceleration doubles.
• So is there another physical quantity that effects
acceleration
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What is easier to pull a bus or a small block of wood?
What is the physical quantity that seperate the wood from the
bus?
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• From the pattern of the experiment we see that
the greater amount of matter pulled the smaller
the acceleration when the same amount of force
is applied.
• The property of an object that affects its
acceleration is called mass
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Mass (another physical quantity)
• Mass is a measure of the amount of matter.
• Mass is represented by the symbol m.
• To measure mass quantitatively, you first define
a standard unit of mass.
• The SI standard unit of mass is the kilogram
(kg).
• The kilogram standard is a cylinder made of a
platinum-iridium alloy stored in a museum of
measurements near Paris.
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Mass
• Mass characterizes the amount of matter in an
object.
• When the same unbalanced force is exerted on
two objects, the object with greater mass has a
smaller acceleration.
• Mass is a scalar quantity, and masses add as
scalars.
• MASS IS AN INHERENT PROPERTY OF AN
OBJECT
• Mass and weight are different quantities; weight
is usually the magnitude of a gravitational (noncontact) force.
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Newton's second law of motion
|a|
• Observation experiments help us construct the
following relationship for the proportionality
between the acceleration of a system object and
the system object's mass:
m
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Newton's second law of motion
• Combining the results of our observational experiment
findings, we have:
• Force is a ubiquitous quantity so it has a unit defined for it
called a newton (N).
• Newton is about equivalent to the force generated by gravity (9.8 m/s2by
a 0.1kg object. (Put the weight in your hand how does it feel) It feels like
a 1 Newton!!!!!. About a 50KiloNewton required to break bone.
• A force of 1 newton (1 N) will cause an object with a mass of 1 kg to
accelerate at 1 m/s2.
• About 95-110 G (1 G equals 9.8m/s2) will cause a concussion. With an
80 kg person that about 78400N. It’s the acceleration that cause the
force that cause concussions!!! 20% of all HS football players will get a
concussion in a 3-4 year playing time.
Making sense of Newton's second law
• The equation we deduced for Newton's second
law is:
– If the mass is infinitely large, the acceleration
is zero.
– If the mass is zero, the acceleration is
infinitely large.
• Both of these extreme cases make sense.
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Acceleration Formulas
Newtons 2nd law is called the cause and affect relationship
Called the dynamics method
Δ𝑣
𝑎 = is called the operational definition of acceleration. It
Δ𝑡
tells us the quantity of acceleration but does not tell us WHY.
This is the kinematics method
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Force components used for forces along
one axis
• Our equation for Newton's second law can be
written in vector component form. For example,
in the x-direction we have:
or  F on system x  msystem asystem x
1. Identify the positive direction of the axis.
2. Find the components of all the forces being
exerted on the system.
3. Forces that point in the positive direction
have a positive component; forces that point
in the negative direction have a negative
component.
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2.7 Gravitational Force Law
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Gravitational force law (little g definition)
• Objects falling in a vacuum (for instance, a tube
with the air removed) show that all objects fall
straight down with the same acceleration.
– This acceleration has a magnitude of
9.8 m/s2.
• Earth (E) exerts the only force on the falling object
(O) (in a vacuum).
– FE on Oy = mOaOy = mO(9.8 m/s2)
– We define g such that:
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Gravitational force law (little g definition)
• Lots of names for little g
– Free Fall acceration
– Gravitational acceleration
– Gravitational constant
• Why is it the same for all objects?
• Force being applied by the Earth changes to accomadate the mass
of an object so that a always equals g.
• Increase the Mass of an object by 10 the FEonO also increases by 10
so that g remains constant.
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ΣF =ma
The trap is that the net force does NOT tell you how the
object is moving - that is, it does not give you any
information about its velocity or displacement. It only tells
you the object's acceleration - its change in velocity.
An object may be moving at 300 km/s, with zero external
force on it, so it has zero acceleration - which just means it
keeps a constant velocity of 300 km/s.
2.8 Skills for applying Newtons 2nd Law
for 1D processes
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Skills for applying Newton's second law for
one-dimensional processes
1. Sketch and translate.
– Sketch the process, choose the system object
and coordinate system, and label the sketch
with everything you know about the situation.
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Weight
• The weight of the object on a planet is the force
that the planet exerts on the object.
• In everyday language, the normal force that a
scale exerts on you (which balances the
downward force you exert on it) is your weight.
• We will not use the term "weight of an object"
because it implies that weight is a property of the
object rather than an interaction between two
objects.
• Labeled as Weight/ W /Fg /mg
• More on weight later!!!
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Elevator Problems
Scales: What do they read!!!
TAKE NOTES: I am putting this on the board
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Couple of Vocabulary Terms
• Apparent Weight: The equation for measuring
apparent weight is F = mg + ma.
• Its what a scale reads (Total Normal Force).
– No acceleration your weight will equal your weight…
– Acceleration… Fn = mg + ma=scale weight
– We use Elevator Problems to discuss Apparent
Weight, the concept of weightlessness, and Free Fall
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Apparent Weight
• The weight of an object is the force of gravity on
that object.
• Your sensation of weight is due to contact forces
supporting you.
• Let’s define your apparent weight wapp in terms
of the force you feel:
• Apparent Weight is defined as Fn
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Apparent Weight
• The only forces acting
on the man are the
upward normal force of
the floor and the
downward weight force:
n = w + ma
wapp = w + ma
• Thus wapp > w and the
man feels heavier than
normal.
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Couple of Vocabulary Terms
• Weightlessness: is simply a sensation experienced by
an individual when there are no external objects touching
one's body and exerting a push or pull upon it.
Weightless sensations exist when all contact forces are
removed.
• These sensations are common to any situation in which
you are momentarily (or perpetually) in a state of free fall
• Weightlessness is only a sensation; it is not a reality
corresponding to an individual who has lost weight. As
you are free falling on a roller coaster ride (or other
amusement park ride), you have not momentarily lost
your weight. Weightlessness has very little to do with
weight and mostly to do with the presence or absence of
contact forces.
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Couple of Vocabulary Terms
• Freefall when your acceleration (a = -g)
• When in free fall, the only force acting upon your body is
the force of gravity - a non-contact force. Since the force of
gravity cannot be felt without any other opposing forces,
you would have no sensation of it. You would feel
weightless when in a state of free fall.
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Weightlessness
• A person in free fall has zero apparent weight.
• “Weightless” does not mean “no weight.”
• An object that is weightless has no apparent
weight.
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Equation Jeopardy Problems
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2.9 Forces Come In Pairs Newtons 3rd
Law
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Forces come in pairs
Suppose you wear rollerblades and push abruptly
on a wheeled cart loaded with a heavy box.
• If you and the cart are on a hard smooth floor,
the cart starts moving away (it accelerates), and
you also start to move and accelerate in the
opposite direction.
• You exerted a force on the cart and the cart
exerted a force on you.
• Because the accelerations were in opposite
directions, the forces must point in opposite
directions.
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Testing experiment: Newton's third law of
motion
• Attach one spring scale to a hook
on the wall and pull on its other end
with a second spring scale.
– If the hypothesis is correct, then
the scale you pull should have
the same reading as the scale
fixed to the wall.
– You find that the scales have
the same readings.
– If you reverse the scales and
repeat the experiment, you find
they always have the same
readings.
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Newton's third law of motion
• When two objects interact, object 1 exerts a
force on object 2. Object 2 in turn exerts an
equal-magnitude, oppositely directed force on
object 1.
• These forces are exerted on different objects
and cannot be added to find the sum of the
forces exerted on one object.
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Tips for Newton's third law of motion
• The forces in Newton's third law are exerted on
two different objects.
– This means that the two forces will never
appear on the same force diagram.
– Also, they should not be added together to
find the sum of the forces.
• You have to choose the system object and
consider only the forces exerted on it!
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3rd Law Conceptual Questions
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Push me and I push back!
• For example, with the palm of your hand, push
on a book, desk or table. You are exerting a
force on the object you are pushing. At the
same time, you can feel a force on your hand.
There seems to be two forces: the one your
hand exerted on the object, and another force
on your hand.
• What is the relationship between these forces?
The man weighs 700 N. The force exerted
•by the table on the man is:
a)
b)
c)
d)
Larger than 700 N
Equal to 700 N
Smaller than 700 N
There is no force.
A hand pushes on a balloon against a wall
with a force of 10 N. The force exerted by the
balloon on the hand is:
a)
b)
c)
d)
Larger than 10 N
Equal to 10 N
Smaller than 10 N
There is no force.
A building is being torn down. The wrecking ball
smashes through a wall. Does the ball put a
larger force on the wall than the wall puts on the
wrecking ball?
Explain your answer.
Imagine that you hold the two force probes,
one probe in each hand. You will notice
that each force probe has a hook on it.
Connect the two force probes together and
pull as seen in the following figure.
Runners and Rockets
• In order for you to walk,
the floor needs to have
friction so that your foot
sticks to the floor as you
straighten your leg,
moving your body forward.
• The friction that prevents
slipping is static friction.
• The static friction has to
point in the forward
direction to prevent your
foot from slipping.
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Runners and Rockets
• The rocket pushes hot gases out the back, and
this results in a forward force (thrust) on the
rocket.
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Exercise
Newton’s Third Law
A fly is deformed by hitting the windshield of a speeding bus.

v
The force exerted by the bus on the fly is,
B. equal to
that exerted by the fly on the bus.
Physics 207: Lecture 8, Pg 112
Exercise 2
Newton’s Third Law
Same scenario but now we examine the accelerations
A fly is deformed by hitting the windshield of a speeding bus.

v
The magnitude of the acceleration, due to this collision, of
the bus is
A. greater than
B. equal to
C. less than
that of the fly.
Physics 207: Lecture 8, Pg 113
Exercise 2
Newton’s Third Law
Solution
By Newton’s third law these two forces form an interaction
pair which are equal (but in opposing directions).

Thus the forces are the same
However, by Newton’s second law Fnet = ma or a = Fnet/m.
So Fb, f = -Ff, b = F0
but |abus | = |F0 / mbus | << | afly | = | F0/mfly |
Answer for acceleration is (C)
Physics 207: Lecture 8, Pg 114
Exercise 3
Newton’s 3rd Law


Two blocks are being pushed by a finger on a horizontal
frictionless floor.
How many action-reaction force pairs are present in this
exercise?
a
A.
B.
C.
D.
b
2
4
6
Something else
Physics 207: Lecture 8, Pg 115
Exercise 3
Solution:
Fa,f
Ff,a
a
Fb,a
FE,a
Fa,b
bF
Fg,a
Fg,b
Fa,g
Fb,g
Fa,E
E,b
Fb,E
6
Physics 207: Lecture 8, Pg 116
Normal Force and Weight
FN
The Normal Force,
FN, is always
perpendicular to the
surface that is
creating it.
mg
Weight, mg, is
always directed
downward.
We know where the weight force comes from - but what is the origin of the
Normal Force?
Normal Force and Weight
The Normal Force is a
consequence of
Newton's Third Law and
is due to the electrons
in the table repelling the
electrons in the box which results in an
upward, Normal Force.
FN
mg
We discuss electron
interactions in more
detail in AP 2 course
The box is being pulled down by gravity (mg), and the Normal Force is
pushing up on the box. Is this a Newton's Third Law action-reaction pair of
forces?
Normal Force and Weight
FN
FN
Fbox on earth
mg
Fbox on
table
mg
No! The Normal force and the gravitational force, mg, both act on the box. Action
reaction force pairs act on different objects. The Normal force and the force that the
box exerts on the table is an action reaction pair.
The force that the earths' gravity (mg) exerts on the box is an action reaction pair with
the gravitational force that the box exerts on the earth.
Normal Force and Weight
FN
mg
If the table is not accelerating in
the y direction and the box is
not moving up and down on the
table, then FN = mg.
Normal Force and Weight
FN
a
But, if the table is in an elevator
and is accelerating upwards,
then we have:
mg
The Normal Force is greater
than the weight. If the box was
replaced with a person, the
person would feel heavier than
their typical weight.
Thus we have another name for the Normal Force - it is
also called the Apparent Weight.
Extra Stuff
Friction
Apparent Weight
Elevator Problems
A 42.3 kg object rests on a table. What is the Normal
force exerted by the table on the object? Use g = 10.0
m/s2.
Answer
15
[This object is a pull tab]
16
A 42.3 kg object rests on a table. The table is placed in
an elevator and accelerates upwards at 1.55 m/s2. What
is the Normal force (Apparent Weight) exerted by the
table on the object? Use g = 10.0 m/s2.
Tension Force
When a cord or rope pulls on an
object, it is said to be under tension,
and the force it exerts on the object is
called a tension force, T or FT.
a
FT
Are the forces shown on the diagram
to the right an action reaction pair?
mg
Tension Force
No, they are not an action reaction
pair. The Tension force and mg are
both operating on the pail. Action
reaction pairs operate on different
objects.
If the hand is pulling the pail up with
a constant velocity, what is the
relationship between FT and mg?
a
FT
mg
Tension Force
They are equal. If the pail is
moving with a constant velocity,
then ay = 0.
FT
a
mg
Friction
When we first discussed Newton's First Law, the
concept of friction as a force that opposes motion was
introduced without any mathematical details, or even
qualitative discussion.
v
Fap
p
It's now time to do that. Look at the box
to the right. You're pulling the box with
an applied Force, Fapp.
• Is it harder to get the box moving
• or keep it moving?
• What happens if you pull the box over a surface of ice,
compared to a surface of sandpaper?
• What happens if you increase the mass of the box?
Friction
You probably found it harder to get the box moving - once
moving, it needed less Fapp to keep it moving.
v
The more massive the box - the more Fapp
was required to start it moving and to keep
it moving.
F
a
p
p
And, it is much easier to pull a box over
an icy surface versus over sandpaper - a
smaller Fapp is needed.
So, the friction force appears to depend on whether the
object was at rest or moving, its mass and the surface it
was moving on.
Friction
We'll first address the issue of the difference in Fapp
required to overcome the friction of a stationary object
and a moving object by distinguishing between two types
of friction - static and kinetic.
Static friction force is the force that works to prevent the
motion of a stationary object.
Kinetic friction force is the force that acts opposite to the
motion of a moving object.
Friction
In both Static and Kinetic friction, it is harder to move a
more massive object - so there is a dependence on the
Normal force - the force that the surface is exerting on the
stationary or moving object.
Also - both types of friction depend on the type of material
that the object and the surface are made of.
This is represented by the coefficient of static friction (μs)
and the coefficient of kinetic friction (μk). These
coefficients have been measured for many material
interfaces.
It is interesting to note that the contact
area between the object and surface
does not affect the friction force.
Mass and Weight
One More Time
© 2015 Pearson Education, Inc.
Mass and Weight
• Mass and weight are not
the same thing.
• Mass is a quantity that
describes an object’s inertia,
its tendency to resist being
accelerated.
• Weight is the gravitational
force exerted on an object by
a planet:
w = –mg
© 2015 Pearson Education, Inc.
Example: Apparent weight in an elevator
Anjay’s mass is 70 kg. He is standing on a scale in
an elevator that is moving at 5.0 m/s. As the
elevator stops, the scale reads 750 N. Before it
stopped, was the elevator moving up or down?
How long did the elevator take to come to rest?
The scale reading as the elevator comes to rest,
750 N, is Anjay’s apparent weight. Anjay’s actual
weight is
w = mg = (70 kg)(9.80 m/s2) = 686 N
© 2015 Pearson Education, Inc.
Example: Apparent weight in an elevator
(cont.)
• The vertical component of Newton’s second law
for Anjay’s motion is
• Fy = n  w = may
• n is the normal force, which is the scale force on
Anjay,
750 N. w is his weight, 686 N. We can thus solve
for ay:
© 2015 Pearson Education, Inc.
Example: Apparent weight in an elevator
(cont.)
The acceleration is positive and so is directed
upward, exactly as we assumed—a good check on
our work. The elevator is slowing down, but the
acceleration is directed upward. This means that
the elevator was moving downward, with a
negative velocity, before it stopped.
© 2015 Pearson Education, Inc.
Example: Apparent weight in an elevator
(cont.)
• To find the stopping time, we can use the
kinematic equation
(vy)f = (vy)i + ay Δt
• The elevator is initially moving downward, so
(vy)i =  5.0 m/s, and it then comes to a halt, so
(vy)f = 0. We know the acceleration, so the time
interval is
© 2015 Pearson Education, Inc.
• Couple of Thoughtful Force
Questions!!!!
© 2014 Pearson Education, Inc.
Question 1
• An object, when pushed with a net force F, has
an acceleration of 2 m/s2. Now twice the force is
applied to an object that has four times the
mass. Its acceleration will be
–
–
–
–
½ m/s2
1 m/s2
2 m/s2
4 m/s2
© 2015 Pearson Education, Inc.
Question 1
• An object, when pushed with a net force F, has
an acceleration of 2 m/s2. Now twice the force is
applied to an object that has four times the
mass. Its acceleration will be
–
–
–
–
½ m/s2
1 m/s2
2 m/s2
4 m/s2
© 2015 Pearson Education, Inc.
Question 2
• A 40-car train travels along a straight track at 40
mph. A skier speeds up as she skis downhill. On
which is the net force greater?
–
–
–
–
The train
The skier
The net force is the same on both.
There’s not enough information to tell.
© 2015 Pearson Education, Inc.
Question 2
• A 40-car train travels along a straight track at 40
mph. A skier speeds up as she skis downhill. On
which is the net force greater?
–
–
–
–
The train
The skier
The net force is the same on both.
There’s not enough information to tell.
© 2015 Pearson Education, Inc.
Question 3
• An object on a rope is lowered at constant
speed. Which is true?
– The rope tension is greater than the object’s
weight.
– The rope tension equals the object’s weight.
– The rope tension is less than the object’s
weight.
– The rope tension can’t be compared to the
object’s weight.
© 2015 Pearson Education, Inc.
Question 3
• An object on a rope is lowered at constant
speed. Which is true?
Constant velocity
Zero acceleration
– The rope tension is greater than the
object’s weight.
– The rope tension equals the object’s
weight.
– The rope tension is less than the object’s
weight.
– The rope tension can’t be compared to the
object’s weight.
© 2015 Pearson Education, Inc.
Question 4
• An object on a rope is lowered at a steadily
decreasing speed. Which is true?
– The rope tension is greater than the
object’s weight.
– The rope tension equals the object’s
weight.
– The rope tension is less than the object’s
weight.
– The rope tension can’t be compared to the
object’s weight.
© 2015 Pearson Education, Inc.
Question 4
• An object on a rope is lowered at a steadily
decreasing speed. Which is true?
Decreasing downward velocity
Acceleration vector points up
points up
– The rope tension is greater than the
object’s weight.
– The rope tension equals the object’s
weight.
– The rope tension is less than the object’s
weight.
– The rope tension can’t be compared to the
object’s weight.
© 2015 Pearson Education, Inc.
Question 5
• A 4.0 kg object is pulled along a frictionless
surface to the right by a 6.0 N force. How long
does it take the object to travel a distance of
25.0 m assuming the object starts at rest?
Solution To Question 5
• Use F=ma to find acceleration.
• 6 Newtons = a*4kg or 1.5 m/s2
then use the acceleration in the equation
1
x= 𝑎𝑡 2 and solve for time.
2
25 =
1
(1.5 𝑥 𝑡 2 )
2
Question 7
An 85.0 kg person stands on a scale that reads weight in Newtons
while standing in an elevator. What is the reading on the scale when
(a) The elevator is stopped?
(b) The elevator is accelerating
upward at 3.5 m/s2?
Question 7
• Normal Up is larger than the
weight down. Hence the
scale reading would be
Greater than if it was not
accelerating at all.
Answer for part b is
1130.5 newton's
Question 9
• An 85.0 kg person stands on a scale that reads
weight in Newtons while standing in an elevator.
What is the reading on the scale when the
elevator is moving upward at a constant speed
of 5.0 m/s?
Summary
© 2014 Pearson Education, Inc.
Summary
© 2014 Pearson Education, Inc.
Summary
© 2014 Pearson Education, Inc.
Summary
© 2014 Pearson Education, Inc.