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Newtons Laws Of Motion
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Objectives
Be able to state, in words, Newtons three laws of motion
Understand the difference between massand weight Be able to define the termforce
Be able to state what is meant by the termfree-body diagram(FBD).
Be able to construct FBDs and use them to aid in solving
problems Be able to apply Newtons Laws of Motion in a systematic wayto solve problems.
Be able to state what is meant by the term Normal Force, andincorporate this definition in solving problems.
By the end of this lesson you should
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A Shift In Focus
Up to this point in the term, we have analyzedmotion (DESCRIBED) without worrying aboutwhat was causing the motion to occur. We said
that such a study of motion was referred to askinematics.
We now concern ourselves with whythe objectis accelerating (or not). In other words, we look
for the causeof the motion. This type of a studyof motion where the cause of motion isconsidered is called dynamics.
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Introduction
Central to this discussion are a set of laws
called Newtons Laws of Motion. This set of
laws is considered to be of fundamental
importance to the study of classical
mechanics. Once introduced, you should be
able to state these laws and apply them
correctly even if stirred from a deep, restfulsleep at 2 oclock in the morning!
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Introduction
In the slides that follow, there are words that are
highlightedin the statements of Newtons 3 Laws ofMotion. This highlightingis to indicate that these
words are critical to the statement of the law, and
you should keep them in mind when applying these
laws so that difficulties can be avoided.
We begin with Newtons first law of motion.
THE LAW OF INERTIA
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Newtons First Law Of Motion
An object in motion with a constant velocitywillremain in motion with that constant velocity
until the object is acted upon by a net,externalforce.
This law is also called the Law of Inertia.
Inertia: The property of an object to resist achange in velocity. Mass is a quantification ofthe inertia of a body.
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Inertia: Newtons First Law
By the end of this section you will understand the
following statement and its implications in physics:
An object in motion with constant velocity will continue
with the same constant velocity unless acted upon by anunbalanced outside force; and,
An object at rest will continue at rest unless acted upon
by an unbalanced outside force.
http://www.dynamicscience.com.au
/tester/solutions/flight/winterolymp
ics/curln.html
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Balanced Forces cause what?
The statement of this law raises a
question: What do you think will happen to
the motion of the object if there isan
unbalanced outside force?
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Balanced Forces Cause What?
Balanced forces cause an inertial
state of motion called
CONSTANT VELOCITY
UNBALANCED FORCES
CAUSE WHAT?
AN ACCELERATION!
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FBD.Free Body Diagrams
The forces acting on the object of interest
must be identified.
Then a special diagram called a free body
diagramcan be constructed. All static
and dynamics problems begin in thisfashion.
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Our Problem Solving Model
The first three steps in constructing a modelare:
1. Identify the object or system.2. Identify the forces acting on the object or
system.
3. Draw a force (or free-body) diagramassuming the object or system as a pointparticle.
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Approaching FBDs
One cardinal rule is that once you identify the object, it
cannot be changed unless you start all over with step
one again and go through all of the steps with the new
object.
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On the sketch, circle the object or
system with a dotted line.
In order to make a consciousdecision to choose the object orsystem, and to avoid changing itmidway through the activity, youwill need to draw a rough sketchof the important parts in thesituation being investigated.
This is the real- worldrepresentation. (At first, the
sketch will be provided for you,but later in the laboratory and inword problems you will need tocomplete the sketches on yourown.)
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Draw all of the forces on the tree in picture below.
Use an arrow () to represent each force and to
indicate the direction of each force. Identify
each force by what is causing it. Write thestatement, force caused by _frictional force,
etc________, next to each arrow. Put the tail
of the arrow at the place on the object where the
force is being applied.
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Identifying the Forces Acting on theObject
The basic definition
of a force is a push
or a pull. While
this definition is
correct, it does
little in helping to
identify thenecessary forces.
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What are the forces?
The forces that need to be identified are those forces
acting on the object or system.
Each of these forces has to be caused by an object
outside of the dotted line circle. It is important to
identify the agents outside the object or system that are
exerting forces on the system.
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Remember your units!
The metric unit for force is the Newton (N).
The English unit is the pound (lb).
Since the world is converting to metrics at a slow
but sure rate, we will only deal with Newtons.This is part of the Standard International
System of Units. (SI)
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Weight and Mass are not the same!!!
Mass is an inherent quantity that all objectshave. It is measured in kilograms (kg). Inthis lecture we only need to deal with the
weight vector. Weight (W) in N = mg = 9.8 m
Units m/s2(kg) = N
The direction of the gravitational force isalways toward the center of the Earth.
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Forces on the object caused by
something outside the object are the
only forces that are used.
Forces at a distance vs. Forces from contact
Weight --- DISTANCE
Normal--- CONTACT
Friction--- CONTACT
Tension--- CONTACT
Thrust --- CONTACT
Drag --- CONTACT
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Types of Forces
There are two categories of forces to
consider:
contact forces
forces at a distance.
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Forces at a Distance
They arise when the object is in
the field caused by another
object, but not in contact with
the object.
Examples of fields areelectrical, magnetic, and
gravitational fields. Since we are
only dealing with mechanics in
this module, the only force at a
distance we will deal with is thegravitational force.
Gravitational force is often
called weight.
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Put the tail of the arrow at the
center of the object. Label thisforce with the symbol Wand
the statement "force caused
by Earth."
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FBD Representations
On the sketch, represent the force by an
arrow. The tail of the arrow will be at the
place of contact and the tip will point in the
direction of the force. Label each forcewith an appropriate symbol and force
caused by ________.
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Contact Forces
The contact forces acting on the system of
interest are identified by going around the
dotted circle that defines that object or
system. There is the likelihood of a forceat any point where something outside the
dotted circle is touching something inside
the circle.
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Contact Forces
There are three contact forces that
deserve special attention.
These contact forces are tension, normal
force, andfriction.
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Tension
Tension forces are caused by ropes orcables. Tension can only be a pull.
Therefore, the direction is always
known. Tension is given the symbol T.
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Normal Force
Any time an object exerts a force on a surface, the surface
also exerts a force on the object. One common example iswhen the object rests on something that supports or helps to
support the object. This supporting force is called the
normal force. The direction of the normal force is always
perpendicular to the surface that is causing the force.
Normal force is given the symbol N.
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The last special contact force to be
discussed is surface friction. Friction
is designated by the lower case letter f.Surface friction occurs whenever two
surfaces rub together. It also can occur
when two surfaces are touching but notmoving with respect to each other.
This relationship bet een magnit de and the direction of
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This relationship between magnitude and the direction of
the force is true for any two surfaces of the same
material when rubbed together.
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Types of Friction
There are two types of friction. When one
surface slides on a second surface, it is
called kinetic friction. When one surface
triesto slide on a second surface but doesnot move, it is called static friction.
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Static Friction
When an object is at rest with respect to a surface,
the frictional force can be greater than when the
objects move across each other. In our model,
imagine that the bumps (or grooves) aredeeply interlaced.
If a small force is applied to the object, the static
friction fswill equal the applied force and cause
the object to remain in equilibrium (a = 0).
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Kinetic Friction
In our model, when the object moves, thegrooves of the object bounce along the
grooves of the surface, and never go as
deep as they do in the static case. Thus,
the kinetic friction force fkhas a smallermagnitude than the static friction force.
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Graph of Frictional Force vs.
Applied Force
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General Rules of Friction in theModel
1. The frictional force has a direction opposite to the force that is causing,or trying to cause, the object to slide. Friction is parallel to the surface;therefore, it opposes the sliding motion.
2. The force trying to cause the object to slide (F) must be greater than
fsmaxfor sliding to occur. When F is smaller than fsmax, the object will notslide.
3. Once the object starts to slide, the static friction (fs) becomes kineticfriction (fk). Kinetic friction is always smaller than maximum staticfriction.
4. Both static friction (fs) and kinetic friction (fk) are proportional to thenormal force.
5. The area of contact between the surfaces does not influence themagnitude of the frictional force.
The speed of the object (assuming a low speed) does not influence themagnitude of the kinetic friction.
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This is the big idea
Isolate the system
Figure out the forces
Label each force
Ask yourself this
question
Are the forces balanced?
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A soccer player starts running to
the right. On the sketch of theplayer, show the point of
application and direction of the
forces (W, N, fs) on the player.
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A car is at rest on a horizontal road.What is the value of the frictional force?
Explain your answer.
For the car in question, show the forces
on the car and the points of application.
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A woman pushes a
book (the object)
across a table to the
left. On the sketch
below, show the
point of applicationand the direction of
the four forces
(W, N, fk, F).
(F is the force of the
woman on the
book.)
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Make a real world to FBD
representation
Recall we are modeling the forces on an object.
We need to examine if the forces are balanced or
if there is a net force to determine the type of
motion present.
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Section Summary
What is inertia?
What is a net force?
What is equilibrium?
What is moving equilibrium?
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Newtons Second Law Of Motion
The acceleration of an object is directlyproportional to the unbalanced,externalforce
acting on the object and inversely proportional
to the mass of the object. The acceleration of theobject is in the same directionas the unbalanced,
external force.
Forces produce accelerations; accelerations donotproduce forces!
m
EXTNET,F
=a
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Newtons Second Law Of Motion
In the expression on the previous slide, m represents themass of the object experiencing the acceleration and Frepresents force.
Force: A push or a pull; any influence that causes anobject to change its velocity. The unit of force is the unitof mass times the unit of acceleration and is measured inNewtons. 1 Newton is the force required to give a 1.0 kgobject an acceleration of 1.0 m/s2.
Newtons Second Law is also referred to as the Law ofAcceleration.
N t Thi d L Of M ti
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Newtons Third Law Of Motion If an object A exerts a force on object B, then
object B exerts a force on A which is equal inmagnitude and opposite in direction.
It is important to remember that the forces inthe action-reaction pair mentioned act ondifferentobjects.
Newtons Third Law is also called the Law ofInteraction.
BAAB FF
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Newtons Third Law Of Motion
Newtons third law tells us that forces always
come in pairsand that the forces in each pair
are of equal magnitude, are opposite in
direction, and act on different objects. Youcan never have a single forcewithout a
counterpart somewhere in the universe.
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Forces come in
two types.
Contact forces
Field forces
How about forces in
Pairs!
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Newtons Third Law
There is one more important piece to thedynamic and static model. It is called NewtonsThird Law. Forces come in pairs. UnderstandNewtons Third law, we can ignore internalforces, and then only search for external forcesacting on the object.
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Push Me and I Push Back!!!
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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?
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The man weighs 700 N. The force
exerted by the table on the man is: a) Larger than 700 N
b) Equal to 700 N
c) Smaller than 700 N
d) There is no force.
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A hand pushes on a balloon against a wall with aforce of 10 N. The force exerted by the balloon on
the hand is:
a) Larger than 10 N
b)
Equal to 10 N c) Smaller than 10 N
d) There is no force.
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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 wreckingball?
Explain your answer.
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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 twoforce probes together and pull as seen in the
following figure.
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Newton's Third Law
Why does it seem that a bug hits a windshield
with more force than the windshield hits the
bug?
The effect on the bug is worse than the effecton the windshield but the force is still the
same!
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Forces come in pairs. But which
pair? Forces come in pairs
An example would bethe weight and normalforce pairs in the leftfigure.
Fg vs. Fg and Fn vs.Fn
The Weight of an
object and NormalForce are sometimesequal but they are notForce Pairs!!!
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Mass and Weight
For good reason, many people think of mass andweight as the same thing. It is difficult todistinguish between the two if your experience is
restricted to on location on the earth. Mass andweight, however, are not the same. Mass is thequantification of an object inertia. That is, massis a measure of an objects resistance to change instate of motion. Weight is a force. Weight is theforce of attraction toward the earth. Mass is ascalar; Weight (Force) is a vector.
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Virtual Field Trip!
Suppose we hopped a shuttle and went to a
remote area in space where there was nothing
around. Since we are in empty space, we wouldall be weightless. Even the 50 lb (weight on
earth) cannon ball I brought with us would be
weightless.
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Virtual Field Trip
Now, I am going to put the cannon ball into acannon and fire it at 100 mph. I would like avolunteer from the class to stand directly in front ofthe cannon and catch the (weightless) cannon ballfor me. What? No takers? And you are wise not tostand in front of the cannon. The cannon ball is
still going to resist a change in state of velocity justthe same as if it were on the earth. The cannon ballstill has inertia, or mass, even though it has noweight!
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Virtual Field Trip
I hope this example helps you to start to
see that there isa difference between mass
and weight. We will explore mass andweight in more detail as we go through this
and the next chapter.
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Foreshadowing We move from a virtual field trip to a thought
experiment in the next slide. I ask you to take some
time and think about the question posed as it is quite
complex. A class of 50 students will generally spend
between 5-10 minutes stating wrong answers to the
question before someone stumbles upon the correct
answer. It is important for you to go through the
same thinking process.
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Try It On Your Own
A person stands on a skateboard and pushesagainst the wall. The wall pushes back on theperson and the skateboard moves (accelerates).According to Newtons 3rd law, the force exertedby the person on the wall and the force exertedby the wall on the person add to zero. If these
two forces add to zero, why is it that theskateboard accelerates? (The correct answerdoes not involve the mass of the earth norfrictional forces.)
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Free Body Diagrams
A free body diagram (FBD) differs from your picture ofthe problem. In a FBD, you isolate the object that youare interested in by drawing it as a single point. Then,draw on this isolated object only those forces that actdirectlyonthe object. Do notinclude forces that theisolated object exerts. Also, include your sign conventionin the FBD.
A well drawn FBD is crucialto the successful solution ofa problem involving Newtons Laws of Motion.
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Free Body Diagrams
The reason that I had you go through theskateboard problem was to illustrate theimportance of the FBD. When you consider only
the forces acting directly on the skateboarder,the force provided by the wall is the onlyexternal force acting on the skateboarder. Sincethere is an unbalanced, external force acting on
the skateboarder, the skateboarder willaccelerate according to Newtons second law ofmotion.
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Example
A car is traveling at a constant velocity
straight ahead on a flat,frictionless road.Draw a free-body diagram for the car.
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Try It On Your Own
The driver in the car fires retro rockets so that
the car is deceleratingwhile traveling on a
straight, flat, and frictionless road. Describe
the free body diagram of the car.
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Normal Force
The last two situations had a force exerted by
a surface on an object. A surface will always
push on an object in a direction that is
perpendicular, ornormal, to the surface. Sucha force exerted by a surface is called a normal
force.
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Example
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?
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Solution To Example
Use F=ma to find acceleration.
6 Newtons = a*4kg or 1.5 m/s2
then use the acceleration in the equation
x=1/2*a8 t^2 and solve for time.25 = .5*1.5*t^2.
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Try It On Your Own
A 4.0 kg object is pulled along a frictionless
surface to the right by a 6.0 N force, directed
30above the horizontal. How long does it
take the object to travel a distance of 25.0 massuming the object starts at rest?
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Example
An 85.0 kg person stands on a scale that reads weight in Newtons whilestanding 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?
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Solution
Normal Up is larger than theweight down. Hence the
scale reading would be
Greater than if it was notaccelerating at all.
Answer for part b is1130.5 newton's
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Try It On Your Own
An 85.0 kg person stands on a scale that readsweight in Newtons while standing in an
elevator. What is the reading on the scale
when the elevator is moving upward at aconstant speed of 5.0 m/s?
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Summary
A correctly drawn free body diagram is essential tosolve problems involving Newtons Laws of Motion.
Newtons Laws of Motion are useful in a wide variety
of situations ranging from the motion of a baseballwhen struck by a bat to the motion of the planets in
the solar system. This wide range of applicability is
why Newtons Laws are so highly regarded.