lesson 5 (forces and netwons laws)

7/27/2019 Lesson 5 (Forces and Netwons Laws)

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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.

lesson 5 (forces and netwons laws)

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