Chapter 4

Chapter 4Chapter 4

Forces and MassForces and Mass

Classical MechanicsClassical Mechanics

Conditions when Classical Mechanics Conditions when Classical Mechanics does not applydoes not apply very tiny objects (< atomic sizes)very tiny objects (< atomic sizes) objects moving near the speed of objects moving near the speed of

lightlight

Newton’s First LawNewton’s First Law

If the net force If the net force F exerted on an F exerted on an object is zerok the object continues object is zerok the object continues in its original state of motion. That in its original state of motion. That is, if is, if F = 0, an object at rest F = 0, an object at rest remains at rest and an object remains at rest and an object moving with some velocity moving with some velocity continues with the same velocity.continues with the same velocity. Contrast with Aristotle!Contrast with Aristotle!

ForcesForces

Usually think of a force as a push Usually think of a force as a push or pullor pull

Vector quantityVector quantity May be contact or field forceMay be contact or field force

Contact and Field ForcesContact and Field Forces

Fundamental ForcesFundamental Forces

TypesTypes Strong nuclear forceStrong nuclear force Electromagnetic forceElectromagnetic force Weak nuclear forceWeak nuclear force GravityGravity

CharacteristicsCharacteristics All field forcesAll field forces Listed in order of decreasing strengthListed in order of decreasing strength Only gravity and electromagnetic in mechanicsOnly gravity and electromagnetic in mechanics

Fundamental ForcesFundamental Forces

TypesTypes Strong nuclear forceStrong nuclear force Electromagnetic forceElectromagnetic force Weak nuclear forceWeak nuclear force GravityGravity

CharacteristicsCharacteristics All field forcesAll field forces Listed in order of decreasing strengthListed in order of decreasing strength Only gravity and electromagnetic in mechanicsOnly gravity and electromagnetic in mechanics

Strong Nuclear ForceStrong Nuclear Force

QCD (Quantum chromodynamics) QCD (Quantum chromodynamics) confines quarks to interior of confines quarks to interior of protons and neutronsprotons and neutrons

Force between protons and Force between protons and neutrons responsible for formation neutrons responsible for formation of nucleiof nuclei

QCD: Exchange of gluonsQCD: Exchange of gluons Nuclear Force: Exchange of pionsNuclear Force: Exchange of pions

Electromagnetic ForceElectromagnetic Force

Opposites attract, like-signs repelOpposites attract, like-signs repel Electric force responsible for Electric force responsible for

binding of electrons to atoms and binding of electrons to atoms and atoms to each otheratoms to each other

Magnetic forces arise from moving Magnetic forces arise from moving charges and currentscharges and currents

Electric motors exploit magnetic Electric motors exploit magnetic forcesforces

Electromagnetic ForceElectromagnetic Force

Opposites attract, like-signs repelOpposites attract, like-signs repel Electric force responsible for Electric force responsible for

binding of electrons to atoms and binding of electrons to atoms and atoms to each otheratoms to each other

Magnetic forces arise from moving Magnetic forces arise from moving charges and currentscharges and currents

Electric motors exploit magnetic Electric motors exploit magnetic forcesforces

Weak Nuclear ForceWeak Nuclear Force

Involves exchange of heavy W or Z Involves exchange of heavy W or Z particleparticle

Responsible for decay of neutronsResponsible for decay of neutrons

GravityGravity

Attractive force between any two Attractive force between any two bodiesbodies

Proportional to both massesProportional to both masses Inversely proportional to square of Inversely proportional to square of

distancedistance

2

1 2

r

mmGF

InertiaInertia

Tendency of an object to continue Tendency of an object to continue in its original motionin its original motion

MassMass

A measure of the resistance of an A measure of the resistance of an object to changes in its motion due object to changes in its motion due to a forceto a force

Scalar quantityScalar quantity SI units are kgSI units are kg

Newton’s Second LawNewton’s Second Law

The acceleration of an object is The acceleration of an object is directly proportional to the net directly proportional to the net force acting on it and inversely force acting on it and inversely proportional to its mass.proportional to its mass.

F and a are both vectorsF and a are both vectors

Units of ForceUnits of Force

SI unit of force is a Newton (N)SI unit of force is a Newton (N)

US Customary unit of force is a US Customary unit of force is a pound (lb)pound (lb) 1 N = 0.225 lb1 N = 0.225 lb

See table 4.1See table 4.1

2s

mkg1N1

WeightWeight The magnitude of the gravitational The magnitude of the gravitational

force acting on an object of mass force acting on an object of mass mm near the Earth’s surface is called near the Earth’s surface is called the weight the weight ww of the object of the object

Weight and MassWeight and Mass

Mass is an inherent propertyMass is an inherent property Weight is Weight is notnot an inherent property an inherent property

of an object of an object Weight depends on locationWeight depends on location

Newton’s Third LawNewton’s Third Law

If two objects interact, the force FIf two objects interact, the force F1212 exerted by object 1 on object 2 is exerted by object 1 on object 2 is equal in magnitude but opposite in equal in magnitude but opposite in direction to the force Fdirection to the force F2121 exerted by exerted by object 2 on object 1.object 2 on object 1. Equivalent to saying a single isolated Equivalent to saying a single isolated

force cannot existforce cannot exist For every action there is an equal and For every action there is an equal and

opposite reactionopposite reaction

Newton’s Third Law cont.Newton’s Third Law cont.

FF1212 may be called may be called the the actionaction force force and Fand F2121 the the reactionreaction force force Either force can Either force can

be the action or be the action or the reaction forcethe reaction force

The action and The action and reaction forces reaction forces act on act on differentdifferent objectsobjects

Some Action-Reaction Some Action-Reaction PairsPairs

n and n’n and n’ n is the n is the normalnormal

force, the force the force, the force the table exerts on the table exerts on the TVTV

n is always n is always perpendicular to perpendicular to the surfacethe surface

n’ is the reaction – n’ is the reaction – the TV on the tablethe TV on the table

n = - n’n = - n’

More Action-Reaction More Action-Reaction pairspairs

FFgg and F and Fgg’’ FFgg is the force the is the force the

Earth exerts on Earth exerts on the objectthe object

FFgg’ is the force ’ is the force the object exerts the object exerts on the earthon the earth

FFgg = -F = -Fgg’’

Forces Acting on an Forces Acting on an ObjectObject

Newton’s Law uses Newton’s Law uses the forces acting the forces acting onon an object an object

n and Fn and Fgg are acting are acting on the objecton the object

n’ and Fn’ and Fgg’ are ’ are acting on other acting on other objectsobjects

Applying Newton’s LawsApplying Newton’s Laws

AssumptionsAssumptions Objects behave as particlesObjects behave as particles

ignore rotational motion (for now)ignore rotational motion (for now) Masses of strings or ropes are Masses of strings or ropes are

negligiblenegligible Interested only in the forces acting on Interested only in the forces acting on

the objectthe object neglect reaction forces neglect reaction forces

Problem Solving StrategyProblem Solving Strategy

Make a Make a free-bodyfree-body diagram diagram Identify Identify object (free body)object (free body) Label all forces acting on objectLabel all forces acting on object Resolve forces into x- and y-Resolve forces into x- and y-

components, using convenient components, using convenient coordinate systemcoordinate system

Apply equations, keep track of signs!Apply equations, keep track of signs!

Examples of Mechanical Examples of Mechanical ForcesForces

Strings, ropes and PulleysStrings, ropes and Pulleys GravityGravity Normal forcesNormal forces FrictionFriction Springs (later in the book)Springs (later in the book)

Some Rules for Ropes and Some Rules for Ropes and PulleysPulleys

When a rope is attached to an When a rope is attached to an object, the force of the rope on object, the force of the rope on that object is away from that that object is away from that objectobject

The magnitude of the force is The magnitude of the force is called the called the tensiontension

The tension does not change when The tension does not change when going over a pulley (if frictionless)going over a pulley (if frictionless)

EquilibriumEquilibrium

An object either at rest or moving An object either at rest or moving with a constant velocity is said to with a constant velocity is said to be in be in equilibriumequilibrium

The net force acting on the object The net force acting on the object is zerois zero

0F

Do Cable Pull DemoDo Cable Pull Demo

ExampleExample

Given that Mlight = 25 kg, find all three tensions

T3 = 245.3, T1 = 147.6 kg, T2 = 195.9 kg

ExampleExample

a) Find accelerationb) Find Tc) Find T3d) Find force ceiling must exert on pulley

a) a=g/6, b) T = 57.2 Nc) T3=24.5 N, d) Fpulley=2T = 114.5 N

Inclined PlanesInclined Planes Choose x along the Choose x along the

incline and y incline and y perpendicular to perpendicular to inclineincline

Replace force of Replace force of gravity with its gravity with its componentscomponents

cos

sin

mgF

mgF

y

x

ExampleExample

Find the acceleration and the tension

a = 4.43 m/s2, T= 53.7 N

Forces of FrictionForces of Friction

ResistiveResistive force between object force between object and neighbors or the mediumand neighbors or the medium

Examples:Examples: Sliding a boxSliding a box Air resistanceAir resistance Rolling resistanceRolling resistance

Sliding Sliding FrictionFriction

Proportional to the Proportional to the normal forcenormal force

Direction is Direction is parallel to surface parallel to surface and opposite other and opposite other forcesforces

Force of friction is nearly independent of the Force of friction is nearly independent of the area of contactarea of contact

The coefficient of friction (µ) depends on the The coefficient of friction (µ) depends on the surfaces in contactsurfaces in contact

Coefficients of Coefficients of FrictionFriction

ks

nf

Static Friction, ƒStatic Friction, ƒss

ss is coefficient of is coefficient of static frictionstatic friction

nn is the normal force is the normal force

FfnF ss

,If

f

F

Kinetic Kinetic Friction, ƒFriction, ƒkk

kk is coefficient of is coefficient of kinetic frictionkinetic friction

Friction force opposes FFriction force opposes F nn is the normal force is the normal force

nf

nF

k

s

,If

F

f

ExampleExample

The man pushes/pulls with a force of 200 N. Thechild and sled combo has a mass of 30 kg and the coefficient of kinetic friction is 0.15. For each case:What is the frictional force opposing his efforts?What is the acceleration of the child?f=59 N, a=4.7 m/s2 / f=29.1 N, a=5.7 m/s2

ExampleExample

Given m1 = 10 kg and m2 = 5 kg:

a) What value of s would stop the block from sliding?b) If the box is sliding and k = 0.2, what is the acceleration?c) What is the tension of the rope?

s = 0.5, a=1.96 m/s2

ExampleExample

What is the minimum s required to prevent the sled from slipping down a hill of slope 30 degrees?

s = 0.577

ExampleExampleYou are calibrating an accelerometer so that you can measure the steady horizontal acceleration of a car by measuring the angle a ball swings backwards.If M = 2.5 kg and the acceleration, a = 3.0 m/s2:a) At what angle does the ball swing backwards?b) What is the tension in the string?

=17 degT= 25.6 N

Quiz, All SectionsQuiz, All Sections1) What is your section number?

Quiz, Section 1Quiz, Section 1

a)a) A onlyA only

b)b) A and B onlyA and B only

c)c) A, B and C onlyA, B and C only

d)d) All statementsAll statements

e)e) None of the statementsNone of the statements

2) Which statements are correct?Assume the objects are static.

A) T1 must = T2

B) T2 must = T3

C) T1 must be < MgD) T1+T2 must be > Mg

cos(10o)=0.985 sin(10o)=0.173


a)a) A onlyA only






A) T1 must = T2

B) T2 must = T3


cos(10o)=0.985 sin(10o)=0.173


a)a) A onlyA only






A) T1 must = T2

B) T2 must = T3


cos(10o)=0.985 sin(10o)=0.173

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Chapter 4