Chapter 3Chapter 3

Newton’s LawsNewton’s Laws

Classical MechanicsClassical Mechanics

Describes the relationship between Describes the relationship between the motion of objects in our everyday the motion of objects in our everyday world and the forces acting on themworld and the forces acting on them

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 lightobjects moving near the speed of light

ForcesForces

Usually think of a force as a push or pullUsually think of a force as a push or pull Vector quantityVector quantity May be a May be a contact forcecontact force or a or a field forcefield force

• Contact forces result from physical contact Contact forces result from physical contact between two objects: pushing, pullingbetween two objects: pushing, pulling

• Field forces act between disconnected objectsField forces act between disconnected objects Also called “action at a distance”Also called “action at a distance” Gravitational force: weight of objectGravitational force: weight of object

Contact and Field ForcesContact and Field Forces

Force as vectorForce as vector

Magnitude + DirectionMagnitude + Direction Components FComponents Fx, x, FFyy

Units: Newton (N), pound(lb)Units: Newton (N), pound(lb) 1lb=4.45N1lb=4.45N

F

sin

cos

FF

FF

y

x

22

tan

yx

x

y

FFF

F

F

Addition of ForcesAddition of Forces

Graphical methodGraphical method

Components methodComponents method

Newton’s First LawNewton’s First Law

An object moves with a velocity that An object moves with a velocity that is constant in magnitude and is constant in magnitude and direction, unless acted on by a direction, unless acted on by a nonzero net forcenonzero net force• The net force is defined as the vector The net force is defined as the vector

sum of all the external forces exerted on sum of all the external forces exerted on the objectthe object

External and Internal ForcesExternal and Internal Forces

External forceExternal force• Any force that results from the Any force that results from the

interaction between the object and its interaction between the object and its environmentenvironment

Internal forcesInternal forces• Forces that originate within the object Forces that originate within the object

itselfitself• They cannot change the object’s They cannot change the object’s

velocityvelocity

InertiaInertia

Is the property of a material to resist Is the property of a material to resist changes in motion.changes in motion.• Is the tendency of an object to continue Is the 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: kgSI units: kg

Condition for EquilibriumCondition for Equilibrium

Net force vanishesNet force vanishes No motionNo motion

0...321 FFFF

0...321 xxxx FFFF

0...321 yyyy FFFF

Newton’s Second LawNewton’s Second Law

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

• F and a are both vectorsF and a are both vectors

amF

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

2s

mkg1N1

Sir Isaac NewtonSir Isaac Newton

1642 – 17271642 – 1727 Formulated basic Formulated basic

concepts and laws concepts and laws of mechanicsof mechanics

Universal Universal GravitationGravitation

CalculusCalculus Light and opticsLight and optics

Newton’s Third LawNewton’s Third Law

If object If object 11 and object and object 22 interact, the interact, the force exerted by object force exerted by object 11 on object on object 22 is equal in magnitude but opposite in is equal in magnitude but opposite in direction to the force exerted by direction to the force exerted by object object 22 on object on object 11..•

• Equivalent to saying a single isolated Equivalent to saying a single isolated force cannot existforce cannot exist

12 21F F

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

FF1212 may be called the may be called the actionaction force and F force and F2121 the the reactionreaction force force• Actually, either force Actually, either force

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

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

Weight vs MassWeight vs Mass

Weight is not mass but they are relatedWeight is not mass but they are related Weight is a forceWeight is a force Consider a Falling objectConsider a Falling object

Weight w=mgWeight w=mg Object on a table?Object on a table?

mgFmaF

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 the near the Earth’s surface is called the weight weight ww of the object of the object• w = m gw = m g is a special case of Newton’s is a special case of Newton’s

Second LawSecond Law gg is the acceleration due to gravity is the acceleration due to gravity

g g can also be found from the Law of can also be found from the Law of Universal GravitationUniversal Gravitation

More about weightMore about weight

Weight is Weight is notnot an inherent property of an inherent property of an object an object • mass mass isis an inherent property an inherent property

Weight depends upon locationWeight depends upon location

Using Second LawUsing Second Law

F=maF=ma Net ForceNet Force

...321 FFFFF

xxxxx maFFFF ...321

yyyyy maFFFF ...321

MethodMethod

Isolate object of interestIsolate object of interest Draw picture, show all forcesDraw picture, show all forces Decide if the object is acceleratingDecide if the object is accelerating Choose appropriate coordinate Choose appropriate coordinate

systemsystem find force componentsfind force components Use F=maUse F=ma

Example (prob. 23)Example (prob. 23)

1200 kg car going 20 m/s collides head 1200 kg car going 20 m/s collides head on with a tree and stops in 2.0m. on with a tree and stops in 2.0m. • What is the average stopping force?What is the average stopping force?

Example (Atwood’s Machine)Example (Atwood’s Machine)

Two masses, 2.0 kg and 2.05 kg, …Two masses, 2.0 kg and 2.05 kg, …

0.5 m above ground.0.5 m above ground.

Find acceleration and the time the Find acceleration and the time the 2.05 kg mass takes to reach the 2.05 kg mass takes to reach the ground.ground.

ExampleExample

Force of 10 N gives a mass Force of 10 N gives a mass acceleration of 1 m/s².acceleration of 1 m/s².• How large a force is needed to How large a force is needed to

accelerate to 0.25 m/s²?accelerate to 0.25 m/s²?• If the mass is increased by a factor of If the mass is increased by a factor of

two, how large of a force will give an two, how large of a force will give an acceleration of 2 m/s²?acceleration of 2 m/s²?

ExampleExample

Two masses mTwo masses m11 (5kg) and m (5kg) and m22 (10kg) (10kg) are connected by a rope on a table are connected by a rope on a table top. Friction forces on mtop. Friction forces on m11 and m and m22 are 15N and 30N respectively. A are 15N and 30N respectively. A pulling force P acts on mpulling force P acts on m22 at 45° at 45° above horizontal and accelerates above horizontal and accelerates the system with 0.2m/s² acc. the system with 0.2m/s² acc.

• Find tension in the ropeFind tension in the rope• Force PForce P

Newton’s law of GravitationNewton’s law of Gravitation

Mutual force of attraction between Mutual force of attraction between any two objectsany two objects

Expressed by Newton’s Law of Expressed by Newton’s Law of Universal Gravitation:Universal Gravitation:

221

g r

mmGF

Universal Gravitation, 2Universal Gravitation, 2

G is the constant of universal G is the constant of universal gravitationalgravitational

G = 6.673 x 10G = 6.673 x 10-11-11 N m² /kg² N m² /kg² This is an example of an This is an example of an inverse inverse

square lawsquare law

Universal Gravitation, 3Universal Gravitation, 3

The gravitational force exerted by a The gravitational force exerted by a uniform sphere on a particle outside uniform sphere on a particle outside the sphere is the same as the force the sphere is the same as the force exerted if the entire mass of the exerted if the entire mass of the sphere were concentrated on its sphere were concentrated on its centercenter• This is called Gauss’ LawThis is called Gauss’ Law

Gravitation ConstantGravitation Constant

Determined Determined experimentallyexperimentally

Henry CavendishHenry Cavendish• 17981798

The light beam and The light beam and mirror serve to mirror serve to amplify the motionamplify the motion

Applications of Universal Applications of Universal GravitationGravitation

Weighing the EarthWeighing the Earth

G

gRm

R

mGg

R

mmGmg

R

mmGFw

EE

E

E

E

E

E

Eg

2

2

2

2

kg 106

6380

/ 8.9 take

24

2

E

E

m

kmR

smg

Applications of Universal Applications of Universal GravitationGravitation

Acceleration due to Acceleration due to gravitygravity

g will vary with g will vary with altitudealtitude

2E

r

MGg

Apparent WeightApparent Weight

The weight of The weight of object in an object in an accelerating frame.accelerating frame.

Consider inside a Consider inside a elevatorelevator

Why do we need 1Why do we need 1stst law?law?

ExampleExample

An object weighing 500 N is uniformly An object weighing 500 N is uniformly accelerated upward during a short accelerated upward during a short elevator ride. If the object’s apparent elevator ride. If the object’s apparent weight was 625 N during the trip, weight was 625 N during the trip, how long did the ride take to move how long did the ride take to move 40 m upward?40 m upward?