The Laws of The Laws of MotionMotion

Classical MechanicsClassical Mechanics

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

Conditions when Classical Conditions when Classical Mechanics does not applyMechanics does 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 Usually think of a force as a push or pullor pull

Result of Result of interactioninteraction between two between two objectsobjects An object doesn’t possess a forceAn object doesn’t possess a force

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

Contact and Field ForcesContact and Field Forces

Newton’s First LawNewton’s First Law If no forces act on an If no forces act on an

object, it continues object, it continues in its original state of in its original state of motion; that is, motion; that is, unless something unless something exerts an external exerts an external force on it, an object force on it, an object at rest remains at at rest remains at rest and an object rest and an object moving with some moving with some velocity continues velocity continues with that same with that same velocity.velocity.

Newton’s First Law, cont.Newton’s First Law, cont.

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

Alternative statement of Newton’s Alternative statement of Newton’s First LawFirst Law When there are no external forces When there are no external forces

acting on an object, the acceleration of acting on an object, the acceleration of the object is zero.the object is zero.

InertiaInertia

Is the tendency of an object to Is the tendency of an object to continue in its original motioncontinue in its original motion

Is the resistance to the change in the Is the resistance to the change in the state of motionstate of motion The more sudden is the change, the more The more sudden is the change, the more

revealing is the inertiarevealing is the inertia

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

SI unit of force is a Newton (N)SI unit of force is a Newton (N) 2s

mkg1N1

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 exerted by object 2 on object 1.by object 2 on object 1. Equivalent to saying a single isolated Equivalent to saying a single isolated

force cannot existforce cannot exist

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 Actually, either Actually, either

force can be the force can be the action or the action or the reaction forcereaction 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 pairsMore Action-Reaction pairs

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 ObjectForces Acting on an Object

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

Free Body DiagramFree Body Diagram

Must identify all the forces acting Must identify all the forces acting onon the object of interest the object of interest

Choose an appropriate coordinate Choose an appropriate coordinate systemsystem

If the free body diagram is If the free body diagram is incorrect, the solution will likely be incorrect, the solution will likely be incorrectincorrect

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 equilibrium:equilibrium: Static equilibriumStatic equilibrium Dynamic equilibriumDynamic equilibrium

The net force acting on the object The net force acting on the object is zerois zero 0F

Equilibrium cont.Equilibrium cont.

Easier to work with the equation in Easier to work with the equation in terms of its components:terms of its components:

0Fx 0Fy

Solving Equilibrium Solving Equilibrium ProblemsProblems

Make a sketch of the situation described Make a sketch of the situation described in the problemin the problem

Draw a free body diagram for the Draw a free body diagram for the isolated object under consideration and isolated object under consideration and label all the forces acting on itlabel all the forces acting on it

Resolve the forces into x- and y-Resolve the forces into x- and y-components, using a convenient components, using a convenient coordinate systemcoordinate system

Apply equations, keeping track of signsApply equations, keeping track of signs Solve the resulting equationsSolve the resulting equations

Equilibrium Example – Equilibrium Example – Free Body DiagramsFree Body Diagrams

Newton’s Second Law Newton’s Second Law ProblemsProblems

Similar to equilibrium exceptSimilar to equilibrium except

Use componentsUse components

aaxx or a or ayy may be zero may be zero

maF

xx maF yy maF

Solving Newton’s Second Solving Newton’s Second LawLawProblemsProblems

Make a sketch of the situation described Make a sketch of the situation described in the problemin the problem

Draw a free body diagram for the Draw a free body diagram for the isolated object under consideration and isolated object under consideration and label all the forces acting on itlabel all the forces acting on it If more than one object is present, draw free body If more than one object is present, draw free body

diagram for each objectdiagram for each object

Resolve the forces into x- and y-Resolve the forces into x- and y-components, using a convenient components, using a convenient coordinate systemcoordinate system

Apply equations, keeping track of signsApply equations, keeping track of signs Solve the resulting equationsSolve the resulting equations

Inclined PlanesInclined Planes

Choose the Choose the coordinate system coordinate system with x along the with x along the incline and y incline and y perpendicular to perpendicular to the inclinethe incline

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

Forces of FrictionForces of Friction When an object is in motion on a surface or When an object is in motion on a surface or

through a viscous medium, there will be a through a viscous medium, there will be a resistance to the motionresistance to the motion This is due to the interactions between the This is due to the interactions between the

object and its environmentobject and its environment They are electromagnetic in originThey are electromagnetic in origin

This is resistance is called the This is resistance is called the force of frictionforce of friction Two types of friction forces:Two types of friction forces:

StaticStatic KineticKinetic

The direction of the frictional force is The direction of the frictional force is opposite the direction of motionopposite the direction of motion

More About FrictionMore About Friction

Static friction:Static friction: Arises when there is just a tendency for Arises when there is just a tendency for

motion: motion: The force of static friction is generally The force of static friction is generally

greater than the force of kinetic frictiongreater than the force of kinetic friction The coefficient of friction (µ) depends on The coefficient of friction (µ) depends on

the surfaces in contactthe surfaces in contact The coefficients of friction are nearly The coefficients of friction are nearly

independent of the area of contactindependent of the area of contact

Static Friction, ƒStatic Friction, ƒss

Arises when there is just a Arises when there is just a tendency for motion: to tendency for motion: to keep the object from keep the object from movingmoving

If F increases, so does ƒIf F increases, so does ƒss If F decreases, so does ƒIf F decreases, so does ƒss cannot exceed a maximum cannot exceed a maximum

value. When this max is value. When this max is reached , the frictional reached , the frictional force will no longer keep force will no longer keep the object in equilibrium the object in equilibrium and the object will moveand the object will move The frictional force becomes The frictional force becomes

kinetic friction forcekinetic friction force

Kinetic FrictionKinetic Friction

The force of kinetic The force of kinetic friction acts when friction acts when the object is in the object is in motionmotion

The force of kinetic The force of kinetic friction is always friction is always less than the less than the maximum value of maximum value of static frictionstatic friction

Connected ObjectsConnected Objects

Apply Newton’s Laws Apply Newton’s Laws separately to each separately to each object object

The acceleration of The acceleration of both objects will be both objects will be the samethe same

The tension is the The tension is the same in each same in each diagramdiagram

Solve the Solve the simultaneous simultaneous equationsequations

More About Connected More About Connected ObjectsObjects

Treating the system as one object Treating the system as one object allows an alternative method or a allows an alternative method or a checkcheck Use only external forcesUse only external forces

Not the tension – it’s internalNot the tension – it’s internal The mass is the mass of the systemThe mass is the mass of the system

Doesn’t tell you anything about Doesn’t tell you anything about any internal forcesany internal forces