Newton’s Laws

Newton’s Laws

Three Laws of MotionThree Laws of Motion

Aristotle’s Motion Natural Motion is up or downNatural Motion is up or down

Down for falling objectsDown for falling objects Up for smokeUp for smoke Circular for heavenly bodies since without Circular for heavenly bodies since without

endend Violent Motion Violent Motion

Due to imposed forces such as wind Due to imposed forces such as wind pushing a ship or someone pulling a cartpushing a ship or someone pulling a cart

Natural state of motion is restNatural state of motion is rest A force is needed to keep something movingA force is needed to keep something moving

Aristotle’s Basic Error

Friction not understood as a forceFriction not understood as a force

Galileo’s Motion

Force is a push or a pullForce is a push or a pull Friction is a force that Friction is a force that

occurs when objects occurs when objects move past each othermove past each other

Friction due to tiny Friction due to tiny irregularitiesirregularities

OnlyOnly when friction is when friction is present is a force present is a force required to keep required to keep something movingsomething moving

Galileo’s Inclined Planes

Ball rolling downhill Ball rolling downhill speeds upspeeds up

Ball rolling uphill Ball rolling uphill slows downslows down

He asked about ball He asked about ball on smooth level on smooth level surfacesurface

Concluded it would Concluded it would roll forever in roll forever in absence of frictionabsence of friction

Inertia

Resistance to change in state of motionResistance to change in state of motion Resistance to Resistance to AccelerationAcceleration Galileo concluded all objects have Galileo concluded all objects have

inertiainertia Contradicted Aristotle’s theory of motionContradicted Aristotle’s theory of motion No force required to keep Earth in No force required to keep Earth in

motion around sun because no frictionmotion around sun because no friction

Newton

Born 1665Born 1665 Built on Galileo’s Built on Galileo’s

ideasideas Proposed three laws Proposed three laws

of motion at age of of motion at age of 2323

Newton’s First Law

Every object continues in its state of rest, or Every object continues in its state of rest, or of motion in a straight line at constant speed, of motion in a straight line at constant speed, unless compelled to change that state by unless compelled to change that state by forces exerted on it.forces exerted on it.

Also called Law of Inertia: things move Also called Law of Inertia: things move according to their own inertiaaccording to their own inertia

Things keep on doing what they are doingThings keep on doing what they are doing Examples: Hockey puck on ice, rolling ball, Examples: Hockey puck on ice, rolling ball,

ball in spaceball in space

Ourtesy www.lakeheadu.ca/~alumni/ hockey.gif

Mass

Amount of inertia depends on amount of Amount of inertia depends on amount of mass…or amount of material (number mass…or amount of material (number and kind of atoms)and kind of atoms)

Measured in kilogramsMeasured in kilograms Question: Which has more mass, a Question: Which has more mass, a

kilogram of lead or a kilogram of kilogram of lead or a kilogram of feathers?feathers?

Mass vs. Volume: volume is how much Mass vs. Volume: volume is how much space something occupiesspace something occupies

Experiencing Inertia

Inertia is resistance to shakingInertia is resistance to shaking Which is easier to shake, a pen or a Which is easier to shake, a pen or a

person?person? Why is it so hard to stop a heavy boat?Why is it so hard to stop a heavy boat?

Mass vs. Weight

Mass is intrinsic property of any objectMass is intrinsic property of any object Weight measures gravitational force on Weight measures gravitational force on

an object, usually due to a planetan object, usually due to a planet Weight depends on location of objectWeight depends on location of object Question 1: How does mass of a rock Question 1: How does mass of a rock

compare when on Earth and on moon?compare when on Earth and on moon? Question 2: How does its weight Question 2: How does its weight

compare?compare?

Review Mass vs. Weight

What is mass?What is mass? Answer: quantity of Answer: quantity of

matter in something matter in something or a measure of its or a measure of its inertiainertia

What is weight?What is weight? Answer: Force on a Answer: Force on a

body due to gravitybody due to gravity

Weight of 1 Kilogram

9.8 Newtons9.8 Newtons About 2.2 poundsAbout 2.2 pounds Compare the weight of 1 kg nails with 1 Compare the weight of 1 kg nails with 1

kg styrofoamkg styrofoam Answer: SameAnswer: Same

Weight Examples

What does a 70 kg person weigh?What does a 70 kg person weigh?

W = mg = 70 kg x 9.80 N/mW = mg = 70 kg x 9.80 N/m2 =2 = 686 N 686 N An object weighs 9800 n on Earth. What An object weighs 9800 n on Earth. What

is its mass?is its mass? m = W/g = 9800 / 9.8 m/sm = W/g = 9800 / 9.8 m/s2 2 == 1000 kg1000 kg

W = mgW = mg

Inertia in a Car Discuss three examples of inertia in Discuss three examples of inertia in

a cara car

•Car hitting a wall

•Car hit from behind by a truck

•Car going around a corner

Newton’s Second Law

Law of AccelerationLaw of Acceleration The acceleration produced by a net force on The acceleration produced by a net force on

an object is directly proportional to the an object is directly proportional to the magnitude of the net force, and is inversely magnitude of the net force, and is inversely proportional to the mass of the body.proportional to the mass of the body.

Acceleration = net force Acceleration = net force ÷mass÷mass

F =maF =ma Acceleration is Acceleration is in direction of net forcein direction of net force

Net Force

Net Force means sum of all forces Net Force means sum of all forces actingacting

Sum is Vector sumSum is Vector sum

F1

F2

Resultant force

Understanding the Second Law The cause of acceleration is…The cause of acceleration is… _________ resists acceleration_________ resists acceleration The greater the force, the ________ theThe greater the force, the ________ the

__________ __________ The greater the mass, the _________ The greater the mass, the _________

the acceleration.the acceleration.

Force

Mass

accelerationless

greater

What Resists Acceleration of Student in Chair? InertiaInertia Friction forceFriction force

These are two completely different These are two completely different thingsthings

Units

F = maF = ma Unit of force is the Newton (N)Unit of force is the Newton (N) 1 N = 1 kg m/s1 N = 1 kg m/s22

F = ma is Three Equations

F F andand a a are vectorsare vectors So So FF = m = maa equation is really three equation is really three

FFxx = ma = max x FFyy = ma = may y FFzz = ma = mazz

Examples

What force is required to accelerate a What force is required to accelerate a 1000 kg car at 2.0 m/s1000 kg car at 2.0 m/s2 2 ??

Answer: F = ma = 1000 kg x 2.0 m/sAnswer: F = ma = 1000 kg x 2.0 m/s2 2 = = 2000 N.2000 N.

What is the acceleration of a 145 g What is the acceleration of a 145 g baseball thrown with a force of 20.0 N?baseball thrown with a force of 20.0 N?

a = F/m = 20N/0.145kg = 138 m/sa = F/m = 20N/0.145kg = 138 m/s22

Newton’s Third Law

Forces always come in pairsForces always come in pairs Two forces on different objectsTwo forces on different objects Whenever one object exerts a force on Whenever one object exerts a force on

a second object, the second exerts an a second object, the second exerts an equal and opposite force on the firstequal and opposite force on the first

Example: hammer hits nailExample: hammer hits nail

Example: pushing on wall

What are the forces when you push on What are the forces when you push on a wall?a wall?

You exert force on wallYou exert force on wall You accelerate in the opposite directionYou accelerate in the opposite direction Wall must have exerted a force on you Wall must have exerted a force on you

in the direction you accelerated (by 2in the direction you accelerated (by 2ndnd Law)Law)

Example: person walking

Foot exerts force Foot exerts force backward on groundbackward on ground

Ground exerts force Ground exerts force forward on footforward on foot

Example: Throwing ball

Pitcher exerts force Pitcher exerts force on ballon ball

Ball exerts equal Ball exerts equal and opposite force and opposite force on pitcheron pitcher

Why doesn’t pitcher Why doesn’t pitcher move?move?

Example: Rocket

Rocket engine Rocket engine exerts rearward exerts rearward force on gas force on gas moleculesmolecules

Molecules exert Molecules exert forward force on forward force on rocket.rocket.

Horse and Cart

Horse exerts force Horse exerts force on carton cart

Cart exerts equal Cart exerts equal and opposite force and opposite force on horseon horse

Net force = zeroNet force = zero Cart can’t moveCart can’t move Huh?Huh?

The net force is NOT zero. Forces on different objects cannot be added to make zero

Book on Table

The mass of the book is one kg. What The mass of the book is one kg. What is the force (magnitude and direction) is the force (magnitude and direction) onon the book exerted by table? the book exerted by table?

9.8 N upward9.8 N upward

More Examples

Can you think of some more examples Can you think of some more examples of Newton’s Third Law in Action?of Newton’s Third Law in Action?

Review: Newton’s Laws of Motion Newton’s First Law:Newton’s First Law: Every object continues in its state of rest, or of motion Every object continues in its state of rest, or of motion

in a straight line at constant speed, unless compelled to in a straight line at constant speed, unless compelled to change that state by forces exerted on it.change that state by forces exerted on it.

Newton’s Second Law:Newton’s Second Law: The acceleration produced by a net force on an object The acceleration produced by a net force on an object

is directly proportional to the magnitude of the net force, is directly proportional to the magnitude of the net force, and is inversely proportional to the mass of the body.and is inversely proportional to the mass of the body.

Newton’s Third Law:Newton’s Third Law: Whenever one object exerts a force on a second Whenever one object exerts a force on a second

object, the second exerts an equal and opposite force object, the second exerts an equal and opposite force on the firston the first

Concept Check 1

Which of these statements about an object Which of these statements about an object in free fall is false?in free fall is false? (a) It accelerates(a) It accelerates (b) It is in equilibrium(b) It is in equilibrium (c) It exerts an upward force on the Earth(c) It exerts an upward force on the Earth (d) It’s mass equals the net force on it (d) It’s mass equals the net force on it

divided by its accelerationdivided by its acceleration (e) Only one force acts on it(e) Only one force acts on it

Derivation of acceleration of block sliding down a plane with friction