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Physical SciencePhysical Science

Force and MomentumForce and Momentum

Slides subject to changeSlides subject to change

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Issac Newton

Isaac Newton last words:"I don't know what I may seem to the world. But as to myself I seem to have been only like a boy playing on the seashore and diverting myself now and then finding a smoother pebble or a prettier shell than the ordinary, whilst the great ocean of truth lay all undiscovered before me.

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ForceForce

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Net ForceNet Force

A A net external forcenet external force on an object is on an object is required to move the object.required to move the object.

Motion results when the Motion results when the forces are unbalanced.forces are unbalanced.

One large One large external forceexternal force

Another small Another small external force.external force.

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Aristotle Said ...Aristotle Said ...

Objects require force to keep moving.Objects require force to keep moving. An object’s natural state is to be at rest.An object’s natural state is to be at rest.

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Newton Said ...Newton Said ...

Objects do Objects do NOTNOT require force to keep require force to keep moving.moving.

An object’s natural state is to keep doing An object’s natural state is to keep doing what it is doing what it is doing – – unless an unless an unbalancedunbalanced force acts on it.force acts on it.

A sliding object - with no friction, A sliding object - with no friction, will will keepkeep moving in a moving in a straightstraight line. line.

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Newton’s First LawNewton’s First Law

11 An object will continue to be in a state of An object will continue to be in a state of restrest or of uniform velocity (speed and or of uniform velocity (speed and straightstraight line direction) line direction) unlessunless acted upon acted upon by an external, unbalanced force.by an external, unbalanced force.

Objects tend to "keep on doing what Objects tend to "keep on doing what they're doing.“they're doing.“

Objects resist changes in their state of Objects resist changes in their state of motion. motion.

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InertiaInertia

This This tendency to resist changestendency to resist changes in state in state of motion is described as of motion is described as inertiainertia..

MassMass is the measure of inertia. is the measure of inertia. Units Units kilogramskilograms..

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MassMass

Which vehicle has more inertia?Which vehicle has more inertia?

Mercedes-Benz Mercedes-Benz Smart CarSmart Car

730 kg730 kg

Hummer H2 SUVHummer H2 SUV

2900 kg2900 kg

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Newton’s Second Law: ForceNewton’s Second Law: Force

22 The acceleration of mass The acceleration of mass mm is directly is directly proportional to the unbalanced force proportional to the unbalanced force FF..

The greater the force, the more The greater the force, the more acceleration. Mathematically, acceleration. Mathematically,

F = maF = ma

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Units of ForceUnits of Force

Units of force in the SI system are Units of force in the SI system are newtonsnewtons (N). (N).

1 N = (1 kg)(1 m/s1 N = (1 kg)(1 m/s22).).

One newton is the force required to accelerate one kilogram One newton is the force required to accelerate one kilogram one meter/sone meter/s22..

mass mass unitsunits

acceleration acceleration unitsunits

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Force is a VectorForce is a Vector

Direction is important.Direction is important.

FF11FF22

m=2.0 kgm=2.0 kg

FF1 1 = + 8.0 N (to = + 8.0 N (to rightright))

FF22 = – 4.0 N (to = – 4.0 N (to leftleft))

++−−

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Find the Net ForceFind the Net Force

GivenGiven FormulaFormula m = m = 2.02.0 kgkg FFnetnet = Sum of = Sum of

forcesforces FF11 = + 8.0 N (to = + 8.0 N (to rightright))

FF22 = – 4.0 N (to = – 4.0 N (to leftleft))

Net force = FNet force = Fnetnet = +8.0 N – 4.0 N = + 4.0 N = +8.0 N – 4.0 N = + 4.0 N

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Find the AccelerationFind the Acceleration

GivenGiven FormulaFormula m = m = 2.02.0 kgkg FFnetnet = = mama

FFnetnet= + 4.0 N= + 4.0 N

From Newton FFrom Newton Fnetnet = = mama 4.0 = 2.04.0 = 2.0 aa a = 2.0 m/sa = 2.0 m/s22

Note, the answer is positive, the mass Note, the answer is positive, the mass accelerates to the right at 2.0 m/saccelerates to the right at 2.0 m/s22. .

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ForceForce What is the acceleration whenWhat is the acceleration when

FF = + 750 N (to = + 750 N (to rightright)) MMcarcar = 1,050 kg = 1,050 kg

MMtrailertrailer = 325 kg = 325 kg

FF ++−−

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ForceForce GivenGiven FormulaFormula

FF = + 750 N (to = + 750 N (to rightright)) FF = = mama MMcarcar = 1,050 kg = 1,050 kg

MMtrailertrailer = 325 kg = 325 kg

MMtotaltotal = M = Mcarcar + + MMtrailertrailer = 1,375 kg = 1,375 kg

FF = = MM aa = + 750 = 1,375 = + 750 = 1,375 aa aa = 0.55 m/s = 0.55 m/s22, acceleration is to the right., acceleration is to the right.

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Newton’s Third LawNewton’s Third Law

33 Whenever two bodies experience an Whenever two bodies experience an interaction, the force of the first body on interaction, the force of the first body on the second is equal and opposite to the the second is equal and opposite to the force of the second body on the first.force of the second body on the first.

““For every action there is an equal but For every action there is an equal but opposite reaction.”opposite reaction.”

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Equal but OppositeEqual but Opposite

She pushes on wall.She pushes on wall. Wall pushes on her.Wall pushes on her. Equal and opposite.Equal and opposite.

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2020

Dragster Seat

ActionAction

ReactionReaction

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Newton’s Law of GravitationNewton’s Law of Gravitation

Every object in the universe attracts every other Every object in the universe attracts every other object with a gravitational force:object with a gravitational force:

FF = = GmGm11mm22

r r 22

GG is a universal constant, 6.67x10 is a universal constant, 6.67x10−11−11 N-m N-m22/kg/kg

mm22

mm11

rr

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Newton’s Law of GravitationNewton’s Law of Gravitation

A body of mass, A body of mass, mm, close to the surface of , close to the surface of the Earth is attracted as if the entire the Earth is attracted as if the entire attracting mass of the Earth (assumed to attracting mass of the Earth (assumed to be spherical) is concentrated at the center be spherical) is concentrated at the center of the Earth.of the Earth.

ME

m

R

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Law of GravitationLaw of Gravitation

Appears to be a universal law.Appears to be a universal law. Extends to an infinite distance.Extends to an infinite distance. Near the Earth’s surface, the force is called “gravitational force,” Near the Earth’s surface, the force is called “gravitational force,”

or “weight or “weight WW.”.”

mm WW = = mm gg

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WeightWeight

W = mgW = mgWeight equals mass times gWeight equals mass times g

It’s a measure of gravitational forceIt’s a measure of gravitational force

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U. S. UnitsU. S. Units

One pound in English units is a unit of One pound in English units is a unit of forceforce..

The force of 2.2 lbs is equal to force of The force of 2.2 lbs is equal to force of gravity on 1.0 kg of mass.gravity on 1.0 kg of mass.

121 lbs121 lbs55 kg55 kg 540 N540 NMassMass Force, Earth SurfaceForce, Earth Surface

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Weight on Sun and MoonWeight on Sun and Moon

On SunOn Sun Gravitation = 28 g’sGravitation = 28 g’s 150 lbs 150 lbs → → 4,200 lbs4,200 lbs

On MoonOn Moon Gravitation = 1/6 gGravitation = 1/6 g 150 lbs 150 lbs → → 25 lbs25 lbs

Web

Astronaut with GearAstronaut with Gear

On Earth 430 lbsOn Earth 430 lbs

On Moon 72 lbsOn Moon 72 lbs

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WeightWeight

On Sunday morning Oct. 13, 2012, Austrian daredevil Felix On Sunday morning Oct. 13, 2012, Austrian daredevil Felix Baumgartner broke the world record for highest-ever skydive, Baumgartner broke the world record for highest-ever skydive,

leaping from a balloon nearly 24 miles (128k feet) above leaping from a balloon nearly 24 miles (128k feet) above Earth’s surface. Earth’s surface.

Is there a gravitational force in Is there a gravitational force in free fall in a free fall in a skydive?

Is there a Is there a gravitational gravitational

force in orbit?force in orbit?

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Basic Units ReviewBasic Units Review

SI, or MetricSI, or Metric USUS

DistanceDistance meter (m)meter (m) foot (ft)foot (ft)

SpeedSpeed m/sm/s ft/sft/s

AccelerationAcceleration m/sm/s22 ft/sft/s22

MassMass kilogram (kg)kilogram (kg) slugslug

ForceForce newton (N)newton (N) pound (lb)pound (lb)

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Centripetal ForceCentripetal Force

From Newton’s Second Law, From Newton’s Second Law, FF = = mama The force that is required to cause circular The force that is required to cause circular

motion is motion is centripetalcentripetal force. force. Centripetal force equals mass times centripetal Centripetal force equals mass times centripetal

acceleration.acceleration.

FFCC = = mamacc = = mvmv22//rr

Directed towards the center of curvature.Directed towards the center of curvature.

FFcc

vv

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Swing Yo-YoSwing Yo-Yo

mm = 45 grams = 45 grams TT = 1.1 s = 1.1 s RR = 0.80 m = 0.80 m

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Find the SpeedFind the Speed

T = period, T = period, time to go around once, time to go around once, T.T. v v = distance/time = 2= distance/time = 2ππr/Tr/T

A yo-yo does a “round-the-world” in 1.1 s. A yo-yo does a “round-the-world” in 1.1 s. The yo-yo is 0.80 meters long. The speed The yo-yo is 0.80 meters long. The speed is −is −

vv = d/t = 2 = d/t = 2ππR/TR/T = = 22ππ(0.8)/1.1 = 4.57 m/s(0.8)/1.1 = 4.57 m/s

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Centripetal ForceCentripetal Force

aacc = = vv22//R = 26.1 m/sR = 26.1 m/s22

FFC C = = mm aacc

mm = 45 grams = 0.045 kg = 45 grams = 0.045 kg

FFC C = (0.045)(26.1) = 1.2 N= (0.045)(26.1) = 1.2 N ... this is the tension in the string... this is the tension in the string

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Swing Yo-YoSwing Yo-Yo

Which way will Which way will the yo-yo fly if the yo-yo fly if the string the string breaks when breaks when the yo-yo is at the yo-yo is at the top of its the top of its “orbit?”“orbit?”

Why?Why?

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Amusement RidesAmusement Rides

In Rotor, ride rotates, In Rotor, ride rotates, riders are pinned to riders are pinned to the wall.the wall.

What holds the riders What holds the riders to the wall?to the wall?

Rotor

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Centrifugal ForceCentrifugal Force

““Center-fleeing” force.Center-fleeing” force. Newton’s equal-but-opposite reaction to Newton’s equal-but-opposite reaction to

centripetal force.centripetal force.

Centripetal: Wall Centripetal: Wall presses on rider presses on rider towards the center towards the center of rotation.of rotation.

Centrifugal: Rider Centrifugal: Rider against wallagainst wall

A Short Ride

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Another RideAnother Ride

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GravitronGravitron

24 rpm.24 rpm. Riders experience 4 g’s.Riders experience 4 g’s.

Gravitron

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Nuclear EnrichmentNuclear Enrichment

Natural uranium approximately Natural uranium approximately 99.3% 99.3% 238238UU and 0.7% and 0.7% 235235UU..

235235UU is lighter and fissionable. is lighter and fissionable.

How to make the uranium with How to make the uranium with higher percentage of higher percentage of 235235U? U?

Use “centrifuges” to separate Use “centrifuges” to separate heavier Uheavier U238238 from lighter U from lighter U235235..

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CentrifugesCentrifuges The centrifuges spin The centrifuges spin

very fast very fast ~ ~ 100,000 100,000 revolutions per minute revolutions per minute (rpm).(rpm).

More massive U-238 More massive U-238 goes to outside, less goes to outside, less massive U=235 forced massive U=235 forced to center of rotation, to center of rotation, and removed.and removed.

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In the NewsIn the News

BBC News: BBC News: Iran unveils 'faster' uranium Iran unveils 'faster' uranium centrifuges.centrifuges.

Iran’s been hiding the enrichment program Iran’s been hiding the enrichment program since 2003. “Only for electricity.”since 2003. “Only for electricity.”

““The IAEA report said 8,610 centrifuges had The IAEA report said 8,610 centrifuges had been installed in known enrichment facilities in been installed in known enrichment facilities in Iran, of which 3,772 were operating.Iran, of which 3,772 were operating.” ”

4/9/104/9/10

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Force on Space StationForce on Space Station

Int’l Space Station altitude Int’l Space Station altitude hh = 400 km. = 400 km.

RR, distance from center of Earth: , distance from center of Earth: RRE E + + hh

= 6,360 + 400 = 6,760 km = = 6,360 + 400 = 6,760 km = 6.76x106.76x1066 m m MMISSISS = = 2.33x102.33x1055 kg kg

MME E = = 6.0x106.0x102424 kg kg

From Newton’s law of GravitationFrom Newton’s law of Gravitation

FFGG = GM = GMEEMMISSISS/R/R22

= 2.04x10= 2.04x1066 N N

... we’ll use this later... we’ll use this later

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Speed of Space StationSpeed of Space Station

Centripetal force comes from gravity. Centripetal force comes from gravity. FFCC = = FFGG

From the From the centripetal forcecentripetal force equation … equation …

FFGG = = mvmv22//RR = 2.04x10 = 2.04x1066 N ( N (from earlier slidefrom earlier slide))

2.04x102.04x1066 = (2.33X10 = (2.33X1055)) vv22/ (6.76x10/ (6.76x1066) )

vv = 7,700 m/s (~17,000 mi/hr) = 7,700 m/s (~17,000 mi/hr)

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Period of an OrbitPeriod of an Orbit

v v = 7,700 m/s= 7,700 m/s Circumference of orbit Circumference of orbit dd

dd = 2 = 2ππRR = 2 (3.14)(= 2 (3.14)(6.76x106.76x1066) = 4.25x10) = 4.25x1077 m m

vv = = dd//tt 7,700 = 4.25x107,700 = 4.25x1077/ / tt tt = 5,500 seconds = 91 minutes = 5,500 seconds = 91 minutes Track

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Linear Momentum

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Linear MomentumLinear Momentum

Abbreviated with symbol “Abbreviated with symbol “pp”” A simple product of mass times velocity.A simple product of mass times velocity.

pp = = mvmv

Momentum is also a vectorMomentum is also a vector—it’s —it’s sign (sign (++ or or – ) in straight line motion – ) in straight line motion is important.is important.

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Momentum

A 0.45-caliber bullet (m = 0.162 kg) leaves the muzzle of a gun at 860 m/s. What is its momentum?

Given Formula m = 0.162 kg p = mv v = 860 m/s

p = (0.162) (860) = 139 kg-m/s

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SystemSystem Total momentum of a system is calculated Total momentum of a system is calculated

by adding momentums, taking direction into by adding momentums, taking direction into accountaccount..

Conservation of Momentum: Conservation of Momentum: With no unbalanced forces on the system, With no unbalanced forces on the system,

there is no change in total momentum.there is no change in total momentum. Momentum of the system is “conserved.”Momentum of the system is “conserved.”

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Conservation of Momentum

A 15-kg medicine ball is thrown at a velocity of 5.0 m/s to a 60-kg person who is at rest on ice.

The person catches the ball and subsequently slides with the ball across the ice.

Determine the velocity of the person and the ball after the collision.

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Find Initial Momentum

Given Formulas mball = 15kg p = mv

vball = +5.0 m/s pinitial = pball + pperson

mperson = 60 kg

vperson = 0 m/s

pball = +75 kg-m/s

pperson = 0 m/s

pinitial = 75 + 0 = +75 kg-m/s

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Find Final Momentum

Given Formulas mball = 15kg p = mv

vball = v pfinal = pball + pperson

mperson = 60 kg

vperson = v

pball = 15v

pperson = 60v

pfinal = 15v + 60v = 75v

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Find Final Velocity

Given Formulas pinitial = 75 kg-m/s pinitial = pfinal

pfinal = 75v

75v = 75 v = 1 m/s

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Another Conservation LawAnother Conservation Law

56565656

Angular MomentumAngular Momentum

When an object of mass When an object of mass mm rotates around an rotates around an axis.axis. mm = mass = mass vv = rotational speed = rotational speed rr = distance from center of rotation = distance from center of rotation LL = = mvrmvr

If you reduce r, v will automatically increase to If you reduce r, v will automatically increase to keep L constant.keep L constant.

CatsCats

Ice SkaterIce Skater

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TorqueTorque

To change momentum, apply a force F.To change momentum, apply a force F. To change angular momentum, we apply a To change angular momentum, we apply a

torquetorque..

Torque is the result of a force acting on a Torque is the result of a force acting on a “lever arm.”“lever arm.”

ττ == rr FF Lever Lever arm rarm r

FF

++

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WrenchesWrenches

Which wrench Which wrench can apply more can apply more torque torque ττ for a for a given force?given force?

59595959

TorqueTorque

Torque = Torque = rr FF Which hand position requires more force Which hand position requires more force

to get the same turning torque?to get the same turning torque?

FFrr rr

FF

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SimilaritiesSimilarities

Linear MotionLinear Motion Circular MotionCircular Motion

MomentumMomentum

pp = = mvmv

Angular MomentumAngular Momentum

LL = = mvrmvr

ForceForce

FF = = mama

TorqueTorque

ττ = = rFrF