Momentum and Energy

Chapter 3

MomentumMomentum• Momentum is inertia in

motion• Mass x velocityy• Has both magnitude

and direction• Large mass or high

speed can give object p g jgreat amount of momentum

Momentum = m•vMomentum m v

• Change momentum byChange momentum by – changing mass

or velocity usually velocity– or velocity—usually velocity• What causes changes in velocity?• Force• Time is also importantp

Momentum and ImpulseMomentum and Impulse

• Apply force over time to change velocityApply force over time to change velocity and momentum

• Greater time of application greater• Greater time of application, greater change in momentumF ti i t l i IMPULSE• Force x time interval is IMPULSE

Impulse = F•tImpulse F t• Force x time intervalForce x time interval• Impulse changes

momentum• Technically: )(mvFt Δ=

• Realistically: vmFt Δ=

Impulse Increasing MomentumImpulse Increasing MomentumvmFt Δ=

• Pushing a child on a swing—the force )(mvFt Δ=g

• Increases momentum• Longer pushLonger push

increases momentum more than a short one

• http://www.bcm.edu/oto/research/cochlea/Volta/16.html

Impulse Decreasing MomentumImpulse Decreasing Momentum

• Stopping the out of control car vmFt Δ=pp g• Change momentum to zero• Less force if time is greaterLess force if time is greater

Impulse Changes MomentumImpulse Changes Momentum

• Can change force by changing timeCan change force by changing time

M i ti d f• Move away increases time, reduces force• Toward decreases time, increases force

Bounce increases impulseBounce increases impulse• There is a change in vmFt Δ=There is a change in

velocity direction, making a greater Δv

vmFt Δ

• So greater force is required

• Water changesdirection, has greateri l h flimpulse than a flatpaddle

Conservation of MomentumConservation of Momentum

• The system: the cannon and the ball• When it fires momentum is conserved• When it fires, momentum is conserved—

they both have momentum: in opposite directionsdirections

• Momentum = m•v

Conservation of MomentumConservation of Momentum

• No net force • Momentum = m•vNo net force• No net momentum

Conservation of MomentumConservation of Momentum

• In the absence of external force theIn the absence of external force, the momentum of the system remains unchangedunchanged

• Momentum = m•v

• Consider individual balls as individual systems: momentum of each does change

Conservation of MomentumConservation of Momentum

• Net momentum is the same before theNet momentum is the same before the collision

• As after the collision• As after the collision

M t• Momentum = m•v

Conservation of MomentumConservation of Momentum

Y ll b ll t t t tia. Yellow ball starts stationaryb. Both balls moving opposite directionsc. Green ball moving faster

• Momentum = m•v

EnergyEnergy

• Property of a system that enables it to doProperty of a system that enables it to do work

• Potential Energy• Potential Energy– Springs

Ch i l– Chemicals– Gravity

• Kinetic Energy

Potential EnergyPotential Energy

• http://www.howstuffworks.com/inside-clock.htm

• http://www.himalayan.pdx.edu/virtualjourney/slideshow/se_photos_web/pages/Boy%20with%20Slingshot%2C%20J.htm

Potential EnergyPotential Energy

• Fuel is chemicalFuel is chemical potential energy

• http://www.alternativefuels.com.au/Biodiesel/dragster.htm

• http://www.lilligren.com/Redneck/redneck_lawnmower.htm

Work is Energy

• Lift heavy ram of pile driver

Work is Energy

Lift heavy ram of pile driver• Work transfers energy to

lift intolift into gravitational potential energy

Gravitational potential energyGravitational potential energy• Due to object’s positionDue to object s position• Relative to a surface= weight x height = mgh= weight x height = mgh• Work done for object to gain

potential energy

Gravitational potential energyGravitational potential energy

Gravitational potential energyGravitational potential energy

EP = mass x (acceleration of gravity) x heightEP = mass x (acceleration of gravity) x height

H i ht i b f l lHeight is above some reference levelPotential energy is always referenced to a zero

level defined in the system

Gravitational potential energyGravitational potential energy

• E = mgh• EP = mgh• mg = weight• h = height

Gravitational potential energyGravitational potential energy• EP = mgh • Path to the height is not factor in E• Path to the height is not factor in EP• Horizontal distance is not factor in EP

Kinetic Energy of MotionKinetic Energy of Motion• EK = mv21EK mv

2

• Work is a change in kinetic energy• W = ∆EKK

• ∆ Delta ‘change’

Kinetic Energy of MotionKinetic Energy of Motion

• HeatHeat• Sound

El t i it d li ht• Electricity and light

Kinetic Energy of MotionKinetic Energy of Motion

• W = ∆E Work is change in kinetic energy• W = ∆EK Work is change in kinetic energy• Work-energy theorem

• Net work = force x distance W = Fd– Due to net force

2mv E

2mv Fd =

2K E = 2 Fd

Conservation of EnergyConservation of Energy

• Cannot be created or destroyedCannot be created or destroyed• Can be converted from one form to another

Kinetic energy and momentumKinetic energy and momentum

• Properties of moving thingsProperties of moving things• Momentum is a vector quantity

b ll d ith it t– can be cancelled with opposite momentum• Kinetic Energy is a scalar quantity

– Cannot ever be cancelled

• http://www.littletheatre.net/Firecracker_Miss/miss_firecracker_contest.htm

Conservation of EnergyConservation of Energy

• Transformation fromTransformation from one form to another

• Potential energy of• Potential energy of stretched rubber of slingshotslingshot

• Transformed to ki ti f kkinetic energy of rock flying through air

Conservation of EnergyConservation of Energy

• Rock transfers itsRock transfers its kinetic energy to the object it hitsobject it hits

• May be transformed to heat upon impactto heat upon impact

• Energy cannot be t d d t dcreated or destroyed

Conservation of EnergyConservation of Energy

• http://science.howstuffworks.com/roller-coaster.htm

Conservation of EnergyConservation of Energy

E 10000 J E 0 J• EP = 10000 J EK = 0 J

• EP = 7500 J EK = 2500 JEP = 7500 J EK = 2500 J

• EP = 5000 J EK = 5000 JP K

• EP = 2500 J EK = 7500 J

• EP = 0 J EK = 10000 J

Conservation of EnergyConservation of Energy

• Does a car use more energy when itsDoes a car use more energy when its lights are on?

• What about when the air conditioner is on?

• How about using the radio when the gengine is off?

WorkWork

Transference of EnergyTransference of EnergyWork = Force x distance

W=FdW=FdWork into system = work out of systemo to syste o out o syste

WorkWork• Lifting load against the force of the weightLifting load against the force of the weight

of the object• Move an object twice as far results in twiceMove an object twice as far results in twice

the work• Move two object (Twice the weight) theMove two object (Twice the weight) the

same distance as one is twice the work• Nothing about time in definitionNothing about time in definition• Slow or fast• Same force same distance = same work• Same force, same distance = same work

Work W=FdWork W Fd

• Twice the weightTwice the weight• Twice the distance

Work W=FdWork W Fd• Units of work are Newton-meters,Units of work are Newton meters,

same as Joules

JmkgmmkgmNdF =⋅

=⋅

==2mkgmmkgmNdF ⋅

=⋅

==2

mNdF = mmkgmNdF =⋅

==dF = Js

ms

mNdF ==⋅=⋅=⋅22 s

ms

mNdF =⋅=⋅=⋅22

mNdF ⋅=⋅ ms

mNdF =⋅=⋅=⋅2

dF =⋅

• SO Work is energy• SO Work is energy

Work is Energy

• Same units

Work is Energy

Same units• Work occurs with transfer of energy

W k h t t ti l• Work occurs when you store potential energy

Work is EnergyMechanical energy

M i thi h t f

Work is Energy

Moving things—has two forms

1. Potential mechanical energyWaiting to workg

2. Kinetic mechanical energy2. Kinetic mechanical energy Work being done

Work is Energy

• Energy stored

Work is Energy

Energy stored in bow

• Work is done to• Work is done to create the potential energypotential energy

PowerPower• Work done over timeWork done over time

i t lti doneWork Power =

intervaltime

k 2• Units: watt

smkg

=⋅3

2

s

PowerPower• Half the timeenergy

P =Twice the powertime

energy P =

• Twice the time=Half the power

Power: P = energy/time

• Fuel burn

Power: P energy/time

Fuel burn• Biodiesel

• http://www.alternativefuels.com.au/Biodiesel/dragster.htm

• http://www.lilligren.com/Redneck/redneck_lawnmower.htm

Work, Energy and PowerWork, Energy and PowerWater b hi d thbehind the dam

Potential energygy

Convert it to electrical energy

Work and EnergyWork and Energy

• EP transformed to another form of energyEP transformed to another form of energy• Kinetic energy of motion