Work, Energy, Power

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What’s the difference?

• Force is the agent of change• Energy is a measure of change• Work is a way of transferring energy from

one system to another

What is work?• Work= force*displac.• W=Fd• Only work if there is

motion- if you push against a brick wall and it doesn’t move, you might be tired but you have done no work

• Unit=Joule (unit of energy)

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Are they work?• Teacher pushes wall and

becomes exhausted• Book falls off table to floor• Waiter carries large tray

across restaurant at constant v

• Starship Enterprise accelerates through space

• No- no displacement

• Yes- force=g and displacement=fall

• No-why?

• Yes- force from engines

So what’s with the waiter???????

Work = 0 • Work = 0 if:–No force–No displacement–force is perpendicular to

displacement

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Power• Power= rate at which work

gets done= work over time• P=W/t• Since W=Fd then P=Fd/t and

d/t=v• P=Fv• Unit= J/s=watt (W) • Careful not to confuse unit W

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Ex: Power

• A mover pushes a large crate mass=75kg across the truck bed for a total distance of 6m. He exerts a steady force of 300N for 20s. What is his power output?

• P=W/t P=Fd/t=(300N)(6m)/20s=90W

Kinetic Energy

• Energy of MOTION• K=1/2mv2

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Example…• Determine the kinetic

energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s

• KE = (1/2)*m*v2

• KE = (0.5) * (625 kg) * (18.3 m/s)2

• KE = 1.05 x105 Joules

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Potential Energy=U

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Energy an object has due to its position or configuration- stored energy that can be retrieved.

Ex- height on a wave gives U, pulling back the string on a bow gives it U, compressing or stretching a spring gives U.

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Potential Energy: Energy of POSITION

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Gravitational Potential

Energy: Ug

• Potential energy due to position relative to surface of the earth

• Ug=mgh• Unit = Joule

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Gravitational Potential Energy: Ug

and Work done by gravity

• Gravity can do + or - work depending on motion

• Path independent- depends on height, not path taken

• Wg=mgΔh • Where h is height

above arbitrary 0 pt

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Examples

• Physicsman (mass=60kg) scales a 40m tall rock face. What is his potential energy (relative to the ground)?

• Ug=mgh=(60kg)(10N/kg)(40m)=24000J

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Mechanical Energy: U and K:Energy because of position or

motion

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Total Mechanical Energy is CONSERVED

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PE

ONLY

PE +

KEKE

ONLY

Take it 1 step further…

• If physicsman (60kg) were to jump of the cliff (remember his U=24000J), what would his velocity be when he hits the ground? Think…U is transformed to K

• At the top he has all U=24000J• At the bottom he has all K=1/2mv2

• Utop=Kbottom

• 24000J=1/2(60kg)v2

• V=28m/s

Work by Conservative vs. Nonconservative Forces

• Conservative forces are path independent–Ex: gravity

• Nonconservative forces depend on path–Ex: kinetic friction-

longer path means more work

Work and Energy

• E=K+U• E=1/2mv2+mgh

– Object’s mechanical energy is sum of kinetic and potential energies

– Since U is relative to position, so is E

• Wnc=ΔK+ΔU– Work done by nonconservative forces is sum of changes in K

and U

Conservation of Energy• Since E=K+U, if no nonconservative forces (friction

for example) act on a system then mechanical energy is conserved

• Ei=Ef • Ki+Ui=Kf+Uf

Ex: conservation of energy

• A ball of mass 2kg is gently pushed off the lab table, 5.0m above the floor. Find the speed of the ball as it strikes the floor

• Ei=Ef or Ki+Ui=Kf+Uf

• 0+mgh=1/2mv2+0