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![Page 1: Work and Energy](https://reader035.fdocuments.in/reader035/viewer/2022062517/56813294550346895d9928a6/html5/thumbnails/1.jpg)
Work and EnergyWork and Energy
Dr. Robert MacKay
Clark College
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Introduction Introduction
What is Energy? What are some of the different forms of
energy? Energy = $$$
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Overview Overview Work (W) Kinetic Energy (KE)
Potential Energy (PE) All Are measured in Units of Joules (J) 1.0 Joule = 1.0 N m
W KE
PE
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Overview Overview
Work Kinetic Energy Potential Energy
W KE
PE Heat LossHeat Loss
Heat Loss
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Crib SheetCrib Sheet
W FD// (JOULES)
KE 12mv2
GPE mgh
SPE 1
2kx 2 F kx
P W
t(J / sWatt )
Wnet KE
E KE PE
E f E0 WNC
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Work and EnergyWork and Energy
Work = Force x distance W = F d Actually Work = Force x Distance parallel to force
d=4.0 m
F= 6.0 N
W= F d = 6.0 N (4.0m) = 24.0 J
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Work and EnergyWork and Energy
Work = Force x Distance parallel to force
d= 8.0 m
F= 10.0 N
W = ?
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Work and EnergyWork and Energy
Work = Force x Distance parallel to force
d= 8.0 m
F= 10.0 N
W = 80 J
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Work and EnergyWork and Energy
Work = Force x Distance parallel to force
d= 8.0 m
F= - 6.0 N
W= F d = -6.0 N (8.0m) =-48 J
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Work and EnergyWork and Energy
Work = Force x Distance parallel to force
d= 6.0 m
F= - 5.0 N
W= F d = ? J
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Work and EnergyWork and Energy
Work = Force x Distance parallel to force
d= 6.0 m
F= - 5.0 N
W= F d = -30 J
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Work and EnergyWork and Energy
Work = Force x Distance parallel to force
d= 6.0 m
F= ? N
W= 60 J
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Work and EnergyWork and Energy
Work = Force x Distance parallel to force
d= 6.0 m
F= 10 N
W= 60 J
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Work and EnergyWork and Energy
Work = Force x Distance parallel to force
d= ? m
F= - 50.0 N
W= 200 J
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Work and EnergyWork and Energy
Work = Force x Distance parallel to force
d= -4.0 m
F= - 50.0 N
W= 200 J
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Work and EnergyWork and Energy
Work = Force x Distance parallel to force
d= 8.0 m
F= + 6.0 N
W= 0(since F and d are perpendicular
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PowerPower
Work = Power x time 1 Watt= 1 J/s 1 J = 1 Watt x 1 sec 1 kilowatt - hr = 1000 (J/s) 3600 s = 3,600,000 J Energy = $$$$$$ 1 kW-hr = $0.08 = 8 cents
Power Worktime
J / s
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PowerPower Work = Power x time W=P t [ J=(J/s) s= Watt * sec ]
work = ? when 2000 watts of power are delivered
for 4.0 sec.
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PowerPower Work = Power x time W=P t [ J=(J/s) s= Watt * sec ]
work = 8000J when 2000 watts of power are delivered
for 4.0 sec.
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PowerPower Energy = Power x time E =P t [ kW-hr=(kW) hr] or [ J=(J/s) s= Watt * sec ]
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PowerPower Energy = Power x time
How much energy is consumed by a 100 Watt lightbulb when left on for 24 hours?
What units should we use? J,W, & sor kW-hr, kW, hr
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PowerPower Energy = Power x time
How much energy is consumed by a 100 Watt lightbulb when left on for 24 hours?
What units should we use? J,W, & sor kW-hr, kW, hr
Energy=0.1 kWatt (24 hrs)=2.4 kWatt-hr
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PowerPower Energy = Power x time
What is the power output of a duck who does 3000 J of work in 0.5 sec?
What units should we use? J,W, & sor kW-hr, kW, hr
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PowerPower Energy = Power x time
What is the power output of a duck who does 3000 J of work in 0.5 sec?power=energy/time =3000 J/0.5 sec =6000 Watts
What units should we use? J,W, & sor kW-hr, kW, hr
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PowerPower Energy = Power x time E =P t [ kW-hr=(kW) hr]
Energy = ? when 2000 watts (2 kW) of power are
delivered for 6.0 hr.
Cost at 8 cent per kW-hr?
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PowerPower Energy = Power x time E =P t [ kW-hr=(kW) hr]
Energy = 2kW(6 hr)=12 kW-hr when 2000 watts (2 kW) of power are delivered for
6.0 hr.
Cost at 8 cent per kW-hr? 12 kW-hr*$0.08/kW-hr=$0.96
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MachinesMachines
Levers D =8 md = 1 m
f=10 NF=?
Work in = Work out
f D = F d
The important thing about a machine is although you can increase force with a machine or increase distance (or speed) with a machine you can not get more work (or power) out than you put into it.
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MachinesMachines
Levers D =8 md = 1 m
f=10 NF=?
Work in = Work out 10N 8m = F 1m
F = 80 N
The important thing about a machine is although you can increase force with a machine or increase distance (or speed) with a machine you can not get more work (or power) out than you put into it.
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MachinesMachines
Pulleys
Dd
f
F
Work in = Work out
f D = F d
The important thing about a machine is although you can increase force with a machine or increase distance (or speed) with a machine you can not get more work (or power) out than you put into it.
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MachinesMachines
Pulleys
Dd
f
F
Work in = Work out
f D = F d
D/d = 4 so F/f = 4
If F=200 N f=?
The important thing about a machine is although you can increase force with a machine or increase distance (or speed) with a machine you can not get more work (or power) out than you put into it.
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MachinesMachines
Pulleys
Dd
f
F
Work in = Work out
f D = F d
D/d = 4 so F/f = 4
If F=200 N f = 200 N/ 4 = 50 N
The important thing about a machine is although you can increase force with a machine or increase distance (or speed) with a machine you can not get more work (or power) out than you put into it.
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MachinesMachines
Hydraulic machine
Dd
fF
Work in = Work out
f D = F d if D=20 cm , d =1 cm, and F= 800 N, what is the minimum force f?
The important thing about a machine is although you can increase force with a machine or increase distance (or speed) with a machine you can not get more work (or power) out than you put into it.
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MachinesMachines
Hydraulic machine
Dd
fF
Work in = Work out
f D = F d
f 20 cm = 800 N (1 cm) f = 40 N
if D=20 cm , d =1 cm, and F= 800 N, what is the minimum force f?
The important thing about a machine is although you can increase force with a machine or increase distance (or speed) with a machine you can not get more work (or power) out than you put into it.
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EfficiencyEfficiency
Effeciency Energyout
Energyin
Ein
Eout
Eloss
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EfficiencyEfficiency
?in
out
Energy
EnergyEfficiency
Ein = 200 J
Eout= 150 J
Eloss= ?
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EfficiencyEfficiency
?in
out
Energy
EnergyEfficiency
Ein = 200 J
Eout= 150 J
Eloss= 50J
=0.75=75%
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Two Machines e1 and e2 Two Machines e1 and e2 connected to each other in seriesconnected to each other in series
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Two Machines e1 and e2Two Machines e1 and e2
Eout=eff (Ein)=0.5(100J)=50J
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Two Machines e1 and e2Two Machines e1 and e2
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Two Machines e1 and e2Two Machines e1 and e2
Total efficiency when 2 machines are connected one after the other is etot=e1 (e2)
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Kinetic Energy, KEKinetic Energy, KE
KE =1/2 m v2
m=2.0 kg and v= 5 m/sKE= ?
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Kinetic EnergyKinetic Energy
KE =1/2 m v2m=2.0 kg and v= 5 m/sKE= 25 J
m=4.0 kg and v= 5 m/sKE= ?
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Kinetic EnergyKinetic Energy
KE =1/2 m v2m=2.0 kg and v= 5 m/sKE= 25 J
m=4.0 kg and v= 5 m/sKE= 50J
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Kinetic EnergyKinetic Energy
KE =1/2 m v2m=2.0 kg and v= 5 m/sKE= 25 J
m=2.0 kg and v= 10 m/sKE= ?
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Kinetic EnergyKinetic Energy
KE =1/2 m v2m=2.0 kg and v= 5 m/sKE= 25 J
m=2.0 kg and v= 10 m/sKE= 100J
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22
2
mv2
142vm
2
1KE
2v vif
mv2
1KE
Double speed and KE increases by 4
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Kinetic EnergyKinetic Energy
KE =1/2 m v2
if m doubles KE doubles if v doubles KE quadruples if v triples KE increases 9x if v quadruples KE increases ____ x
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Work Energy TheormWork Energy Theorm
KE =1/2 m v2
F = m a
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Work Energy TheormWork Energy Theorm
K =1/2 m v2
F = m a F d = m a d
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Work Energy TheormWork Energy Theorm
KE =1/2 m v2
F = m a F d =m a d F d = m (v/t) [(v/2)t]
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Work Energy TheormWork Energy Theorm
K E=1/2 m v2
F = m a F d = m a d F d = m (v/t) [(v/2)t] W = 1/2 m v2
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Work Energy TheormWork Energy Theorm
KE =1/2 m v2
F = m a F d = m a d F d = m (v/t) [(v/2)t] W = 1/2 m v2
W = ∆ KE
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Work EnergyWork Energy W = ∆KE
How much work is required to stop a 2000 kg car traveling at 20 m/s (45 mph)?
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Work EnergyWork Energy W = ∆KE
How much work is required to stop a 2000 kg car traveling at 20 m/s (45 mph)?
W= ∆KE =-1/2 m v2
=-1/2(2000 kg)(20 m/s)2
= - 1000kg (400 m 2 /s 2) = - 400,000 Joules
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Work EnergyWork Energy W = ∆KE
How much work is required to stop a 2000 kg car traveling at 20 m/s? If the friction force equals its weight, how far will it skid?
W= ∆K = - 400,000 Joules F=weight=mg=-20,000 N
W=F d d=W/F=-400,000 J/-20,000N = 20.0 m
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Work EnergyWork Energy W = ∆KE v = 20 m/s
d=? m
v = 10 m/s
d= 15 m
Same Friction Force
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Work EnergyWork Energy W = ∆KE v = 20 m/s
d=60m(4 times 15m)
v = 10 m/s
d= 15 m
Same Friction Force
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Potential Energy, PEPotential Energy, PE
• Gravitational Potential Energy Gravitational Potential Energy • SpringsSprings• ChemicalChemical• PressurePressure• Mass (Nuclear)Mass (Nuclear)
• Measured in JoulesMeasured in Joules
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Potential Energy, PEPotential Energy, PE
• Gravitational Potential Energy Gravitational Potential Energy • SpringsSprings• ChemicalChemical• PressurePressure• Mass (Nuclear)Mass (Nuclear)
The energy required to put something in its place (state)
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Potential EnergyPotential Energy
Gravitational Potential Energy = weight x height
PE=(mg) h
4.0 m
m = 2.0 kg
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Potential EnergyPotential EnergyPE=(mg) h
4.0 m
m = 2.0 kg
K=?
PE=80 J
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Potential Energy to Kinetic EnergyPotential Energy to Kinetic EnergyPE=(mg) h
2.0 m
m = 2.0 kg
KE=?
PE=40 J
1.0 m
K E= 0 J
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Conservation of EnergyConservation of Energy
Total Mechanical Energy, E = PE +K
Energy can neither be created nor destroyed only transformed from one form to another
In the absence of friction or other non-conservative forces the total mechanical energy of a system does not change
E f=Eo
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Conservation of EnergyConservation of Energy
10.0 m
m = 1.02 kg (mg = 10.0 N)
K = 0 JPE=100 J
PE = 75 J
PE = 50 J
PE = 0 J
PE= 25 J
K = ?
K= ?
K = 50 J
K = 25 J Constant E{E = K + PE}
Ef = Eo
No frictionNo Air resistance
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Conservation of EnergyConservation of Energy
5.0 m
m = 2.0 kgK=0 J
PE=100 J
PE = 0 J
K = ?
Constant E{E = K + U}Constant E{E = K + PE}Ef=Eo
No friction
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Conservation of EnergyConservation of Energy
5.0 m
m = 2.0 kgK = 0 J
PE =100 J
v = ?
K = 100 J
Constant E{E = K + U}Constant E{E = K + PE}Ef=Eo
No friction
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