do now two people exert a 10 newton force for 2 meters. person 1 exerts the force at a 50 degree...
TRANSCRIPT
Do NowDo Now
Two people exert a 10 Newton force Two people exert a 10 Newton force for 2 meters Person 1 exerts the for 2 meters Person 1 exerts the force at a 50 degree angle Calculate force at a 50 degree angle Calculate the work done on the box by each the work done on the box by each personperson
Person 1 Person 2
W = Fdcosθ = (10N)(2m)cos50˚
= 129 J
W = Fdcosθ = (10N)(2m)cos0˚
= 20 J
Net WorkNet Work 12) An object is pulled by a 20N force 12) An object is pulled by a 20N force
due east for 5 meters and then due due east for 5 meters and then due north by the same force for 3 meters north by the same force for 3 meters How much work was done How much work was done
5m
3m
Note The net work is related to the path traveledIt is NOT related to the resultant displacement
R
W1 = (20N)(5m) = 100 J
WT= W2 + W3 = 160 J
W2 = (20N)(3m) = 60 J
LiftingLifting 14) I decide to get my pet frog to 14) I decide to get my pet frog to
do a little weight lifting (but Irsquom do a little weight lifting (but Irsquom going to start him off slow) He going to start him off slow) He lifts 2 kg up from the floor over lifts 2 kg up from the floor over his head 2 cm How much work his head 2 cm How much work did he dodid he do
W = Fd cosθFlift = Weight
Flift = mg = 2kg(98ms2)
Weight
Flift = 196 N
W = (196N)(002m)
W = 0392 J
Why is it easier to lift the boulder with this simple machine than to pick it up directlyDoes it take less Work to lift the boulder this way
Input Work = Output Work
W= 1N x 4m W= 4N x 1m
4 J 4 J
4 m
1 m
Distance of Applied ForceDistance of Applied Force Distance of Distance of OutputOutput
Simple machines donrsquot change the Simple machines donrsquot change the amount of work we do but it can make amount of work we do but it can make
work ldquoeasierrdquo to dowork ldquoeasierrdquo to do In sports Baseball bats golf clubs In sports Baseball bats golf clubs
hockey sticks helliphockey sticks hellip httpscience360govobjvideohttpscience360govobjvideo
c5be5456-2e39-49a7-8118-c5be5456-2e39-49a7-8118-218868df89ebwork-energy-218868df89ebwork-energy-power power
Compound pulleys Compound pulleys reduce the force needed reduce the force needed
to do workto do work What distance would the rope have to be What distance would the rope have to be pulled to make the weight rise 1 meterpulled to make the weight rise 1 meter
W = Fd
W = (100N)(1m)
W = 100 J
W = Fd100 J = (25N)d
d = (100J)(25N)
d = 4m
15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless
20kg
F
x
Begin by calculating the force necessary tomove the object
gF mg220 98g
mF kgs
196gF N
gFW F d
196 50W N m 9800W J
GraphsGraphs 16) What does the slope of a 16) What does the slope of a
Force versus Displacement graph Force versus Displacement graph representrepresent
Forc
e (
N)
Displacement (m)
yslope
x
Fslope
d
FNothing
d
1)Write down a formula that uses the variables onthe x and y axis
W F d
GraphsGraphs 17) What does the area under the 17) What does the area under the
curve representcurve represent
Forc
e (
N)
AREA
Displacement (m)
How do you find the area
A length height
A displacement force
A F d
W F d
Area Work
W F d
GraphsGraphs
18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75
A F d
W F d
Area Work
5 11W N m
55W J
GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an
object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75 12A b h
Area Work
1 10 752A m N
375A N m Work
What is PowerWhat is Power
Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed
= F v
Units of PowerUnits of Power
20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in
secondsseconds
WP
t
JoulesP
Second 1
11
Joulewatt
Second
Power is measured in WattsWe will examine mechanical power rather than
Electrical power
PowerPower 21) What are some common 21) What are some common
devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power
Examples Motors heaters and Examples Motors heaters and other machinesother machines
22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
Net WorkNet Work 12) An object is pulled by a 20N force 12) An object is pulled by a 20N force
due east for 5 meters and then due due east for 5 meters and then due north by the same force for 3 meters north by the same force for 3 meters How much work was done How much work was done
5m
3m
Note The net work is related to the path traveledIt is NOT related to the resultant displacement
R
W1 = (20N)(5m) = 100 J
WT= W2 + W3 = 160 J
W2 = (20N)(3m) = 60 J
LiftingLifting 14) I decide to get my pet frog to 14) I decide to get my pet frog to
do a little weight lifting (but Irsquom do a little weight lifting (but Irsquom going to start him off slow) He going to start him off slow) He lifts 2 kg up from the floor over lifts 2 kg up from the floor over his head 2 cm How much work his head 2 cm How much work did he dodid he do
W = Fd cosθFlift = Weight
Flift = mg = 2kg(98ms2)
Weight
Flift = 196 N
W = (196N)(002m)
W = 0392 J
Why is it easier to lift the boulder with this simple machine than to pick it up directlyDoes it take less Work to lift the boulder this way
Input Work = Output Work
W= 1N x 4m W= 4N x 1m
4 J 4 J
4 m
1 m
Distance of Applied ForceDistance of Applied Force Distance of Distance of OutputOutput
Simple machines donrsquot change the Simple machines donrsquot change the amount of work we do but it can make amount of work we do but it can make
work ldquoeasierrdquo to dowork ldquoeasierrdquo to do In sports Baseball bats golf clubs In sports Baseball bats golf clubs
hockey sticks helliphockey sticks hellip httpscience360govobjvideohttpscience360govobjvideo
c5be5456-2e39-49a7-8118-c5be5456-2e39-49a7-8118-218868df89ebwork-energy-218868df89ebwork-energy-power power
Compound pulleys Compound pulleys reduce the force needed reduce the force needed
to do workto do work What distance would the rope have to be What distance would the rope have to be pulled to make the weight rise 1 meterpulled to make the weight rise 1 meter
W = Fd
W = (100N)(1m)
W = 100 J
W = Fd100 J = (25N)d
d = (100J)(25N)
d = 4m
15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless
20kg
F
x
Begin by calculating the force necessary tomove the object
gF mg220 98g
mF kgs
196gF N
gFW F d
196 50W N m 9800W J
GraphsGraphs 16) What does the slope of a 16) What does the slope of a
Force versus Displacement graph Force versus Displacement graph representrepresent
Forc
e (
N)
Displacement (m)
yslope
x
Fslope
d
FNothing
d
1)Write down a formula that uses the variables onthe x and y axis
W F d
GraphsGraphs 17) What does the area under the 17) What does the area under the
curve representcurve represent
Forc
e (
N)
AREA
Displacement (m)
How do you find the area
A length height
A displacement force
A F d
W F d
Area Work
W F d
GraphsGraphs
18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75
A F d
W F d
Area Work
5 11W N m
55W J
GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an
object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75 12A b h
Area Work
1 10 752A m N
375A N m Work
What is PowerWhat is Power
Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed
= F v
Units of PowerUnits of Power
20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in
secondsseconds
WP
t
JoulesP
Second 1
11
Joulewatt
Second
Power is measured in WattsWe will examine mechanical power rather than
Electrical power
PowerPower 21) What are some common 21) What are some common
devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power
Examples Motors heaters and Examples Motors heaters and other machinesother machines
22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
LiftingLifting 14) I decide to get my pet frog to 14) I decide to get my pet frog to
do a little weight lifting (but Irsquom do a little weight lifting (but Irsquom going to start him off slow) He going to start him off slow) He lifts 2 kg up from the floor over lifts 2 kg up from the floor over his head 2 cm How much work his head 2 cm How much work did he dodid he do
W = Fd cosθFlift = Weight
Flift = mg = 2kg(98ms2)
Weight
Flift = 196 N
W = (196N)(002m)
W = 0392 J
Why is it easier to lift the boulder with this simple machine than to pick it up directlyDoes it take less Work to lift the boulder this way
Input Work = Output Work
W= 1N x 4m W= 4N x 1m
4 J 4 J
4 m
1 m
Distance of Applied ForceDistance of Applied Force Distance of Distance of OutputOutput
Simple machines donrsquot change the Simple machines donrsquot change the amount of work we do but it can make amount of work we do but it can make
work ldquoeasierrdquo to dowork ldquoeasierrdquo to do In sports Baseball bats golf clubs In sports Baseball bats golf clubs
hockey sticks helliphockey sticks hellip httpscience360govobjvideohttpscience360govobjvideo
c5be5456-2e39-49a7-8118-c5be5456-2e39-49a7-8118-218868df89ebwork-energy-218868df89ebwork-energy-power power
Compound pulleys Compound pulleys reduce the force needed reduce the force needed
to do workto do work What distance would the rope have to be What distance would the rope have to be pulled to make the weight rise 1 meterpulled to make the weight rise 1 meter
W = Fd
W = (100N)(1m)
W = 100 J
W = Fd100 J = (25N)d
d = (100J)(25N)
d = 4m
15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless
20kg
F
x
Begin by calculating the force necessary tomove the object
gF mg220 98g
mF kgs
196gF N
gFW F d
196 50W N m 9800W J
GraphsGraphs 16) What does the slope of a 16) What does the slope of a
Force versus Displacement graph Force versus Displacement graph representrepresent
Forc
e (
N)
Displacement (m)
yslope
x
Fslope
d
FNothing
d
1)Write down a formula that uses the variables onthe x and y axis
W F d
GraphsGraphs 17) What does the area under the 17) What does the area under the
curve representcurve represent
Forc
e (
N)
AREA
Displacement (m)
How do you find the area
A length height
A displacement force
A F d
W F d
Area Work
W F d
GraphsGraphs
18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75
A F d
W F d
Area Work
5 11W N m
55W J
GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an
object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75 12A b h
Area Work
1 10 752A m N
375A N m Work
What is PowerWhat is Power
Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed
= F v
Units of PowerUnits of Power
20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in
secondsseconds
WP
t
JoulesP
Second 1
11
Joulewatt
Second
Power is measured in WattsWe will examine mechanical power rather than
Electrical power
PowerPower 21) What are some common 21) What are some common
devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power
Examples Motors heaters and Examples Motors heaters and other machinesother machines
22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
Why is it easier to lift the boulder with this simple machine than to pick it up directlyDoes it take less Work to lift the boulder this way
Input Work = Output Work
W= 1N x 4m W= 4N x 1m
4 J 4 J
4 m
1 m
Distance of Applied ForceDistance of Applied Force Distance of Distance of OutputOutput
Simple machines donrsquot change the Simple machines donrsquot change the amount of work we do but it can make amount of work we do but it can make
work ldquoeasierrdquo to dowork ldquoeasierrdquo to do In sports Baseball bats golf clubs In sports Baseball bats golf clubs
hockey sticks helliphockey sticks hellip httpscience360govobjvideohttpscience360govobjvideo
c5be5456-2e39-49a7-8118-c5be5456-2e39-49a7-8118-218868df89ebwork-energy-218868df89ebwork-energy-power power
Compound pulleys Compound pulleys reduce the force needed reduce the force needed
to do workto do work What distance would the rope have to be What distance would the rope have to be pulled to make the weight rise 1 meterpulled to make the weight rise 1 meter
W = Fd
W = (100N)(1m)
W = 100 J
W = Fd100 J = (25N)d
d = (100J)(25N)
d = 4m
15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless
20kg
F
x
Begin by calculating the force necessary tomove the object
gF mg220 98g
mF kgs
196gF N
gFW F d
196 50W N m 9800W J
GraphsGraphs 16) What does the slope of a 16) What does the slope of a
Force versus Displacement graph Force versus Displacement graph representrepresent
Forc
e (
N)
Displacement (m)
yslope
x
Fslope
d
FNothing
d
1)Write down a formula that uses the variables onthe x and y axis
W F d
GraphsGraphs 17) What does the area under the 17) What does the area under the
curve representcurve represent
Forc
e (
N)
AREA
Displacement (m)
How do you find the area
A length height
A displacement force
A F d
W F d
Area Work
W F d
GraphsGraphs
18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75
A F d
W F d
Area Work
5 11W N m
55W J
GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an
object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75 12A b h
Area Work
1 10 752A m N
375A N m Work
What is PowerWhat is Power
Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed
= F v
Units of PowerUnits of Power
20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in
secondsseconds
WP
t
JoulesP
Second 1
11
Joulewatt
Second
Power is measured in WattsWe will examine mechanical power rather than
Electrical power
PowerPower 21) What are some common 21) What are some common
devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power
Examples Motors heaters and Examples Motors heaters and other machinesother machines
22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
Input Work = Output Work
W= 1N x 4m W= 4N x 1m
4 J 4 J
4 m
1 m
Distance of Applied ForceDistance of Applied Force Distance of Distance of OutputOutput
Simple machines donrsquot change the Simple machines donrsquot change the amount of work we do but it can make amount of work we do but it can make
work ldquoeasierrdquo to dowork ldquoeasierrdquo to do In sports Baseball bats golf clubs In sports Baseball bats golf clubs
hockey sticks helliphockey sticks hellip httpscience360govobjvideohttpscience360govobjvideo
c5be5456-2e39-49a7-8118-c5be5456-2e39-49a7-8118-218868df89ebwork-energy-218868df89ebwork-energy-power power
Compound pulleys Compound pulleys reduce the force needed reduce the force needed
to do workto do work What distance would the rope have to be What distance would the rope have to be pulled to make the weight rise 1 meterpulled to make the weight rise 1 meter
W = Fd
W = (100N)(1m)
W = 100 J
W = Fd100 J = (25N)d
d = (100J)(25N)
d = 4m
15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless
20kg
F
x
Begin by calculating the force necessary tomove the object
gF mg220 98g
mF kgs
196gF N
gFW F d
196 50W N m 9800W J
GraphsGraphs 16) What does the slope of a 16) What does the slope of a
Force versus Displacement graph Force versus Displacement graph representrepresent
Forc
e (
N)
Displacement (m)
yslope
x
Fslope
d
FNothing
d
1)Write down a formula that uses the variables onthe x and y axis
W F d
GraphsGraphs 17) What does the area under the 17) What does the area under the
curve representcurve represent
Forc
e (
N)
AREA
Displacement (m)
How do you find the area
A length height
A displacement force
A F d
W F d
Area Work
W F d
GraphsGraphs
18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75
A F d
W F d
Area Work
5 11W N m
55W J
GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an
object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75 12A b h
Area Work
1 10 752A m N
375A N m Work
What is PowerWhat is Power
Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed
= F v
Units of PowerUnits of Power
20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in
secondsseconds
WP
t
JoulesP
Second 1
11
Joulewatt
Second
Power is measured in WattsWe will examine mechanical power rather than
Electrical power
PowerPower 21) What are some common 21) What are some common
devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power
Examples Motors heaters and Examples Motors heaters and other machinesother machines
22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
Distance of Applied ForceDistance of Applied Force Distance of Distance of OutputOutput
Simple machines donrsquot change the Simple machines donrsquot change the amount of work we do but it can make amount of work we do but it can make
work ldquoeasierrdquo to dowork ldquoeasierrdquo to do In sports Baseball bats golf clubs In sports Baseball bats golf clubs
hockey sticks helliphockey sticks hellip httpscience360govobjvideohttpscience360govobjvideo
c5be5456-2e39-49a7-8118-c5be5456-2e39-49a7-8118-218868df89ebwork-energy-218868df89ebwork-energy-power power
Compound pulleys Compound pulleys reduce the force needed reduce the force needed
to do workto do work What distance would the rope have to be What distance would the rope have to be pulled to make the weight rise 1 meterpulled to make the weight rise 1 meter
W = Fd
W = (100N)(1m)
W = 100 J
W = Fd100 J = (25N)d
d = (100J)(25N)
d = 4m
15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless
20kg
F
x
Begin by calculating the force necessary tomove the object
gF mg220 98g
mF kgs
196gF N
gFW F d
196 50W N m 9800W J
GraphsGraphs 16) What does the slope of a 16) What does the slope of a
Force versus Displacement graph Force versus Displacement graph representrepresent
Forc
e (
N)
Displacement (m)
yslope
x
Fslope
d
FNothing
d
1)Write down a formula that uses the variables onthe x and y axis
W F d
GraphsGraphs 17) What does the area under the 17) What does the area under the
curve representcurve represent
Forc
e (
N)
AREA
Displacement (m)
How do you find the area
A length height
A displacement force
A F d
W F d
Area Work
W F d
GraphsGraphs
18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75
A F d
W F d
Area Work
5 11W N m
55W J
GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an
object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75 12A b h
Area Work
1 10 752A m N
375A N m Work
What is PowerWhat is Power
Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed
= F v
Units of PowerUnits of Power
20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in
secondsseconds
WP
t
JoulesP
Second 1
11
Joulewatt
Second
Power is measured in WattsWe will examine mechanical power rather than
Electrical power
PowerPower 21) What are some common 21) What are some common
devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power
Examples Motors heaters and Examples Motors heaters and other machinesother machines
22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
Simple machines donrsquot change the Simple machines donrsquot change the amount of work we do but it can make amount of work we do but it can make
work ldquoeasierrdquo to dowork ldquoeasierrdquo to do In sports Baseball bats golf clubs In sports Baseball bats golf clubs
hockey sticks helliphockey sticks hellip httpscience360govobjvideohttpscience360govobjvideo
c5be5456-2e39-49a7-8118-c5be5456-2e39-49a7-8118-218868df89ebwork-energy-218868df89ebwork-energy-power power
Compound pulleys Compound pulleys reduce the force needed reduce the force needed
to do workto do work What distance would the rope have to be What distance would the rope have to be pulled to make the weight rise 1 meterpulled to make the weight rise 1 meter
W = Fd
W = (100N)(1m)
W = 100 J
W = Fd100 J = (25N)d
d = (100J)(25N)
d = 4m
15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless
20kg
F
x
Begin by calculating the force necessary tomove the object
gF mg220 98g
mF kgs
196gF N
gFW F d
196 50W N m 9800W J
GraphsGraphs 16) What does the slope of a 16) What does the slope of a
Force versus Displacement graph Force versus Displacement graph representrepresent
Forc
e (
N)
Displacement (m)
yslope
x
Fslope
d
FNothing
d
1)Write down a formula that uses the variables onthe x and y axis
W F d
GraphsGraphs 17) What does the area under the 17) What does the area under the
curve representcurve represent
Forc
e (
N)
AREA
Displacement (m)
How do you find the area
A length height
A displacement force
A F d
W F d
Area Work
W F d
GraphsGraphs
18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75
A F d
W F d
Area Work
5 11W N m
55W J
GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an
object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75 12A b h
Area Work
1 10 752A m N
375A N m Work
What is PowerWhat is Power
Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed
= F v
Units of PowerUnits of Power
20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in
secondsseconds
WP
t
JoulesP
Second 1
11
Joulewatt
Second
Power is measured in WattsWe will examine mechanical power rather than
Electrical power
PowerPower 21) What are some common 21) What are some common
devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power
Examples Motors heaters and Examples Motors heaters and other machinesother machines
22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
Compound pulleys Compound pulleys reduce the force needed reduce the force needed
to do workto do work What distance would the rope have to be What distance would the rope have to be pulled to make the weight rise 1 meterpulled to make the weight rise 1 meter
W = Fd
W = (100N)(1m)
W = 100 J
W = Fd100 J = (25N)d
d = (100J)(25N)
d = 4m
15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless
20kg
F
x
Begin by calculating the force necessary tomove the object
gF mg220 98g
mF kgs
196gF N
gFW F d
196 50W N m 9800W J
GraphsGraphs 16) What does the slope of a 16) What does the slope of a
Force versus Displacement graph Force versus Displacement graph representrepresent
Forc
e (
N)
Displacement (m)
yslope
x
Fslope
d
FNothing
d
1)Write down a formula that uses the variables onthe x and y axis
W F d
GraphsGraphs 17) What does the area under the 17) What does the area under the
curve representcurve represent
Forc
e (
N)
AREA
Displacement (m)
How do you find the area
A length height
A displacement force
A F d
W F d
Area Work
W F d
GraphsGraphs
18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75
A F d
W F d
Area Work
5 11W N m
55W J
GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an
object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75 12A b h
Area Work
1 10 752A m N
375A N m Work
What is PowerWhat is Power
Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed
= F v
Units of PowerUnits of Power
20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in
secondsseconds
WP
t
JoulesP
Second 1
11
Joulewatt
Second
Power is measured in WattsWe will examine mechanical power rather than
Electrical power
PowerPower 21) What are some common 21) What are some common
devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power
Examples Motors heaters and Examples Motors heaters and other machinesother machines
22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
15) The box in the diagram below 15) The box in the diagram below needs to be raised a distance of needs to be raised a distance of 50 meters How much work is 50 meters How much work is required to lift the box assuming required to lift the box assuming the pulley is frictionlessthe pulley is frictionless
20kg
F
x
Begin by calculating the force necessary tomove the object
gF mg220 98g
mF kgs
196gF N
gFW F d
196 50W N m 9800W J
GraphsGraphs 16) What does the slope of a 16) What does the slope of a
Force versus Displacement graph Force versus Displacement graph representrepresent
Forc
e (
N)
Displacement (m)
yslope
x
Fslope
d
FNothing
d
1)Write down a formula that uses the variables onthe x and y axis
W F d
GraphsGraphs 17) What does the area under the 17) What does the area under the
curve representcurve represent
Forc
e (
N)
AREA
Displacement (m)
How do you find the area
A length height
A displacement force
A F d
W F d
Area Work
W F d
GraphsGraphs
18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75
A F d
W F d
Area Work
5 11W N m
55W J
GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an
object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75 12A b h
Area Work
1 10 752A m N
375A N m Work
What is PowerWhat is Power
Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed
= F v
Units of PowerUnits of Power
20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in
secondsseconds
WP
t
JoulesP
Second 1
11
Joulewatt
Second
Power is measured in WattsWe will examine mechanical power rather than
Electrical power
PowerPower 21) What are some common 21) What are some common
devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power
Examples Motors heaters and Examples Motors heaters and other machinesother machines
22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
GraphsGraphs 16) What does the slope of a 16) What does the slope of a
Force versus Displacement graph Force versus Displacement graph representrepresent
Forc
e (
N)
Displacement (m)
yslope
x
Fslope
d
FNothing
d
1)Write down a formula that uses the variables onthe x and y axis
W F d
GraphsGraphs 17) What does the area under the 17) What does the area under the
curve representcurve represent
Forc
e (
N)
AREA
Displacement (m)
How do you find the area
A length height
A displacement force
A F d
W F d
Area Work
W F d
GraphsGraphs
18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75
A F d
W F d
Area Work
5 11W N m
55W J
GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an
object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75 12A b h
Area Work
1 10 752A m N
375A N m Work
What is PowerWhat is Power
Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed
= F v
Units of PowerUnits of Power
20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in
secondsseconds
WP
t
JoulesP
Second 1
11
Joulewatt
Second
Power is measured in WattsWe will examine mechanical power rather than
Electrical power
PowerPower 21) What are some common 21) What are some common
devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power
Examples Motors heaters and Examples Motors heaters and other machinesother machines
22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
GraphsGraphs 17) What does the area under the 17) What does the area under the
curve representcurve represent
Forc
e (
N)
AREA
Displacement (m)
How do you find the area
A length height
A displacement force
A F d
W F d
Area Work
W F d
GraphsGraphs
18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75
A F d
W F d
Area Work
5 11W N m
55W J
GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an
object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75 12A b h
Area Work
1 10 752A m N
375A N m Work
What is PowerWhat is Power
Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed
= F v
Units of PowerUnits of Power
20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in
secondsseconds
WP
t
JoulesP
Second 1
11
Joulewatt
Second
Power is measured in WattsWe will examine mechanical power rather than
Electrical power
PowerPower 21) What are some common 21) What are some common
devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power
Examples Motors heaters and Examples Motors heaters and other machinesother machines
22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
GraphsGraphs
18) How much work was done on 18) How much work was done on the 5 kg object represented by the 5 kg object represented by the graph belowthe graph below
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75
A F d
W F d
Area Work
5 11W N m
55W J
GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an
object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75 12A b h
Area Work
1 10 752A m N
375A N m Work
What is PowerWhat is Power
Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed
= F v
Units of PowerUnits of Power
20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in
secondsseconds
WP
t
JoulesP
Second 1
11
Joulewatt
Second
Power is measured in WattsWe will examine mechanical power rather than
Electrical power
PowerPower 21) What are some common 21) What are some common
devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power
Examples Motors heaters and Examples Motors heaters and other machinesother machines
22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
GraphsGraphs 19) A Changing force acts on an 19) A Changing force acts on an
object represented by the graph object represented by the graph below How much work was done below How much work was done on the objecton the object
Forc
e (
N)
Displacement (m)
5
10
2 4 6 8 10 12
25
75 12A b h
Area Work
1 10 752A m N
375A N m Work
What is PowerWhat is Power
Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed
= F v
Units of PowerUnits of Power
20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in
secondsseconds
WP
t
JoulesP
Second 1
11
Joulewatt
Second
Power is measured in WattsWe will examine mechanical power rather than
Electrical power
PowerPower 21) What are some common 21) What are some common
devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power
Examples Motors heaters and Examples Motors heaters and other machinesother machines
22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
What is PowerWhat is Power
Power is defined as the Power is defined as the rate at rate at which work or energywhich work or energy is done or is done or transformedtransformed
= F v
Units of PowerUnits of Power
20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in
secondsseconds
WP
t
JoulesP
Second 1
11
Joulewatt
Second
Power is measured in WattsWe will examine mechanical power rather than
Electrical power
PowerPower 21) What are some common 21) What are some common
devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power
Examples Motors heaters and Examples Motors heaters and other machinesother machines
22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
Units of PowerUnits of Power
20) What are the units for 20) What are the units for PowerPower Work is measured in joules time in Work is measured in joules time in
secondsseconds
WP
t
JoulesP
Second 1
11
Joulewatt
Second
Power is measured in WattsWe will examine mechanical power rather than
Electrical power
PowerPower 21) What are some common 21) What are some common
devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power
Examples Motors heaters and Examples Motors heaters and other machinesother machines
22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
PowerPower 21) What are some common 21) What are some common
devices that do work and devices that do work and produceuse mechanical powerproduceuse mechanical power
Examples Motors heaters and Examples Motors heaters and other machinesother machines
22) Question Is Power a vector or 22) Question Is Power a vector or scalar quantityscalar quantity Work is scalar time scalarWork is scalar time scalarPower is a Scalar quantity no direction
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
PowerPower
23) How long would it take a 23) How long would it take a machine to do 1000J of work if machine to do 1000J of work if the power rating on the machine the power rating on the machine is 75 wattsis 75 watts
WP
t
100075
JW
t
133t s
1000
75
Given
W J
P W
t
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
Sample problemSample problem 25) A motor has an output of 20 25) A motor has an output of 20
watts When the motor is watts When the motor is working at full capacity how working at full capacity how long will it take to lift a 10 long will it take to lift a 10 Newton box 50 metersNewton box 50 metersW F d
Pt t
10 5020
N mW
t
10 50
20
N mt
W
25t s
20
50
10
Given
P W
d m
F N
t
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
Sample ProblemSample Problem26) A student with a mass of 660 kg 26) A student with a mass of 660 kg climbs up a ladder in 440 s If the climbs up a ladder in 440 s If the distance between the base and the top of distance between the base and the top of the ladder is 140 m how much power will the ladder is 140 m how much power will the student deliver by climbing the stairsthe student deliver by climbing the stairs
W F dP
t t
266 98 6468
mkg N
s
The force necessary to climb the ladder is equalto the weight of the student
gF mg
F dP
t
6468 14
44
N mP
s
2058W
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
ConceptualConceptual
27) Examine the Power formula 27) Examine the Power formula below How can we re-write it in below How can we re-write it in relation to movementrelation to movement
F dP
t
dvelocity
t P F v
As the velocity of an object increases does the rate at which energy is used increase or decrease assuming a constant force
Answer Power Increases
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
PowerPower
28) A 45kg cyclist climbs a hill at 28) A 45kg cyclist climbs a hill at a constant speed of 25ms by a constant speed of 25ms by applying an average force of 85 applying an average force of 85 Newtons How much power does Newtons How much power does the cyclist usethe cyclist useP F v 85 25mP N s 212P W
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
GraphsGraphs 29) What does the slope of a 29) What does the slope of a
Work vs Time graph representWork vs Time graph represent
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75 yslope
x
Wslope
t
Wslope Power
t
1)Write down a formula that uses the variables onthe x and y axis W
Pt
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
GraphGraph 30) How much power is 30) How much power is
developed by the system developed by the system represented by the graph belowrepresented by the graph below
Work
(J)
Time s
5
10
2 4 6 8 10 12
25
75
Wslope Power
t
75 0
10 0
J jPower
s s
075P W
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley
31) What is the power of the 31) What is the power of the Electric motorElectric motor
motor
1000kg
d=10mt = 20seconds
F dP
t
21000 98mF kgs
9800 10
20
N mP
s
4900P Watts
Pulley