Transcript Work Graphs & Power 1-14-15

Do Now
Two people exert a 10 Newton force for 2 meters.
Person 1 exerts the force at a 50 degree angle.
Calculate the work done on the box by each
person.
Person 1
W = Fdcosθ
= (10N)(2m)cos50˚
= 12.9 J
Person 2
W = Fdcosθ
= (10N)(2m)cos0˚
= 20 J
Net Work
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12) An object is pulled by a 20N force due
east for 5 meters and then due north by
the same force for 3 meters. How much
work was done?
W1 = (20N)(5m) = 100 J
W2 = (20N)(3m) = 60 J
R
5m
3m
WT= W2 + W3 = 160 J
Note: The net work is related to the path traveled,
It is NOT related to the resultant displacement.
Lifting
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14) I decide to get my pet frog to do a little
weight lifting (but I’m going to start him off
slow!). He lifts 2 kg up from the floor, over
his head 2 cm. How much work did he do?
Flift = Weight
W = F·d cosθ
Flift = mg = 2kg(9.8m/s2)
Flift = 19.6 N
Weight
W = (19.6N)(0.02m)
W = 0.392 J
Why is it easier to lift the boulder with this simple
machine than to pick it up directly?
Does it take less Work to lift the boulder this way?
1m
4m
Input Work = Output Work
W= 1N x 4m
W= 4N x 1m
4J
4J
Distance of Applied Force
Distance of
Output
Simple machines don’t change the amount of work
we do, but it can make work “easier” to do.
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In sports: Baseball bats, golf clubs, hockey
sticks, …
http://science360.gov/obj/video/c5be54562e39-49a7-8118-218868df89eb/work-energypower
Compound pulleys reduce the
force needed to do work.
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What distance would the rope have to be pulled
to make the weight rise 1 meter?
W = Fd
W = Fd
100 J = (25N)d
W = (100N)(1m)
d = (100J)/(25N)
W = 100 J
d = 4m
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15) The box in the diagram below needs to
be raised a distance of 50 meters. How
much work is required to lift the box
assuming the pulley is frictionless?
Begin by calculating the force necessary to
move the object.
x
F
20kg
Fg
Fg  mg
Fg  20kg 9.8 m 2
s
Fg  196 N
W F d
W  196 N 50m
W  9800 J
Graphs
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16) What does the slope of a Force versus
Displacement graph represent?
1) Write down a formula that uses the variables on
the x and y axis
W F d
Force (N)
y
slope 
x
F
slope 
d
Displacement (m)
F
 Nothing
d
Graphs
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17) What does the area under the curve
represent?
W F d
How do you find the area?
A  length height
Force (N)
A  displacement force
A F d
AREA
W F d
Area  Work
Displacement (m)
Graphs
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18) How much work was done on the 5 kg
object represented by the graph below?
A F d
Force (N)
10
W F d
7.5
Area  Work
5
W  5 N 11m
W  55 J
2.5
2
4
6
8
10
Displacement (m)
12
Graphs
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19) A Changing force acts on an object
represented by the graph below. How much
work was done on the object?
Area  Work
Force (N)
10
A 1 b h
2
7.5
A  1 10m 7.5 N
2
5
2.5
A  37.5 N m  Work
2
4
6
8
10
Displacement (m)
12
What is Power?
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Power is defined as the rate at which work or
energy is done or transformed.
=F·v
Units of Power
W
P
t
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20) What are the units for Power?
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Work is measured in joules, time in seconds
Joules
P
Second
1Joule
 1watt
1Second
Power is measured in Watts.
We will examine mechanical power rather than
Electrical power.
Power
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21) What are some common devices that do
work and produce/use mechanical power?
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Examples : Motors, heaters and other
machines.
22) Question? Is Power a vector or scalar
quantity?
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Work is scalar, time scalar.
Power is a Scalar quantity, no direction
Power
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23) How long would it take a machine to do
1,000J of work if the power rating on the
machine is 75 watts?
Given :
W  1,000 J
P  75W
t ?
W
P
t
1000 J
75W 
t
t  13.3s
Sample problem
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25) A motor has an output of 20 watts.
When the motor is working at full capacity,
how long will it take to lift a 10 Newton box
50 meters?
Given
P  20W
d  50m
F  10 N
t ?
W F d
P 
t
t
10 N  50m
20W 
t
10 N  50m
t
20W
t  25s
Sample Problem
26) A student with a mass of 66.0 kg climbs up a ladder
in 44.0 s. If the distance between the base and the top of
the ladder is 14.0 m, how much power will the student
deliver by climbing the stairs?
W F d
P 
t
t
The force necessary to climb the ladder is equal
to the weight of the student.
m
Fg  mg  66kg  9.8 2  646.8 N
s
F d
646.8 N 14m
P
P
t
44 s
 205.8W
Conceptual
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27) Examine the Power formula below, How
can we re-write it in relation to movement?
F d
P
t
d
 velocity
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
Power
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28) A 45kg cyclist climbs a hill at a constant
speed of 2.5m/s by applying an average force
of 85 Newtons. How much power does the
cyclist use?
PF v
P  85 N 2.5 m
s
P  212 W
Graphs
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29) What does the slope of a Work vs. Time
graph represent?
Work(J)
10
7.5
5
1) Write down a formula that uses the variables on
the x and y axis
W
P
t
y
slope 
x
W
slope 
t
2.5
2
4
6
8
Time s
10
12
W
slope  Power 
t
Graph
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30) How much power is developed by the
system represented by the graph below?
W
slope   Power
t
Work(J)
10
7.5
7.5 J  0 j
Power 
10s  0s
5
2.5
P  0.75W
2
4
6
8
Time s
10
12
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31) What is the power of the Electric motor?
Pulley
motor
1000kg
d=10m
t = 20seconds
F d
P
t
F  1000kg  9.8 m
9800 N 10m
P
20 s
P  4900Watts
s2