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Energy Power

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Title: Energy Power


1
Energy Power
  • Energy of Motion and Simple Machines

2
Energy Comes in many forms among these
  • Kinetic Energy
  • (Energy of moving Objects)
  • KE 1/2 mv2
  • Gravitational Potential Energy
  • (Energy of falling objects)
  • PE mgh

3
Kinetic Energy of a two liter bottle of water
moving at 1 m/s
KE 1/2 mv2 KE 1/2 2kg (1m/s)2 KE 1 kg m 2
/s 2 1 Joule (J)
1 m/s
4
Gravitational Potential Energy is simply energy
afforded by relative height, the potential to
fall. This energy can convert to Kinetic
Energy. So, lets say a 100 kg person stands on a
10 m cliff near sea level GPE mgh GPE
(100kg)(9.8m/s2)(10m) GPE 9800 kgm2/s2
5
James Prescott Joule
British largely self-trained physicist 1818-1889
Fascinated by electricity, he and his brother
used to experiment by giving shocks to each
other and the family servants Credited with the
First law of Thermodynamics
6
Mechanical Equivalent of Heat
7
The falling mass yields energy according to GPE
mgh
The water gains heat Energy by being
stirred Kinetic energy, temperature
8
A visit with Tarzan and family
9
50 m above the forest floor, the Tarzans wait to
swing. 100 kg Tarzan swings and grabs a banana
from the forest floor. How fast Is he
going? Why cant he make it back to the branch
he started on?
10
Tarzans Swing
  • GPE mgh
  • GPE (100kg)(9.8 m/s2)(50m)
  • GPE 49,000 Joules
  • If all GPE becomes KE at the bottom of the Swing
    GPE KE 1/2 mv2
  • 49,000 kgm2/s2 1/2 100kg v2
  • v 31.3 m/s 112 km/h

11
Why doesnt Tarzan make it back to the branch?
Energy is lost to the system
Drag in airair and vine get warmer as Tarzan
swings.
12
Energy is the ability to do Work (W) W Fd
Lets say I push with a 500 N Force for 100 m W
50,000 N-m W 50,000 J
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Force exerted at an angle to the direction of
effective work is proportional to the cosine of
the angle W F d cos Q
16
So lets say I push the mower for 60 m with a
force of 200 N at a 50 degree angle to the
horizontal. How much work gets done on my lawn
mower. W F d cos Q W (200N)(60m)(cos
50o) W 7700 J
17
Lift a wheelbarrow at 30o above the horizontal,
push for 75 m, with a force of 500 N
  • W F d cos Q
  • W (500N)(75m) (cos 30o)
  • W 32,500 J

18
Backing a wheelbarrow up a stair makes the
pulling vector more in alignment with the
direction of desired work
19
Power is the rate at which work or energy can be
produced P W/t
20
Power is the rate at which work or energy can be
produced P W/t
Power is measured in J/s Watts
21
Power Plant
22
Atlantic City wind turbines
23
Wind Power, rate produced
  • (3) 50m x 1 m blades in a 10 m/s wind.
  • Air has a density of about 1.2 kg/m3
  • 150 m2 hit w/ 1.2 kg/m3 x 10 s 1800 kg/s
  • KE/s (1/2 mv2 ) /s
  • KE/s (1/2 1800 kg (10 m/s)2 )/s
  • KE/s (90,000 kg m 2 /s2 )/s
  • KE/s 90,000 J/s 90 kW

24
Atlantifc city wind turbines each produces 1.5 MW
http//www.njwind.com/webcam.html
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Hoover Dam, CA NV
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A 50 m Hydroelectric Dam 1 m3 water passes the
turbine in 0.6 s
  • What power is produced?
  • PE/s 1/2 mgh/t
  • PE/s 1/2(1000kg)(9.8m/s2)(50m)
  • /(0.6s)
  • PE/s 408,000 W Power of that turbine

(avg PE for water column 1/2mgh)
30
Simple Machinesmechanical advantage
31
Lever terminology
32
Advantage of lever Force ratios are proportional
to lever arms
  • MA Fr/Fe
  • MA mechanical advantage
  • Fr resistance force (exerted by the
    machine)
  • Fe exertion force (exerted by you)

33
What force is necessary in the gluteus maximus
to lift 115 lbs if the torso is 10x the length
of the pelvis?
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35
A Third class lever
36
A machine can increase force but it cant
increase energy
Great Moments in Physics 2006 Jake
Wulff invents Privy Prop
37
What kind of lever is Homer?
  • Homer has a fulcrum at his waist, so 1st class
  • If you push his head down 5cm with a force of 40
    N, how much force is applied to lift the edge of
    the cap rising 0.5 cm?
  • Wi Wo, Fed Frd
  • (40N)( .05m) Fr(.005m)
  • 400N Fr

38
What kind of lever is this?
  • Fulcrum ahead of the resistance, so 2nd class
  • If you push the handle down 4 cm with a
    force of 40 N, how much force is applied to lift
    the edge of the cap rising 0.5 cm?
  • Wi Wo, Fed Frd
  • (40N)( .04m) Fr(.005m)
  • 320 N Fr

39
The ratio of lengths of lever to fulcrum are the
same as dedr
  • Longer lever, more mechanicaal advantage
  • MA Fr/Fe

40
Lets say the rock is 1500 N the man weighs 1000.
N, the lever is 3 meters long and the fulcrum is
placed 1 meter from the end
  • Whats the AMA
  • MA Fr/Fe
  • MA 1500N/1000N
  • AMA 1.5

41
How efficient is this system?
  • AMA/ IMA Efficiency
  • 1.5/2 75
  • Or Wout/Win Efficiency
  • Eff (1500 N) 0.1m /(1000N) 0.2
  • 75

42
What does a bat do?
  • Lets say I can swing with a force of 200N, my
    second hand is the fulcrum, 5 cm away. The bat
    is 60 cm to the sweet spotHow much force do I
    apply there?

43
Third class lever a bat
  • Fe de Fr dr
  • (200N)(.05m) Fr(0.6m)
  • 16.7 Nso why does the bat work?
  • The distance traveled by a mass at the end is
    much greater, so much faster

44
  • 3 vertical lines raising object
  • MA 3
  • Fr 600N
  • Whats Fe ?
  • Fe 200N

45
Block fixed to ceiling, single line through block
attached to mass
  • Observe number of lines lifting object
  • MA
  • 1
  • Fe then is ?
  • 10 N
  • This pulley just changes direction of effort

Fe
10 N
46
Cable fixed to ceiling, single block attached to
mass
  • Observe number of lines, twice the distance of
    cable would be used
  • MA
  • 2
  • Fe then is ?
  • 5 N

10 N
47
Block and tackle fixed to ceiling,
  • Observe number of lines, quadruple the distance
    of cable would be used
  • MA
  • 4
  • Fe then is ?
  • 2.5 N
  • What about friction?

10 N
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49
MA for inclined planes
slope
rise
MA slope/rise
50
The Inclined Plane at Ronquieres,Belgium a
moving boat lock.
Slope is 1432 m long Rise is 68 m high MA ?
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52
91m x 12m x 3.5m of water in a caisson with a
mass of 10 tones
Assuming 80 efficiency what is the force
necessary to raise to lock?
53
Effort force at the Roquières Inclined Plane
  • (91m x 12 x 3.5m) 10 tones 3833 tones
  • 3,833,000 kg x 9.8 m/s2 Fr
  • Fr 3.75634 x 107 N
  • MA s/r 1432m / 68m
  • MA 21.06
  • MA Fr/Fe
  • Fe 3.75634 x 107 N / 21.06
  • Fe 1.78 x 106N (for ideal mechanical advantage)

54
Efficiency of the Roquières Inclined Plane
  • Fe 1.78 x 106N (for ideal mechanical
    advantage)
  • But friction causes reduced mechanical advantage
    or Actual Mechanical Advantage (AMA)
  • Efficiency AMA/IMA Fo/Fi Wo/ Wi
  • Efficiency 80 0.8 1.78 x 106N / Fi
  • It will require 2.23 x 106 N to move the caisson

55
Work Input in the Roquières Inclined Plane
  • It will require 2.23 x 106 N to move the caisson.
  • Its got to move 1432mW Fd
  • W 2.23 x 106 N x 1432m
  • W 3.192 x 109 N-m


56
Power Input in the Roquières Inclined Plane
  • It takes 45 minutes total, 20 minutes to rise, at
    a speed of 1.2 m/s.
  • How much power is required to move the caisson?
  • 2.23 x 106 N to move the caisson.
  • P Fv
  • P 2.23 x 106 N x1.2 m/s
  • P 2.68 x 106 N-m/s 2.68 MW
  • P W/t
  • P (3.192 x 109N-m) / (20min)(60s/min)
  • P 2.66 x 106 W 2.66 MW


57
Another type
58
Elastic Potential Energy (U)
  • U average F X d

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Henry V
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Agincourt
64
Falkirk
65
What stretches?
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If the spring constant (k) is known U Elastic
potential energy X the draw length
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A bow stores potential energy
U 1/2 Ffd d U 1/2 (45lbs)( 4.45N/lb)
(0.38m) U (100N) (0.38m) U 38 Joules
70
The bow converts the elastic potential to Kinetic
Energy
KE 1/2mv2 38 Joules (1/2) 0.035 kg)(v2) v
46.6 m/s
71
If the arrow is fired at 45o what is the range?
R vo2 sin2q
g
R (46.6m/s)2 sin2(45o)
9.8 m/s2
R 220 m
72
OK so lets fire an arrow into the air. If our t
is really half the flight
v vo at, so vo 9.8 m/s2 (t/2)
Range R vo sin2q/g R vo sin2(45o)/g
73
OK so lets fire an arrow into the air. If our t
is really half the flight
v vo at, so vo 9.8 m/s2 (t/2)
Range R vo sin2q/g R vo sin2(45o)/g
74
A compound bow
cam
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4186.8 J/Kcal
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