Energy + Power Energy of Motion and Simple Machines.
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Transcript of Energy + Power Energy of Motion and Simple Machines.
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Energy + Power
Energy of Motion and Simple Machines
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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
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1 m/s
KE = 1/2 mv2
KE = 1/2 2kg (1m/s)2
KE = 1 kg m 2 /s 2 = 1 Joule (J)
Kinetic Energy of a two liter bottle of water moving at 1 m/s
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Gravitational Potential Energy is simply energy afforded by relative height, the potential to fall. This energy can convert toKinetic Energy.
So, lets say a 100 kg person stands on a 10 m cliff near sea levelGPE = mgh
GPE = (100kg)(9.8m/s2)(10m)
GPE = 9800 kgm2/s2
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James Prescott Joule:
British largely self-trained physicist1818-1889
Fascinated by electricity, he and his brother usedto experiment by giving shocks to each other and the family servants
Credited with the First law ofThermodynamics
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Mechanical Equivalent of Heat
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The falling mass yields energy according to GPE = mgh
The water gains heat Energy by being stirred…Kinetic energy, temperature
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A visit with Tarzan and family:
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50 m above the forest floor, the Tarzans wait to swing.
100 kg Tarzan swings and grabs a banana from the forest floor. How fastIs he going?
Why can’t he make it back to the branch hestarted on?
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Tarzan’s 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
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Why doesn’t Tarzan make it back to the branch? Energy is lost…to the system:
Drag in air…air and vine get warmer as Tarzan swings.
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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
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So lets say I push the mower for 60 m with a force of 200 N at a50 degree angle to the horizontal. How much work gets done on my lawn mower.
W = F d cos
W = (200N)(60m)(cos
W = 7700 J
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Lift a wheelbarrow at 30o above the
horizontal, push for 75 m, with a force of
500 N • W = F d cos • W = (500N)(75m) (cos
• W = 32,500 J
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Backing a wheelbarrow up a stair makes the pulling vector more in alignment with the direction of desired work
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Power is the rate at which work or energy can be produced
P = W/t
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Power is the rate at which work or energy can be produced
P = W/t Power is measured in J/s = Watts
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Power Plant
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Atlantic City wind turbines
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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
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http://www.njwind.com/webcam.html
Atlantifc city wind turbines each produces 1.5 MW
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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)
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Simple Machines:mechanical advantage
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Lever terminology
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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)
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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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A Third class lever
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A machine can increase force but it can’t increase energy…
Great Moments in Physics:
2006Jake Wulff invents “Privy Prop”
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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
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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
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The ratio of lengths of lever to fulcrum are the same as de:dr• Longer lever,
more mechanicaal advantage
• MA = Fr/Fe
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Let’s 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
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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%
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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 spot”…How much force do I apply there?
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Third class lever: a bat
• Fe de= Fr dr
• (200N)(.05m) = Fr(0.6m)• 16.7 N…so why does the bat work?
• The distance traveled by a mass at the end is much greater, so much faster
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• 3 vertical lines raising object…
• MA = 3
• Fr = 600N
• What’s Fe ?
• Fe = 200N
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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…
10 N
Fe
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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
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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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MA for inclined planes
slope
rise
MA = slope/rise
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The Inclined Plane at Ronquieres,Belgium: a moving boat lock.
Slope is 1432 m longRise is 68 m high
MA = ?
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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?
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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)
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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
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Work Input in the Roquières Inclined
Plane• It will require 2.23 x 106 N to move the caisson.
• Its got to move 1432m…W = Fd
• W = 2.23 x 106 N x 1432m
• W = 3.192 x 109 N-m
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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
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Another type
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Elastic Potential Energy (U)
• U = average F X d
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Henry V
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Agincourt
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Falkirk
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What stretches?
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If the spring constant (k) is knownU = Elastic potential energyX = the draw length
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A bow stores potential energy
U = 1/2 Ffd dU = 1/2 (45lbs)( 4.45N/lb) (0.38m)U = (100N) (0.38m)U = 38 Joules
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The bow converts the elastic potential to
Kinetic EnergyKE = 1/2mv2
38 Joules = (1/2) 0.035 kg)(v2)
v = 46.6 m/s
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If the arrow is fired at 45o what is the
range?
R = vo2 sin2
g
R = (46.6m/s)2 sin2(45o 9.8 m/s2
R = 220 m
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OK so let’s 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 sin2/g
R = vo sin2(/g
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OK so let’s 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 sin2/g
R = vo sin2(/g
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A compound bow
cam
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4186.8 J/Kcal
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