1 5 overview energy and the joule unit. energy transformation. energy storage. power and watt unit....
TRANSCRIPT
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5 Overview
• Energy and the Joule Unit.
• Energy transformation.
• Energy storage.
• Power and Watt Unit.
• Homework:
• 2, 6, 9, 11, 13, 15, 27, 33, 37, 45, 49, 53, 75, 77, 79, 81, 85, 101.
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Energy and Transformation
• chemical fuel energy vehicle motion
• electric energy turning mixer, drill, etc.
• wind turbine electrical energy turn mixer
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definitions
• Energy: The work that a physical system is capable of doing in changing from its actual state to a specified reference state … (American Heritage Dictionary)
• Energy: The capacity to do work. (Physics)
• What is Work?
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Work
• Work is force x distance.
• energy required
• Less stored energy is available after productive work is done.
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Work
Work, W SI Unit: J = (N)(m)
Work ~ component of force in direction of motion.
dFWF )cos(
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Example of Work
Work = Fcosx = (80N)(cos40)(11m) = 674 J
Given: F = 80N, Angle is 40°, x is 11m,
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Energy
• Positional (Potential), e.g. compressed spring
• Motional (Kinetic), e.g. moving car
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Energy
• Kinetic, K: energy of motionK = ½mv2.
• Ex: 2000kg car moving at 10m/s has kinetic energy of 100,000J.
• Potential, U: stored energy
• Ex: 1 gallon of gasoline > 100,000,000J.
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Work-Energy Theorem: The net work done on an object is equal to its change in Kinetic Energy.
2212
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ifnet mvmvW
Ex. Net work = 250J. If m = 20kg, vo = 0, Then final speed is 5m/s: 250 = ½(20)52 – 0.
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Example
• A 20kg mass is moving at 5m/s. 250J of work (net) are done on it. What is its final speed?
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• A 20kg block slides across a floor. The frictional force on it is 50N. How much work is done on the block by friction in moving 3m?
• If its initial speed was 5m/s, what is its speed after moving 3m?
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• A 20kg block is pushed with 75N of force. The frictional force on it is 50N. How much net work is done on the block in moving 3m?
• If its initial speed was 5m/s, what is its speed after moving 3m?
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• How much work does a force perpendicular to an objects displacement do?
• Answer: Zero. The angle between F and displacement is 90, cos90 = 0.
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Some Potential Energies
• Spring: Usp.
• Gravitational: Ug
• Thermal: Uth
• Chemical, Nuclear
• first three used in this class
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Springs
• Fsp = -kx, Usp = ½kx2.
• k = “spring constant” in N/m and x is the change in length of the spring.
• Ex: A 100N/m spring is compressed 0.2m. It exerts (100N/m)(0.2m) = 20N of force. It stores ½(100N/m)(0.2m)2 = 2J of energy.
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Gravity
• Fg = mg, Ug = mgy
• Ex: 2kg weighs (2kg)(9.8N/kg) = 19.6N. 3m above floor
Ug = (2kg)(9.8N/kg)(3m) = 48.8J.
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Conservation of Energy
• Individual energy levels change.
• Net energy is constant.
• Change in energy is called “work”
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Energy Conservation
• Total Energy E = sum of all energies
• E = K + U
• example:
• t = 0: K = 0J U = 4000J
• later: K = 3000J U = 1000J
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Conservation of Energy
Example: Falling Ball
KE increases
U (gravitational) decreases
E = K + Ug = constant
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Energy E1 E2 E3
Kinetic 0 ½mv22 0
PE-g 0 0 mgh
PE-spring
½kx2 0 0
Totals
½kx2 ½mv22 mgh
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Energy E(h) E(y)
Kinetic 0 ½mv2
PE-g mgh mgy
Totals mgh ½mv2 + mgy
Energies and speeds are same at height y
Accelerations at y are not same
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Energy Ei Ef
Kinetic ½mvi2 0
PE-g 0 0
Thermal 0 fks
Totals ½mvi2 fks
Example: The smaller the frictional force fk, the larger the distance, s, it will travel before stopping.
s
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A 2.00kg ball is dropped from rest from a height of 1.0m above the floor. The ball rebounds to a height of 0.500m. A movie-frame type diagram of the motion is shown below.
Type E1 E2 E3 E4 E5
gravita-tional
mg(1) 0 0 0 mg(1/2)
kinetic 0 ½ m(v2)2 0 ½ m(v4)2 0
elastic 0 0 PE-elastic 0 0
thermal 0 0 PE-thermal PE-thermal PE-thermal
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By energy conservation, the sum of all energies in each column is the same, = E1 = mg(1) = 19.6J
Calculate v2: (use 1st and 2nd columns)mg(1) = ½ m(v2)2.
g = ½ (v2)2.v2 = 4.43m/s
Calculate PE-thermal: (use 1st and 5th columns)mg(1) = mg(1/2) + PE-thermal
mg(1/2) = PE-thermalPE-thermal = 9.8J
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Calculate PE-elastic: (use 1st and 3rd columns)PE-elastic + PE-thermal = mg(1)
PE-elastic + 9.8 = 19.6PE-elastic = 9.8J
Calculate v4: (use 1st and 4th columns)½ m(v4)2 + PE-thermal = mg(1)
½ m(v4)2 + 9.8 = 19.6½ m(v4)2 = 9.8 (v4)2 = 2(9.8)/2
v4 = 3.13m/s
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Terminology
• E: total energy of a system
• E-mech = total energy minus the thermal energy
• E-mech = E – Uth.
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Power: The time rate of doing work.
SI Unit: watt, W = J/s]time
workPavg
Example: How much average power is needed to accelerate a 2000kg car from rest to 20m/s in 5.0s?
work = KE 2212
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if mvmv 2
212
21 )/0)(2000()/20)(2000( smkgsmkg
J000,400
s
J
t
workPavg 0.5
000,400 watts000,80
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avgavg vFt
sF
t
sF
t
WP )(cos)(cos
)(cos
Another equation for Power:
Ex: A car drives at 20m/s and experiences air-drag of 400N. The engine must use (400N)(20m/s) = 8,000 watts of engine power to overcome this force. 8,000 watts = 10.7 hp.
What air drag force acts at 40m/s? How much hp is needed to overcome this drag?
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Summary
• Energy measured in joules, related to motion (kinetic) or configuration (potential)
• work is an energy transfer mechanism (thus can be + or -)
• power is the rate of energy transfer in joules/s = watts
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hpwatt
hpwatts107
746
1000,80
Horsepower: 1 hp = 746 watts
For the previous example:
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What size electric motor is needed to raise 2000lbs = 9000N of bricks at 10cm/s?
Minimum Power:
Pavg = Fvavg = (9000N)(0.1m/s)
P = 900 W = 1.2 hp
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