Energy and Transformation

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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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Some 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.
• It takes energy to do work.
• Less stored energy is available after productive
  work is done.

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Physics Definition of Work
Work, W SI Unit J (N)(m) Work is the
useful part of a force times the distance the
object moves (s) useful means in direction of
motion
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Example of Work
Given F 80N, Angle is 40, Dx is 11m,
Work FcosqDx (80N)(cos40)(11m) 674 J
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Energy

• Kinetic, K energy of motion K ½mv2.
• Ex 2000kg car moving at 10m/s has kinetic energy
  of 100,000J.
• Potential, U stored energy
• Ex One gallon of gasoline stores 138,000,000J.

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Work-Energy Theorem The net work done on an
object is equal to its change in Kinetic Energy.
Example The net work done on a 20kg mass is
250J. If the mass started from rest its final
speed is 5m/s ½(20)52 0 250.
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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 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 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 s is 90,
  cos90 0.

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The Dot Product
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Example A (1, 1, 1), B (5, 0, 0)
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Example Find the angle between A (1, 1, 1)
and B (5, 0, 0)
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2006 Ford MustangCurb Weight 3450 lbs.
Performance Acceleration (0-60 mph) 5.1 sec.
Braking Distance (60-0 mph) 121.37 ft. Engine
Type V8 Horsepower 300 hp
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What size motor?
Cube of bricks 1 ton 1 ton 2000 lbs 9000 N
Operating Speed 10cm/s
Minimum Power P Fv (9000N)(0.1m/s) P
900 W 1.2 hp
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Types of Energy

• Kinetic, K energy due to motion
• Potential, U energy due to position

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Some Potential Energies

• Spring Us
• Gravitational Ug
• Thermal Uth
• Chemical Uch
• We use the first three of these.

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Springs

• Fs -kx, Us 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 A 2kg object experiences weight
  (2kg)(9.8N/kg) 19.6N. At 3m above the floor it
  has a stored energy of (2kg)(9.8N/kg)(3m)
  48.8Nm 48.8J.

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Conservation of Energy

• Individual energy levels change.
• Sum of all individual energies is constant.
• Change in energy is called work

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Energy Conservation

• Total Energy E sum of all energies
• E SK SU
• example
• t 0 K 0J, U 4000J
• later K 2000J, U 2000J

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K
E
Ug
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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
1
2
3
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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.
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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-thermal PE-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 19.6 PE-elastic 9.8J
Calculate v4 (use 1st and 4th columns) ½ m(v4)2
PE-thermal mg(1) ½ m(v4)2 9.8 19.6 ½
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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Example How much average power is needed to
accelerate a 2000kg car from rest to 20m/s in
5.0s?
work DKE
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Horsepower 1 hp 746 watts
For the previous example
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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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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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An object moves in a vertical circle with
constant mechanical energy.

• What does this imply about its speed?

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A mass on a string moves in a horizontal circle.

• Does the tension in the string vary?
• Does the tension in the string do work on the
  mass?

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Mechanical Advantage

• F1d1 F2d2 (E conservation)
• F2/F1 d1/d2 mechanical advantage
• Example A Jack moves a car 10cm upward with
  fifty 20cm strokes. Mechanical advantage is
  50x20/10 100.

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