Physics Work, Energy, and Machines · 2016-06-01 · Physics Work, Energy, and Machines ... Energy...
Transcript of Physics Work, Energy, and Machines · 2016-06-01 · Physics Work, Energy, and Machines ... Energy...
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Physics
Work, Energy, and Machines
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• Fd = work = change in energy
• PE = potential energy = mgh
• KE = kinetic energy = 1/2 mv^2
• Energy is conserved! (always)
• PE+KE stays the same
• Power = work / time, or change in energy / time
• mechanical advantage = F(out) / F(in)
• Proportional changes in energy when you change the height, mass, velocity.
• Find velocity, given KE and mass.
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Agenda
•Work/Conservation of Energy
•Kinetic and potential energy
•Formulas
•Conservation
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California State Standards
Physics: Conservation of Energy and Momentum
2. The laws of conservation of energy and momentum provide a way to predict and describe the movement of objects. As a basis for understanding this concept:
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California State Standards
a. Students know how to calculate kinetic energy by using the formula E = (1/2)mv2
b. Students know how to calculate changes in gravitational potential energy near Earth by using the formula (change in potential energy) = mgh (h is the change in the elevation).
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California State Standards
c. Students know how to solve problems involving conservation of energy in simple systems, such as falling objects.
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California State Standards
Physics: Heat & Thermodynamics
3. Energy cannot be created or destroyed, although in many processes energy is transferred to the environment as heat. As a basis for understanding this concept:
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Energy and Work
• Work = force x distance = change in energy
• Units are “Joules (J)” = Newton · meters Newton · meter = kg · m2/s2
• Energy is not a vector (no direction)
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Power
• Power = work / time or energy / time
• Joules/second or Watts
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Kinetic Energy
• KE = 1/2 mv2
• Double the speed = 4 times the KE
• Triple the speed = ? times the KE
• Quadruple the speed = ? times the KE
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Gravitational Potential Energy
• “Energy of position”
• PE = mgh (gravitational potential energy)
• m = mass
• g = acceleration of gravity (10 m/s2)
• h = height
• Twice the height = twice the PE
• Triple the height = ? times the PE
• Quadruple the height = ? times the PE
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Potential Energy (Stored Energy) (Gravitational)
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Potential Energy
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Potential Energy
• Only depends on height
• Does not depend on the path to get there
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Conservation of Energy
• If no friction, etc.:
• PE + KE = constant
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Conservation of Energy
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Path Doesn’t Matter
Only the change in height affects the kinetic energy Potential energy + Kinetic energy stays the same
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Path Doesn’t Matter
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Compute Potential Energy
• What is the PE of a 100 kg man on top of a 10 meter diving platform?
• PE = mgh
• PE = 100 kg x 10 m/s2 x 10 m = 10,000 J
• What is the PE of the man when he has fallen half the distance?
• 5,000 J
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Compute Kinetic Energy
• What is the KE and velocity of the man when he is half way down?
• KE = 1/2 mv2
• KE + PE = 10,000 J
• PE = 5000 J, so
• KE = (10,000 – 5000) J = 5000 J
• KE = 5000 N·m = 1/2 mv2
• v2 = (5000 x 2) / 100 kg = 100 m2/s2
• v = 10 m/s
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Sample Problems:
• How far does an object fall in “t” seconds?
• 1s: 0.5(10m/s/s)1^2= 5 m
• 2s: 0.5(10m/s/s)2^2= 20 m
• 5s: 0.5(10m/s/s)5^2= 125 m
• 6s: 0.5(10m/s/s)6^2= 180 m
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Cont.
• So, if something falls from 180 m, how high is it after “t” seconds?
• 1s: 180m – 5m = 175m
• 2s: 180m – 20m = 160m
• 5s: 180m – 125m = 55 m
• 6s: 180m – 180m = 0 m
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Cont.
• How much potential energy will those objects have after “t” seconds (assume 2kg mass)?
• 1s: 2kg x 10m/s/s x 175m = 3500 J
• 2s: 2kg x 10m/s/s x 160m = 3200 J
• 5s: 2kg x 10m/s/s x 55m = 1100 J
• 6s: 2kg x 10m/s/s x 0m = 0 J
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What’s the velocity after “t” seconds?
• 1s: 10m/s/s x 1s = 10m/s
• 2s: 10m/s/s x 2s = 20 m/s
• 5s: 10m/s/s x 5s = 50 m/s
• 6s: 10m/s/s x 6s = 60 m/s
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What is the kinetic energy after “t” seconds? (Still 2kg)
• 1s: 0.5 x 2kg x 10m/s x 10 m/s =100 J
• 2s: 0.5 x 2 kg x 20m/s x 20 m/s = 400 J
• 5s: 0.5 x 2 kg x 50m/s x 50 m/s = 2500 J
• 6s: 0.5 x 2 kg x 60m/s x 60 m/s = 3600 J
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Machines
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Machines
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Machines
• Can change the size of the force
• Increase or decrease
• By changing the distance
• Can also change the direction of the force
• Force is a vector (direction matters)
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Fd = Work = Change in Energy
This picture assumes no friction
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Machines Can Multiply Force and Change Direction
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Give me a lever long enough and a fulcrum on which to place it, and I shall move the world.
-Archimedes
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Machines Can Multiply Force
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Three Types of Levers
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Three Types of Levers
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The Law of See-Saws
In order to balance: F1 x D1 = F2 x D2
(your weight x your distance = their weight x their distance
F1
d1
F2
d2
Fulcrum
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The Law of See-Saws