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Physics 218, Lecture XIV 1
Physics 218Lecture 14Dr. David Toback
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Physics 218, Lecture XIV 2
Checklist for Today•Things due awhile ago:–Read Chapters 7, 8 & 9
•Things that were due Yesterday:–Problems from Chap 7 on WebCT
•Things that are due Tomorrow in Recitation–Chapter 8–Reading for Lab
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Physics 218, Lecture XIV 3
The ScheduleThis week: (3/3) • Chapter 7 due in WebCT• 5th and 6th lectures (of six) on Chapters 7, 8 & 9• Chapter 8 in recitation Next week: (3/10) Spring Break!!!Following Week: (3/17)• Chapter 8 due in WebCT• Reading for Chapters 10 & 11• Lecture on Chapters 10 & 11• Chapter 9 and Exam 2 Review in recitation Following Week: (3/24)• Chapter 9 due in WebCT• Exam 2 on Tuesday• Recitation on Chapters 10 & 11• Reading for Chapters 12 & 13 for Thursday• Lecture 12 & 13 on Thursday
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Physics 218, Lecture XIV 4
Before:– Work and Energy– The Work-Energy relationship– Potential Energy– Conservation of Mechanical Energy
This time and next time:– Conservation of Energy– Lots of problems
Chapters 7, 8 & 9 Cont
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Physics 218, Lecture XIV 5
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Physics 218, Lecture XIV 6
Different Style Than the Textbook
I like teaching this material using a different style than the textbook
1. Teach you the concepts2. Give you the important
equations3. Then we’ll do lots of problems
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Physics 218, Lecture XIV 7
Mechanical Energy
•We define the total mechanical energy in a system to be the kinetic energy plus the potential energy
•Define E≡K+U
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Physics 218, Lecture XIV 8
Conservation of Mechanical Energy• For some types of problems, Mechanical
Energy is conserved (more on this next week)
• E.g. Mechanical energy before you drop a brick is equal to the mechanical energy after you drop the brick
K2+U2 = K1+U1Conservation of Mechanical Energy
E2=E1
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Physics 218, Lecture XIV 9
Problem Solving• What are the types of examples we’ll encounter?– Gravity– Things falling– Springs
• Converting their potential energy into kinetic energy and back againE = K + U = ½mv2 + mgy
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Physics 218, Lecture XIV 10
Z Z
Before After
C
Falling onto a SpringWe want to measure the spring constant of a certain spring. We drop a ball of known mass mfrom a known height Zabove the uncompressed spring. Observe it compresses a distance C.
What is the spring constant?
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Physics 218, Lecture XIV 11
Quick Problem
A refrigerator with mass M and speed V0 is sliding on a dirty floor with coefficient of friction μ.
Is mechanical energy conserved?
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Physics 218, Lecture XIV 12
Non-Conservative Forces•We’ve talked about three different types of forces:1.Gravity: Conserves mechanical
energy2.Normal Force: Conserves
mechanical energy (doesn’t do work)
3.Friction: Doesn’t conserve mechanical energy
•Since Friction causes us to lose mechanical energy (doesn’t conserve mechanical energy) it is a Non-Conservative force!
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Physics 218, Lecture XIV 13
Law of Conservation of Energy• Mechanical Energy NOT always conserved
• If you’ve ever watched a roller coaster, you see that the friction turns the energy into heating the rails, sparks, noise, wind etc.
• Energy = Kinetic Energy + Potential Energy + Heat + Others…–Total Energy is what is conserved!
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Physics 218, Lecture XIV 14
Conservative ForcesIf there are only conservative forces in the
problem, then there is conservation of mechanical energy
• Conservative: Can go back and forth along any path and the potential energy and kinetic energy keep turning into one another– Good examples: Gravity and Springs
• Non-Conservative: As you move along a path, the potential energy or kinetic energy is turned into heat, light, sound etc… Mechanical energy is lost.– Good example: Friction (like on Roller Coasters)
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Physics 218, Lecture XIV 15
Law of Conservation of Energy• Even if there is friction, Energy is conserved
• Friction does work– Can turn the energy into heat– Changes the kinetic energy
•Total Energy = Kinetic Energy + Potential Energy + Heat + Others…– This is what is conserved
• Can use “lost” mechanical energy to estimate things about friction
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Physics 218, Lecture XIV 16
Roller Coaster with FrictionA roller coaster of mass m starts at rest at height y1 and falls down the path with friction, then back up until it hits height y2 (y1 > y2). Assuming we don’t know anything about the friction or the path, how much work is done by friction on this path?
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Physics 218, Lecture XIV 17
Energy SummaryIf there is net work done on an object, it
changes the kinetic energy of the object (Gravity forces a ball falling from height hto speed up Work done.)
Wnet = ΔKIf there is a change in the potential energy,
some one had to do some work: (Ball falling from height h speeds up→ work done → loss of potential energy. I raise a ball up, I do work which turns into potential energy for the ball)
ΔUTotal = WPerson =-WGravity
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Physics 218, Lecture XIV 18
Energy SummaryIf work is done by a non-conservative force
it does negative work (slows something down), and we get heat, light, sound etc.
EHeat+Light+Sound.. = -WNCIf work is done by a non-conservative
force, take this into account in the total energy. (Friction causes mechanical energy to be lost)
K1+U1 = K2+U2+EHeat…K1+U1 = K2+U2-WNC
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Physics 218, Lecture XIV 19
Friction and SpringsA block of mass m is traveling on a rough surface. It reaches a spring (spring constant k) with speed Vo and compresses it a total distance D. Determine μ
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Physics 218, Lecture XIV 20
ll
Bungee JumpYou are standing on a
platform high in the air with a bungee cord (spring constant k) strapped to your leg. You have mass m and jump off the platform.
1.How far does the cord stretch, l in the picture?
2.What is the equilibrium point around which you will bounce?
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Physics 218, Lecture XIV 21
Coming up…•Lectures:– Last lectures on Chaps 7, 8 and 9
•Chapter 7 was due in WebCT on Monday
•For Recitation– Chap 8 problems due – Lab reading
•Reading for Lecture next week– Chaps 10 & 11: Momentum