Physics 218, Lecture XIV 1

Physics 218Lecture 14Dr. David Toback

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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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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