Physics 218, Lecture XIII 1

Physics 218Lecture 13Dr. David Toback

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Checklist for Today•Things due for Last Thursday:–Read Chapters 7, 8 & 9

•Things that were due Last Monday:– Chap 5&6 turned in on WebCT

•Things that were due for Wednesday’s Recitation:– Problems from Chap 7

•Things due for this coming Monday:– Problems from Chap 7 on WebCT– Chaps 5&6 if you haven’t done them already

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The ScheduleThis week: (2/25) • HW on Chaps 5&6 on WebCT• 3rd and 4th lectures (of six) on Chapters 7, 8 & 9• Chapter 7 in recitationNext week: (3/3) • Chapter 7 due in WebCT• 5th and 6th lectures (of six) on Chapters 7, 8 & 9• Chapter 8 in recitation Following 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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Last time:– Work and Energy– The Work-Energy relationship

This time and next time:– Potential Energy– Conservation of Mechanical Energy– 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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Potential Energy•Things with potential: COULD do work– “This woman has great potential as an engineer!”

•Here we kinda mean the same thing•E.g. Gravitation potential energy:– If you lift up a brick it has the potential to do damage

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Example: Gravity & Potential Energy

You lift up a brick (at rest) from the ground and then hold it at a height Z

• How much work has been done on the brick?

• How much work did you do?• If you let it go, how much work will be done by gravity by the time it hits the ground?

We say it has potential energy: U=mgZ

–Gravitational potential energy

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Other Potential Energies: Springs

Last week we calculated that it took ½kx2 of work to compress a spring by a distance xHow much potential energy does it now how have?U(x) = ½kx2

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Force and Potential EnergyIf we know the potential energy, U, we can find the force

This makes sense… For example, the force of gravity points down, but the potential increases as you go up

dxdU

x −=

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Force and Potential Energy

Draw some examples…–Gravity–Spring

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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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Problem Solving

For Conservation of Energy problems:

BEFORE and AFTER diagrams

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Conservation of Energy Problems

Before…

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After

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Quick Problem

We drop a ball from a height D above the ground

Using Conservation of Energy, what is the speed just before it hits the ground?

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Potential EnergyA brick held 6 feet in the air has potential energy

•Subtlety: Gravitational potential energy is relative to somewhere!

Example: What is the potential energy of a book 6 feet above a 4 foot high table? 10 feet above the floor?

• ΔU = U2-U1 = Wext = mg (h2-h1)•Write U = mgh•U=mgh + ConstOnly change in potential energy is really meaningful

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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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Coming up…•Lectures:– Last lectures on Chaps 7, 8 and 9

•HW due in WebCT on Monday– Chapter 7

•Reading for Lecture next week– Chaps 10 & 11: Momentum

•Recitation next week – Chapter 8