Physics 218, Lecture XII 1

Physics 218Lecture 12Dr. David Toback

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This week…

• This week we will finish up Chapters 6 & 7–Last set of topics for Exam 2

• Exam 2: Thurs, October 26th

• Covers chapters 1-7

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The ScheduleThis week: (10/9) • Finish up Chapters 6&7 in lecture• Chapter 6 in recitationNext week: (10/16) • Chapter 6 HW due• Chapter 8 in lecture (reading questions due)• Chapter 7 in recitationFollowing week: (10/23)• HW 7 due• Chapter 9 in lecture on Tuesday (reading questions due)• Chapter 8 in Recitation• Exam 2 on Thursday October 26th

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Energy• Conservation of

Mechanical Energy problems

• Conservative Forces• Conservation of Energy

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

meaningful

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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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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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Z Z

Before After

C

Falling onto a Spring

We 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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Roller CoasterYou are in a roller coaster car of mass M that

starts at the top, height Z, with an initial speed V0=0. Assume no friction.

a) What is the speed at the bottom?b)How high will it go again?c) Would it go as high if there were friction?

Z

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Non-Conservative Forces• In this problem there are three different

types of forces acting:1. Gravity: Conserves mechanical energy2. Normal Force: Conserves mechanical

energy3. 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 on an object, it changes the

kinetic energy of the object (Gravity forces a ball falling from height h to speed up Work done.)

Wnet = ∆KIf there is a change in the potential energy, some one

had to do some work: (Ball falling from height hspeeds up→ work done → loss of potential energy. I raise a ball up, I do work which turns into potential energy for the ball)

∆UTotal = WPerson =-WGravity

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Energy Summary

If 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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Next time…

•More problems on Chapters 6 & 7

•Recitation on Chapter 6 problems

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