Physics 218, Lecture XVII1 Physics 218 Lecture 17 Dr. David Toback.
Physics 218 Lecture 12tobackgroup.physics.tamu.edu/toback/218/LastSemester/Lecture12.… · Physics...
Transcript of Physics 218 Lecture 12tobackgroup.physics.tamu.edu/toback/218/LastSemester/Lecture12.… · Physics...
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Physics 218, Lecture XII 1
Physics 218Lecture 12Dr. David Toback
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Physics 218, Lecture XII 2
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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Physics 218, Lecture XII 12
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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Physics 218, Lecture XII 17
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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