Physics 218, Lecture XXIV1 Physics 218 Lecture 24 Dr. David Toback.
Physics 218, Lecture XXIII1 Physics 218 Lecture 23 Dr. David Toback.
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Transcript of Physics 218, Lecture XXIII1 Physics 218 Lecture 23 Dr. David Toback.
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Physics 218, Lecture XXIII 1
Physics 218Lecture 23 Dr. David Toback
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Physics 218, Lecture XXIII 2
Schedule for the Rest of the Semester
• Today: Chapter 13, Part 2
• Next Tuesday: Final Exam Review – I’ll give you a handout at the end of class
No lectures next Thursday, Reading day
Final exam is Monday December 11th
We will skip Chapter 15
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Physics 218, Lecture XXIII 3
Next Semester
Some of you continue to ask about next semester:
• I am NOT teaching 208
• However I am planning on teaching a new course: “Big Bang, Black Holes, No Math”
– Cosmology Without The Math
– Based on “A Brief History of Time” by Stephen Hawking
– If you can’t take it, you might pass this info along to friends
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Physics 218, Lecture XXIII 4
Chap 13 Overview: Oscillations• Last time:
– Oscillations and vibrations
– Equations of motion
– Our spherical cow: Mass on a spring
– Simple Harmonic Motion
• This time:– Energy
– Uniform Circular Motion
– Pendulums
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Physics 218, Lecture XXIII 5
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Physics 218, Lecture XXIII 6
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Physics 218, Lecture XXIII 7
Review: Simple Harmonic Motion
Mass on a Spring
Amplitude: Max distance
Period: Time it takes to get back to here
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Physics 218, Lecture XXIII 8
Questions
Simple Harmonic Motion
x = A sin(t + )Can you answer the following:• What is the amplitude?• What is the phase?• What is the angular frequency?• What is the velocity at the end points?• What is the velocity at the middle?
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Physics 218, Lecture XXIII 9
Energy in SHO’s
• Potential Energy for a springU = ½kx2
• Kinetic Energy for a blockKE = ½mv2
• Total EnergyE = U+KE = ½kx2 +½mv2
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Physics 218, Lecture XXIII 10
Energy Example
A box of mass m is attached to a spring of constant k, stretched to a distance Xo, held in place and then and released. Ignore gravity and friction.
As a function of time:
1. What is the position?
2. What is the velocity?
3. What is the kinetic energy?
4. What is the potential energy?
5. What is the total energy of the system?
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Physics 218, Lecture XXIII 11
Uniform Circular Motion
It turns out Uniform Circular Motion is really Simple Harmonic Motion but in two dimensions
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Physics 218, Lecture XXIII 12
Uniform Circular Motion in 2D
A ball is moving anti-clockwise in uniform circular motion with a radius R and speed V. At t=0 we set 0=0.
1. What is the equation of motion for ?2. What is the equation of motion in the x
direction?3. What is the displacement at all times?4. What is the velocity at all times?5. What is the speed at all times?
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Physics 218, Lecture XXIII 13
Mass on a spring with gravity
h
Initial Final
Take an un-stretched spring. Gently add a mass and let go. The total stretch from equilibrium is a distance h before it starts to rise again. It then oscillates
What is the angular velocity, , of motion?
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Physics 218, Lecture XXIII 14
Pendulums
• Pendulums can be a pretty good Simple Harmonic Oscillator
• The amount of swing has to be small
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Physics 218, Lecture XXIII 15
Example: Pendulum
For small swing ( small) show that the motion of a ball on a pendulum is simple harmonic
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Physics 218, Lecture XXIII 16
Period of a Pendulum
Show that the period of a pendulum doesn’t depend on the mass.
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Physics 218, Lecture XXIII 17
Challenge Exam• 2nd Announcement of this semester’s 218 Challenge
Exam: Monday December 4th at 6:00PM– Not required (just for fun)– Does not (will not!!!) count as part of your final grade
• Test your skills against the best Aggies from all the Physics 218 sections (not just this lecture) on Physics 218 material
• Students who perform well will be recognized as Mechanics Scholars, and honored at a banquet in their honor. Other prizes, including cash.
• Handout information on the web now• If you have a 95% exam average or above, I believe you
have an Excellent chance of winning!
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Physics 218, Lecture XXIII 18
Coming up…• Tuesday: Last class meeting
– Review for the final, we’ll skip Chapter 15
– Do all the problems on the handout before class– Be prepared to vote for which type of problem you want
to review most
• Monday December 11th Final Exam, 1PM. Here– The material in Chapters 12 and 13 will be on the final– I guarantee there will be at least one problem from each
chapter on the final
• Homework 13 and FCI II are due Wednesday• A 100% on all homework is required in order to
pass the class
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Physics 218, Lecture XXIII 19
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Physics 218, Lecture XXIII 20
Next Lecture
• Notes on the final:– Chapter 14 will be on the final.
– Nothing from Chapter 15 on the final.
– I guarantee there will be at least one problem from these last two weeks on the final
– Final is Monday Dec 15th, 1:00PM-3:00PM, here
• Next time– Review
– Come prepared with questions
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Physics 218, Lecture XXIII 21
Draw position as a function of Time?
Spring and Mass
Paper which tells
us what happens
as a function of time
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Physics 218, Lecture XXIII 22
Ballistic Pendulum• A bullet plows into a
block of wood which is part of a pendulum.
• We know m, M and v.
• How high, h, does the block of wood go?
• What is the equation of motion after the collision?
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Physics 218, Lecture XXIII 23
Some Useful Relations and Weird Results
amplitude on the dependt doesn' Period
2 T But
2 T
2
:by T Period the torelated is
locity angular ve seen the ve we'As
2
k
m
m
k
T
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Physics 218, Lecture XXIII 24
Doing a mass on a spring with g
Take an un-stretched spring with constant k. Add a mass, m. Slowly stretch to -x0, and bring to rest and let go.
What is the equation of motion?
Add a massStretch