Physics 218
Lecture 23
Dr. David Toback
Physics 218, Lecture XXIII
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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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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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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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Review: Simple Harmonic Motion
Mass on a Spring
Amplitude: Max distance
Period: Time it takes to get
back to here
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Questions
Simple Harmonic Motion
x = A sin(wt + f)
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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Energy in SHO’s
• Potential Energy for a spring
U = ½kx2
• Kinetic Energy for a block
KE = ½mv2
• Total Energy
E = U+KE = ½kx2 +½mv2
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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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Uniform Circular Motion
It turns out Uniform
Circular Motion is
really Simple Harmonic
Motion but in two
dimensions
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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 Q0=0.
1. What is the equation of motion for Q?
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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Mass on a spring with gravity
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, w, of motion?
Initial
Final
h
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Pendulums
• Pendulums can
be a pretty good
Simple
Harmonic
Oscillator
• The amount of
swing has to be
small
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Example: Pendulum
For small swing
(q small) show
that the motion
of a ball on a
pendulum is
simple
harmonic
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Period of a Pendulum
Show that the period of a
pendulum doesn’t
depend on the mass.
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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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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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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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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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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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Some Useful Relations and Weird Results
As we' ve seen the angular ve locity w
is related to the Period T by :
2
2
w
T
T
w
k
m
2
But w   T  2
m
k
Period doesn' t depend on the amplitude
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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 mass
Stretch
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