Physics 218, Lecture XXIII 1

Physics 218Lecture 23 Dr. David Toback

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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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(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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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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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 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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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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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 ( 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

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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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