physics 218, lecture xxv1 physics 218 lecture 25 dr. david toback

Physics 218, Lecture XXV 1

Physics 218Lecture 25

Dr. David Toback


Checklist for Today

•Things due earlier this week–Chapter 15 & 16 in WebCT–Chapter 18 reading–Chapter 18 problems for Recitation

•Today: LAST LECTURE•Things due Monday

–Chapter 18 in WebCT


The ScheduleThis Week (4/21)• Monday: Chapter 15 & 16 due in WebCT• Tues: Reading & Lecture: Chapter 18• Wed: Recitation on Chapter 18, Lab• Thurs: Last lecture, Chapter 18

– Not covering Chapter 19Next Week (4/28)• No lectures or recitations• Chapter 18 HW due in WebCT• Example final problems athttp://faculty.physics.tamu.edu/toback/218/Lectures/

FinalReview.pdf

• Finish your HW on WebCT and do the Mini-Practice Exam

Week after that (5/5) • Final: Monday May 5th, 1PM-3PM in this room


Next SemesterSome 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”– Intro to Cosmology (PHYS289)– Based on “A Brief History of Time” by Stephen Hawking

– If you can’t take it, you might pass this info along to friends


Chap 18 Overview: Oscillations

•Oscillations and vibrations

•Equations of motion•Simple Model: Mass on a spring

•Simple Harmonic Motion•Energy


Review: Simple Harmonic Motion

Mass on a Spring

Amplitude: Max distance

Period: Time it takes to get back to here


Summary: Equation of Motion

Mass m on a spring with spring constant k:

x = A sin(t + )Where

2 = k/mA is the Amplitude is the “phase”

(phase just allows us to set t=0 when we want)


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?


Simple Harmonic Motion

At some level sinusoidal motion is the definition of Simple Harmonic Motion

A system that undergoes simple harmonic motion

is called a simple harmonic

oscillator


Check:

This looks like a cosine. Makes sense… Spring and

MassPaper which

tells us what

happens as a

function of time


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 oscillatesWhat is the equation of motion?


Energy in SHO’s

•Potential Energy for a spring

U = ½kx2

•Kinetic Energy for a blockKE = ½mv2

•Total EnergyE = U+KE = ½kx2 +½mv2


Energy ExampleA 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?


Understanding Phase: Initial Conditions

A block with mass m is attached to the end of a spring, with spring constant k. The spring is stretched a distance D and let go at t=0– What is the position of the mass

at all times?– Where does the maximum speed

occur?– What is the maximum speed?


Example: Spring with a Push

We have a spring system–Spring constant: K–Mass: M

–Initial position: X0

–Initial Velocity: V0

Find the position at all times


Challenge Exam• Announcement of this semester’s 218

Challenge Exam: Monday April 28th 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 my WebSite


That’s it!•Next Week:

–No classes or Recitations–HW for Chapter 18 due– Example final problems at

http://faculty.physics.tamu.edu/toback/218/Lectures/FinalReview.pdf

– Finish your HW on WebCT, do the Mini-Practice Exam

•Final: Monday May 5th, 1PM-3PM in this room–Chapters 14 -16 and 18 will be on the final– I guarantee a problem from each

•Good luck studying for Finals!


Uniform Circular Motion

It turns out Uniform Circular Motion is really Simple Harmonic Motion but in two dimensions


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?


Pendulums

• Pendulums can be a pretty good Simple Harmonic Oscillator

• The amount of swing has to be small


Example: Pendulum

For small swing ( small) show that the motion of a ball on a pendulum is simple harmonic


Period of a Pendulum

Show that the period of a pendulum doesn’t depend on the mass.


Coming up…•Thursday: 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


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


Draw position as a function of Time?

Spring and Mass

Paper which tells

us what happens

as a function of time


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?


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


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

physics 218, lecture xxv1 physics 218 lecture 25 dr. david toback

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