12/05/2013phy 113 c fall 2013 -- lecture 261 phy 113 c general physics i 11 am – 12:15 pm mwf olin...

PHY 113 C Fall 2013 -- Lecture 26 112/05/2013

PHY 113 C General Physics I11 AM – 12:15 PM MWF Olin 101

Plan for Lecture 26:

1. Comments on preparing for Final Exam2. Comprehensive review – Part II3. Course assessment


Final exam schedule for PHY 113 C


Comments on Final Exam It will be comprehensive (covering material

from Chapters 1-22) It is scheduled for 9 AM Dec. 12th in Olin 101 In class format only; no time pressure May bring 4 equation sheets Format will be similar to previous exams; may

see problems similar to those on previous exams


General advice on how to prepare for Final Exam

Review fundamental concepts and their corresponding equations

Develop equation sheets that help you solve example problems on all of the material. (You can assume that empirical constants and parameters will be given to you; they need not take up space on your equation sheet.)

Practice problem solving techniques. If you find mysteries, unanswered questions, etc.,

please contact me.


Review of some basic concepts

Vectors Keep track of 2 or

more components (or magnitude and direction)

Examples Position vector Velocity Acceleration Force Momentum

Scalars Single (signed)

quantity Examples

Time Energy Kinetic energy Work Potential energy Pressure Temperature Mass Density Volume



Newton’s second law

F

pv

Frv

Fa

dt

d

dt

mddt

dm

dt

dm

m

2

2

system) extended of mass ofcenter (or particlepoint singleFor

ii

i

i

ii

iii

dt

d

m

Fp

Fa

particles of systemFor



Newton’s second law for angular motion

τFr

Lprpr

Fp

dt

d

dt

d

dt

ddt

d


rFr

r

dWf

i

fi : workof Definition

Review of energy concepts:

2

2

1 :energy kinetic of Definition mvK

22

2

1

2

1

:oremenergy the kinetic-Work

if

f

i

totaltotal

fi mvmvdW rF


22

2

1

2

1

:oremenergy the kinetic-Work

if

f

i

totaltotal

fi mvmvdW rF

Summary of work, potential energy, kinetic energy relationships

edissipativ

fiiiff

ifedissipativ

fiiftotal

fi

WUKUK

KKWUUW

:gRearrangin

rr

edissipativfiif

edissipativfi

veconservatifi

totalfi

WUU

WWW


Extension of concepts of energy conservation to extended objects

rotationtotal KKK mass ofcenter

energy Kinetic

edissipativfiiiff WUKUK


22

2

1

2

1

:object rolling

ofenergy kinetic Total

CM

CMrollingtotal

MvI

KKK

CMvRdt

dR

dt

dsdt

d

: thatNote

2

2

22

2

2

1

2

1

2

1

CM

CM

CMrollingtotal

vMR

I

MvRR

I

KKK

22

2

1

2

1

:object rolling

ofenergy kinetic Total

CM

CMrollingtotal

MvI

KKK

CMvRdt

dR

dt

dsdt

d

: thatNote

2

2

22

2

2

1

2

1

2

1

CM

CM

CMrollingtotal

vMR

I

MvRR

I

KKK

CMCM


Three round balls, each having a mass M and radius R, start from rest at the top of the incline. After they are released, they roll without slipping down the incline. Which ball will reach the bottom first?

AB C

2MRI A 22 5.0

2

1MRMRIB

22 4.05

2MRMRIC

2

22

/1

2

012

10

MRI

ghv

vMR

IMMgh

UKUK

CM

CM

ffii


iclicker exercise:In previous example which of the equations on your equation sheet would be most useful?

B &A C.

rollingFor ;2

1

2

1 B.

A.

22 RvIMvK

UKUK

CMCMtotal

ffii

2/1

2 D.

MRI

ghvCM


From your questions -- (question from Exam 2)

21

21

12221

2112 0 ˆ

RR

mGmU

RR

mGm

τrF


Comment on circular motion -- uniform circular motion

ra ˆ

:ison accelerati lcentripeta

theanddirection radial in the

onaccelerati then the, If

2

r

v

vvv

c

fi


r

ra

ra

ra

ˆ2

ˆ2

ˆ

2

2

2

rf

rT

r

v

c

c

c

T

rv

2

In terms of time period T for one cycle:

In terms of the frequency f of complete cycles:

πfrvT

f 2 ;1

Comment on circular motion -- uniform circular motion


Comment on circular motion -- uniform circular motion – effects on gravitationally attractive bodies

221

21

1

21

1

1221

21111

12221

2112

ˆˆ

ˆ

RR

mGm

R

vm

RR

mGmam

RR

mGm

RR

rF

221

21

2

1

2

RR

GmR

T


Comment on circular motion -- non-uniform circular motion

r

ra

ra

ra

ˆ2

ˆ2

ˆ

2

2

2

rf

rT

r

v

c

c

c

At each instant of time

Note that if speed v is not constant, then there will also be a tangential component of acceleration:

θa ˆdt

dv

acaq



a. Neglecting any possible dissipative forces acting on this system, determine the magnitude of the velocity of the ball vf as it is caught by the person at the coordinates (xf,yf).

b. What is the angle qf?c. Determine the net work of gravity on the

ball at it moves from the initial to final positions in its trajectory: .



a. Neglecting any possible dissipative forces acting on this system, determine the magnitude of the velocity of the ball vf as it is caught by the person at the coordinates (xf,yf).

b. What is the angle qf?c. Determine the net work of gravity on the

ball at it moves from the initial to final positions in its trajectory: .

)( :gravityby Work (c)

(b)for for Solve coscos

:constant is velocity horizontal that Note

(a)for for Solve 2

10

2

1

:energy ofon conservati usingSolution

22

if

fffii

fffi

ffii

yymgW

vv

vmgymvmv

UKUK


From your questions -- force diagrams

m

q1

q2

F1F2

mg

0sinsin

0coscos

0 :mequilibriuin systemFor

2211

2211

mgFF

FF

i

i

F


mg(-j)

r

T F=ma

T- mg cos 0

mg sin maq

t=I a r mg sin = mr2 a mraq

From your questions -- pendulum

r

g

r

g

dt

d

dt

dmr

dt

mrdmgr

dt

dLτ

sin :equations Pendulum

sin

:elyAlternativ

2

2

2

22

2


From your questions -- driven Harmonic oscillator


From your questions -- driven Harmonic oscillator

tmk

mFt

m

kAtx

tFkxdt

xdm

Fma total

sin/

cos)( :solution General

sin

2

0

02

2


Similar problem from webassign:

Damping is negligible for a 0.165-kg object hanging from a light, 6.30-N/m spring. A sinusoidal force with an amplitude of 1.70 N drives the system. At what frequency will the force make the object vibrate with an amplitude of 0.600m?

tmk

mFt

m

kAtx

sin

/cos)(

2

0

(usually neglected)

m

F

m

kmk

mF

6.0

6.0/

:case In this

02

2

0


Examples of two-dimensional collision; balls moving on a frictionless surface

smsmsm

v

smsmsm

vvv

smsm

vv

vmvm

vmvmvm

smv

smvkgmm

oof

o

fif

o

ff

ff

ffi

f

i

/11.188.17cos

/060.1

88.17sin

/342.0

88.71 060.1

342.0tan

/060.120cos/1/2

coscos

/342.020sin/1

sinsin

sinsin0

coscos

20 ,/1

,/2 ,06.0 :Suppose

1

o

211

21

2211

221111

o2

121


Examples of two-dimensional collision; balls moving on a frictionless surface – energy conservation?

Note: In these collision analyses, we are neglecting forces and potential energy

iclicker questionWhy?

A. We are cheating physicsB. We are applying the laws of

physics correctly


Examples of two-dimensional collision; balls moving on a frictionless surface – energy conservation?

Assuming that we applying the laws of physics correctly – we can ask the question – Is (kinetic) energy conserved?

processin lost or addedEnergy If

conserved isEnergy If2

1

2

1

02

1

222

211

211

fi

fi

fff

ii

KK

KK

vmvmK

vmK


From your questions -- conservation of angular momentum

mm

d1 d1

mm

d2 d2

I1=2md12 I2=2md2

2

I1 1=I2 2 2= 1 I1/I2

1 2

constant is then 0, If

LττL

vrL

dt

d

ILmi

iii


Example form Webassign #11

X

t1

t3

t2

iclicker exerciseWhen the pivot point is O, which torque is zero?

A. t1?B. t2?C. t3?


An example of the application of torque on a rigid object:

A horizontal 800 N merry-go-round is a solid disc of radius 1.50 m and is started from rest by a constant horizontal force of 50 N applied tangentially to the cylinder. Find the kinetic energy of solid cylinder after 3 s.

K = ½ I 2 t I a i at = atIn this case I = ½ m R2 and t = FR

R F

Js

N

N

mg

tFg

RI

tFt

I

FRIIK

Rg

mgIt

I

FRtIFR

625.275)3(800

50m/s8.9

/2

1

2

1

2

1

2

1

22

222

2

2222

2

aa


Webassign questions on fluids (Assignment #17)

A hypodermic syringe contains a medicine with the density of water (see figure below). The barrel of the syringe has a cross-sectional area A = 2.40 10-5 m2, and the needle has a cross-sectional area a = 1.00 10-8 m2. In the absence of a force on the plunger, the pressure everywhere is 1.00 atm. A force of magnitude 2.65 N acts on the plunger, making medicine squirt horizontally from the needle. Determine the speed of the medicine as it leaves the needle's tip.

122121

22222

111

212

1

;/ ; :case In this AvavAFPPyy

PgyvPgyv

22

1

2

Aa

A

Fvv


Send email or come to see me if you have further questions.

THANKS!

12/05/2013phy 113 c fall 2013 -- lecture 261 phy 113 c general physics i 11 am – 12:15 pm mwf olin...

Documents

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c general physics i11

review of energy concepts

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extension of concepts

uniform circular motion

final exam schedule