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PHY 113 C General Physics I 11 AM – 12:15 P M MWF Olin 101 Plan for Lecture 26: Comments on preparing for Final Exam Comprehensive review – Part II Course assessment. Final exam schedule for PHY 113 C. Comments on Final Exam - PowerPoint PPT Presentation
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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
PHY 113 C Fall 2013 -- Lecture 26 212/05/2013
PHY 113 C Fall 2013 -- Lecture 26 312/05/2013
Final exam schedule for PHY 113 C
PHY 113 C Fall 2013 -- Lecture 26 412/05/2013
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
PHY 113 C Fall 2013 -- Lecture 26 512/05/2013
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.
PHY 113 C Fall 2013 -- Lecture 26 712/05/2013
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
PHY 113 C Fall 2013 -- Lecture 26 812/05/2013
Review of some basic concepts
Newton’s second law
Fpv
FrvFa
dtd
dtmd
dtdm
dtdm
m
2
2
system) extended of mass ofcenter (or particlepoint singleFor
ii
i
i
ii
iii
dtd
m
Fp
Fa particles of systemFor
PHY 113 C Fall 2013 -- Lecture 26 912/05/2013
Review of some basic concepts
Newton’s second law for angular motion
τFrLprpr
Fp
dtd
dtd
dtd
dtd
PHY 113 C Fall 2013 -- Lecture 26 1012/05/2013
rFr
r
dWf
i
fi : workof Definition
Review of energy concepts:
2
21 :energy kinetic of Definition mvK
22
21
21
:oremenergy the kinetic-Work
if
f
itotal
totalfi mvmvdW rF
PHY 113 C Fall 2013 -- Lecture 26 1112/05/2013
22
21
21
:oremenergy the kinetic-Work
if
f
itotal
totalfi 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
PHY 113 C Fall 2013 -- Lecture 26 1212/05/2013
Extension of concepts of energy conservation to extended objects
rotationtotal KKK mass ofcenter
energy Kinetic
edissipativfiiiff WUKUK
PHY 113 C Fall 2013 -- Lecture 26 1312/05/2013
22
21
21
:object rolling ofenergy kinetic Total
CM
CMrollingtotal
MvI
KKK
CMvRdtdR
dtds
dtd
: thatNote
22
222
21
21
21
CM
CM
CMrollingtotal
vMRI
MvRRI
KKK
22
21
21
:object rolling ofenergy kinetic Total
CM
CMrollingtotal
MvI
KKK
CMvRdtdR
dtds
dtd
: thatNote
22
222
21
21
21
CM
CM
CMrollingtotal
vMRI
MvRRI
KKK
CMCM
PHY 113 C Fall 2013 -- Lecture 26 1412/05/2013
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
21 MRMRIB
22 4.052 MRMRIC
2
22
/12
01210
MRIghv
vMR
IMMgh
UKUK
CM
CM
ffii
PHY 113 C Fall 2013 -- Lecture 26 1512/05/2013
iclicker exercise:In previous example which of the equations on your equation sheet would be most useful?
B &A C.
rollingFor ;21
21 B.
A.
22 RvIMvK
UKUK
CMCMtotal
ffii
2/12 D.
MRIghvCM
PHY 113 C Fall 2013 -- Lecture 26 1612/05/2013
From your questions -- (question from Exam 2)
21
21
12221
2112 0 ˆ
RRmGmU
RRmGm
τrF
PHY 113 C Fall 2013 -- Lecture 26 1712/05/2013
Comment on circular motion -- uniform circular motion
ra ˆ
:ison accelerati lcentripeta theanddirection radial in the
onaccelerati then the, If
2
rv
vvv
c
fi
PHY 113 C Fall 2013 -- Lecture 26 1812/05/2013
r
ra
ra
ra
ˆ2
ˆ2
ˆ
2
2
2
rf
rT
rv
c
c
c
Trv 2
In terms of time period T for one cycle:
In terms of the frequency f of complete cycles:πfrv
Tf 2 ;1
Comment on circular motion -- uniform circular motion
PHY 113 C Fall 2013 -- Lecture 26 1912/05/2013
Comment on circular motion -- uniform circular motion – effects on gravitationally attractive bodies
221
21
1
21
1
1221
21111
12221
2112
ˆˆ
ˆ
RRmGm
Rvm
RRmGmam
RRmGm
RR
rF
221
21
2
1
2 RR
GmRT
PHY 113 C Fall 2013 -- Lecture 26 2012/05/2013
Comment on circular motion -- non-uniform circular motion
r
ra
ra
ra
ˆ2
ˆ2
ˆ
2
2
2
rf
rT
rv
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 ˆdtdv
aca
PHY 113 C Fall 2013 -- Lecture 26 2112/05/2013
From your questions -- (question from Exam 1)
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 f?c. Determine the net work of gravity on the
ball at it moves from the initial to final positions in its trajectory: .
PHY 113 C Fall 2013 -- Lecture 26 2212/05/2013
From your questions -- (question from Exam 1) 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 f?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 210
21
:energy ofon conservati usingSolution
22
if
fffii
fffi
ffii
yymgW
vv
vmgymvmv
UKUK
PHY 113 C Fall 2013 -- Lecture 26 2312/05/2013
From your questions -- force diagrams
m
1 2
F1F2
mg
0sinsin0coscos
0 :mequilibriuin systemFor
2211
2211
mgFFFF
i
i
F
PHY 113 C Fall 2013 -- Lecture 26 2412/05/2013
mg(-j)
r
T F=ma
T- mg cos 0
mg sin ma
t=I a r mg sin = mr2 a mra
From your questions -- pendulum
rg
rg
dtd
dtdmr
dtmrdmgr
dtdLτ
sin :equations Pendulum
sin
:elyAlternativ
2
2
2
22
2
PHY 113 C Fall 2013 -- Lecture 26 2512/05/2013
From your questions -- driven Harmonic oscillator
PHY 113 C Fall 2013 -- Lecture 26 2612/05/2013
From your questions -- driven Harmonic oscillator
tmk
mFtmkAtx
tFkxdt
xdm
Fma total
sin/cos)( :solution General
sin
2
0
02
2
PHY 113 C Fall 2013 -- Lecture 26 2712/05/2013
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
mFtmkAtx
sin/cos)(
2
0
(usually neglected)
mF
mk
mk
mF
6.0
6.0/ :case In this
02
2
0
PHY 113 C Fall 2013 -- Lecture 26 2812/05/2013
Examples of two-dimensional collision; balls moving on a frictionless surface
smsmsmv
smsmsm
vvvsmsm
vv
vmvm
vmvmvm
smv
smvkgmm
oof
o
fif
o
ff
ff
ffi
f
i
/11.188.17cos/060.1
88.17sin/342.0
88.71 060.1342.0tan
/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
PHY 113 C Fall 2013 -- Lecture 26 2912/05/2013
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
PHY 113 C Fall 2013 -- Lecture 26 3012/05/2013
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 If21
21
021
222
211
211
fi
fi
fff
ii
KK
KK
vmvmK
vmK
PHY 113 C Fall 2013 -- Lecture 26 3112/05/2013
From your questions -- conservation of angular momentum
mm
d1 d1
mm
d2 d2
I1=2md12 I2=2md2
2
I11=I22 2=1 I1/I2
1 2
constant is then 0, If
LττL
vrL
dtd
ILmi
iii
PHY 113 C Fall 2013 -- Lecture 26 3212/05/2013
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?
PHY 113 C Fall 2013 -- Lecture 26 3312/05/2013
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
JsN
Nmg
tFgRItFt
IFRIIK
Rg
mgItI
FRtIFR
625.275)3(80050m/s8.9
/21
21
21
21
22
222
2
2222
2
aa
PHY 113 C Fall 2013 -- Lecture 26 3412/05/2013
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 AvavAFPPyyPgyvPgyv
22
1
2
AaA
Fvv
PHY 113 C Fall 2013 -- Lecture 26 3512/05/2013
Send email or come to see me if you have further questions.
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