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PHY 113 C Fall 2013-- Lecture 8 19/19/2013
PHY 113 C General Physics I11 AM-12:15 PM MWF Olin 101
Plan for Lecture 8:
Chapter 8 -- Conservation of energy
1. Potential and kinetic energy for conservative forces
2. Energy and non-conservative forces
3. Power
PHY 113 C Fall 2013-- Lecture 8 29/19/2013
PHY 113 C Fall 2013-- Lecture 8 39/19/2013
Comments on preparation for next Thursday’s exam
PHY 113 C Fall 2013-- Lecture 8 49/19/2013
Comments on preparation for next Thursday’s exam -- continued
PHY 113 C Fall 2013-- Lecture 8 59/19/2013
Comments on preparation for next Thursday’s exam – continued
What you should bring to the exam (in addition to your well-rested brain): A pencil or pen Your calculator An 8.5”x11” sheet of paper with your favorite
equations (to be turned in together with the exam)
What you should NOT use during the exam Electronic devices (cell phone, laptop, etc.) Your textbook
PHY 113 A Fall 2013 -- Lecture 1 6
Advice:
1. Keep basic concepts and equations at the top of your head.
2. Practice problem solving and math skills
3. Develop an equation sheet that you can consult.
Equation Sheet
dt
ddt
d
m
rv
va
aF
Problem solving skills
Math skills
8/27/2013
PHY 113 C Fall 2013-- Lecture 8 79/19/2013
iclicker questionWhich of the following best describes your opinion about the equation sheet:
A. I have not prepared my equation sheet yet but hope to do so soon
B. I have a preliminary equation sheet but have not used it for doing homework
C. I have a preliminary equation sheet and have used it for doing homework
D. I am dreaming about preparing the equation sheet, but have not done it yet
E. In my opinion, the equation sheet is not really necessary
PHY 113 C Fall 2013-- Lecture 8 89/19/2013
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
PHY 113 C Fall 2013-- Lecture 8 99/19/2013
Some questions from webassign Assignment #7
In 1990 Walter Arfeuille of Belgium lifted a 281.5-kg object through a distance of 17.1 cm using only his teeth.
(a) How much work was done on the object by Arfeuille in this lift, assuming the object was lifted at constant velocity?
T
mg
T
mg
yf
yi
if
iffifi
yymg
yyTWdW
mgTmgTf
i
0
rFr
r
PHY 113 C Fall 2013-- Lecture 8 109/19/2013
Some questions from webassign Assignment #7
In 1990 Walter Arfeuille of Belgium lifted a 281.5-kg object through a distance of 17.1 cm using only his teeth.
How much work was done on the object by gravity?
T
mg
T
mg
yf
yi
iffifi yymgWdWf
i
rFr
r
PHY 113 C Fall 2013-- Lecture 8 119/19/2013
Some questions from webassign Assignment #7
What is the work done as the particle moves from x=0 to x=3m?
N75.6m3N5.42
13
0
dxxFdW xfi
f
i
rFr
r
PHY 113 C Fall 2013-- Lecture 8 129/19/2013
Some questions from webassign Assignment #7 -- continued
What is the work done as the particle moves from x=8 to x=10m?
N5.2m2N32
110
8
dxxFdW xfi
f
i
rFr
r
PHY 113 C Fall 2013-- Lecture 8 139/19/2013
Some questions from webassign Assignment #7
A 4.34-kg particle is subject to a net force that varies with position as shown in the figure. The particle starts from rest at x = 0. What is its speed at x = 5.00 m?
02
1
2
1
2
1
25
0
22
fxtotal
fi
if
f
i
totaltotal
fi
mvdxxFW
mvmvdW rF
PHY 113 C Fall 2013-- Lecture 8 149/19/2013
Work and potential energy
rFr
r
dWf
i
fi : workof Definition
rFrr
r
r dWUref
ref
:energy potential of Definition
Note: It is assumed that F is conservative
PHY 113 C Fall 2013-- Lecture 8 159/19/2013
rFrr
r
r dWUref
ref :energy potential of Definition
Work and potential energy -- continued
mg
mg
y
yref
Example – gravity near the surface of the Earth:
ref
y
y
ref
yymg
dymgyU
dWU
ref
ref
' )(
rFrr
r
r
PHY 113 C Fall 2013-- Lecture 8 169/19/2013
Work and potential energy for gravity (near Earth’s surface)
mg
mg
yf
yi
ref
y
y
ref
yymg
dymgyU
dWU
ref
ref
' )(
rFrr
r
r
yref
iffi
iffifi
UUddW
yymgWdW
i
ref
f
ref
f
i
rrrFrF
rF
r
r
r
r
r
r
:elyAlternativ
PHY 113 C Fall 2013-- Lecture 8 179/19/2013
Work and potential energy continued
iffi UUddWi
ref
f
ref
rrrFrFr
r
r
r
rFrr
r
r dWUref
ref :energy Potential
iclicker questionWhy is there a strange “-” sign in the definition of potential energy?
A. Physicists like to be annoyingB. No reason at allC. There is a somewhat good reason
PHY 113 C Fall 2013-- Lecture 8 189/19/2013
22
2
1
2
1
:oremenergy the kinetic-Work
if
f
i
totaltotal
fi mvmvdW rF
Work and potential energy continued
iffi UUddWi
ref
f
ref
rrrFrFr
r
r
r
For the case that the total force acting on the system is conservative, we can use the definition of potential energy with the work-kinetic energy theorem
(contant) :gRearrangin
EUKUK
KKUUW
iiff
ififtotal
fi
rr
PHY 113 C Fall 2013-- Lecture 8 199/19/2013
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
PHY 113 C Fall 2013-- Lecture 8 209/19/2013
ExampleA block, initially at rest at a height h, slides down a frictionless incline. What is its final velocity?
hh=0.5m
i
f
2
2
1 ;0 ;0 :
; ;0 :
fff
ii
mvEUvf
mghEmghUvi
r
r
m/s 3.13
5.08.92
2
2
1 2
ghv
mghmv
f
f
PHY 113 C Fall 2013-- Lecture 8 219/19/2013
Energy diagram
E
yiyf
K
U
U,
K,
E (
J)
m
PHY 113 C Fall 2013-- Lecture 8 229/19/2013
2
212
21
2212
21
)( and )(
:force spring of Example
iiff
if
x
x
f
i
fi
kxUkxU
kxkxdxxkdWf
i
rr
rF
k
PHY 113 C Fall 2013-- Lecture 8 239/19/2013
Energy diagrams 22
2
1
2
1kxmvE
2max2
1221
2max2
1
max
,0(0)
:0 when :Note
,0
: when :Note
kxmvU
x
kxEv
xx
PHY 113 C Fall 2013-- Lecture 8 249/19/2013
Example: Model potential energy function U(x) representing the attraction of two atoms
PHY 113 C Fall 2013-- Lecture 8 259/19/2013
dx
dUxF
dxxFWxU
dWU
x
x
xref
ref
ref
ref
:tiveAntideriva
'')( :dimension oneIn
' :energy Potential rFrr
r
r
Comment on relationship between potential energy and (conservative) force:
PHY 113 C Fall 2013-- Lecture 8 269/19/2013
Example: Mass sliding on frictionless looping track
i
iclicker exercise:In order for the ball completes the loop at A, what must the value of h?
A. h=RB. h=2RC. h>2RD. Not enough
information.
PHY 113 C Fall 2013-- Lecture 8 279/19/2013
i
Example: Mass sliding on frictionless looping track
RmgmvE
mghmvE
A
i
22
12
1
2
2
mgRmv
R
vmmgn
A
A
2
1
2
1
:Aat on track stayingfor Condition
2
2
0
0
Rh
mgRmgRmgRRmgmvmghE A
2
52
52
2
12
2
1 2
PHY 113 C Fall 2013-- Lecture 8 289/19/2013
Another example; first without friction
Mass m1 (=0.2kg) slides horizontally on a frictionless table and is initially at rest. What is its velocity when it moves a distance Dx=0.1m (and m2 (=0.3kg) falls Dy=0.1m)?
iclicker exercise:What is the relationship of the final velocity of m1 and m2?
A. They are equalB. m2 is faster than m1.C. m1 is faster than m2.
PHY 113 C Fall 2013-- Lecture 8 299/19/2013
Another example; first without friction
Mass m1 (=0.2kg) slides horizontally on a frictionless table and is initially at rest. What is its velocity when it moves a distance Dx=0.1m (and m2 (=0.3kg) falls Dy=0.1m)?
T
T
m2 g
21
2
22122
22
212
2
2
12
1
mm
xgmv
vmmxgmyygm
gymvmmgym
UKUK
f
ffi
ffi
ffii
xgmm
mmxTW
gmm
mmT
amgmT
amT
21
21
21
21
22
1
PHY 113 C Fall 2013-- Lecture 8 309/19/2013
Another example; now with friction
Mass m1 (=0.2kg) slides horizontally on a table with kinetic friction and is initially at rest. What is its velocity when it moves a distance Dx=0.1m (and m2 (=0.3kg) falls Dy=0.1m)?
T
T
m2 g
f
PHY 113 C Fall 2013-- Lecture 8 319/19/2013
21
12
122
21
1222
21
2
2
12
1
mm
xgmgmv
xgmxgmvmm
xgmgymgymvmm
WUKUK
kf
kf
kiff
edissipativfiiiff
PHY 113 C Fall 2013-- Lecture 8 329/19/2013
iclicker exercise:Assume a mass m starts at rest at A and moves on the frictionless surface as shown. At what position is the speed the largest?
A. AB. BC. CD. none of these.
PHY 113 C Fall 2013-- Lecture 8 339/19/2013
Power
Watt(s)
(Joules) : Units
: thatNote
: workof change of rate timeas Defined
P
dt
d
dt
dW
ddWdt
dW P
vFr
F
rF
PHY 113 C Fall 2013-- Lecture 8 349/19/2013
Watts106/3102
/3 ,102For
:motorby exertedPower
44
4
smNP
smvNT
Tvdt
dW P vF