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PHY 113 A General Physics I 9-9:50 AM MWF Olin 101 Plan for Lecture 13: Chapter 8 -- Conservation of energy Potential and kinetic energy for conservative forces Energy and non-conservative forces Power. - PowerPoint PPT Presentation
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PHY 113 A Fall 2012 -- Lecture 13 19/28/2012
PHY 113 A General Physics I9-9:50 AM MWF Olin 101
Plan for Lecture 13:
Chapter 8 -- Conservation of energy
1. Potential and kinetic energy for conservative forces
2. Energy and non-conservative forces
3. Power
PHY 113 A Fall 2012 -- Lecture 13 29/28/2012
PHY 113 A Fall 2012 -- Lecture 13 39/28/2012
Note: Because of PHY 114 exams on Sunday and Monday, the tutorials those nights will be moved from Olin 101 – check for signs – this week only.
PHY 113 A Fall 2012 -- Lecture 13 49/28/2012
EUmvUmv
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:forces veconservatiFor
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:oremenergy the kinetic- workGeneral
PHY 113 A Fall 2012 -- Lecture 13 59/28/2012
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
21 ;0 ;0 :
; ;0 :
fff
ii
mvEUvf
mghEmghUvi
r
r
m/s 3.13
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221 2
ghv
mghmv
f
f
PHY 113 A Fall 2012 -- Lecture 13 69/28/2012
Energy diagram
E
yiyf
K
U
PHY 113 A Fall 2012 -- Lecture 13 79/28/2012
Energy diagrams 22
21
21 kxmvE
2max2
1221
2max2
1
max
,0(0)
:0 when :Note ,0
: when :Note
kxmvU
x kxEv
xx
PHY 113 A Fall 2012 -- Lecture 13 89/28/2012
Example: Model potential energy function U(x) representing the attraction of two atoms
PHY 113 A Fall 2012 -- Lecture 13 99/28/2012
Example:Simplified version:
(Assume that the sandbag is massive enough to provide the tension in the rope and R=3m.) If the actor starts at vi=0 and q=60o, what is vf?
m/s 5.4
5.0138.92221
21
)cos1(21
22
2
if
fff
ii
gyv
mvmgymvE
mgRmgymvE q0
0
PHY 113 A Fall 2012 -- Lecture 13 109/28/2012
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 A Fall 2012 -- Lecture 13 119/28/2012
iExample: Mass sliding on frictionless looping track
RmgmvE
mghmvE
A
i
22121
2
2
mgRmv
Rvmmgn
A
A
21
21
:Aat on track stayingfor Condition
2
2
0
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Rh
mgRmgRmgRRmgmvmghE A
25
252
212
21 2
PHY 113 A Fall 2012 -- Lecture 13 129/28/2012
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 A Fall 2012 -- Lecture 13 139/28/2012
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
21
21
221
21
mmxgmv
vmvmxTW
f
if
D
D0
xgmm
mmxTW
gmm
mmT
amgmTamT
D
D
21
21
21
21
22
1
PHY 113 A Fall 2012 -- Lecture 13 149/28/2012
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
21
21 2
121
if vmvmxfTW D
0
f
PHY 113 A Fall 2012 -- Lecture 13 159/28/2012
xfmm
mxgmm
mmxfTW
fmm
mgmm
mmT
amgmTamfT
D
D
D
21
1
21
21
21
2
21
21
22
1
gmfmm
xfxgmv
vmxfTW
k
f
f
1
21
2
21
2221
DD
D
PHY 113 A Fall 2012 -- Lecture 13 169/28/2012
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 A Fall 2012 -- Lecture 13 179/28/2012
Power
Watt(s)
(Joules) : Units
: thatNote
: workof change of rate timeas Defined
P
dtd
dtdW
ddWdt
dW P
vFrF
rF
PHY 113 A Fall 2012 -- Lecture 13 189/28/2012
Watts106/3102
/3 ,102For
:motorby exertedPower
44
4
smNP
smvNT
Tvdt
dW P vF
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