Transcript 2/19/03 2

Physics 103: Lecture 9
Energy Conservation, Power
Reminders:
Hour Exam I, Tuesday February 24, 5:45 PM
Material from Chapters 1-4 inclusive
One page of notes (8.5” x 11”) allowed
20 multiple choice questions
Scantron will be used - bring #2 HB pencils + calculator
Today’s lecture will cover
Potential Energy
Conservation of Energy
Power
Usefulness of these concepts in problem solving.
2/19/03
Physics 103, Spring 2004, U. Wisconsin
1
Summary of Previous Lecture
• Work, W = |F| |Dx| cos 
• Kinetic Energy, KE = mv2/2
• Work-Kinetic Energy Theorem:
 change in kinetic energy of an object
= net work done on the object by all the forces

net W  mv  mv
1
2
2
1
2
2
0
• Gravitational Potential Energy: mgh
• Spring Potential Energy: kx2/2
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Physics 103, Spring 2004, U. Wisconsin
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Lecture 9, Preflight 1&2
Which of the following statements correctly define a Conservative Force:
1. A force is conservative when the work it does on a moving object is
independent of the path of the motion between the object's initial and final
positions.
2. A force is conservative when it does no net work on an object moving around a
closed path, starting and finishing at the same point.
3. Both of the above statements are correct.
4. Neither of the above statements is correct.
Gravity is a conservative force
60
50
40
A
B
C
D
30
20
Define PE=0 on ground.
PE=PEmax at the top of the path.
When it returns PE=0.
Net work done is zero.
10
0
Preflight 9.1
2/19/03
Pretty Sure
Not Quite Sure
Just Guessing
Physics 103, Spring 2004, U. Wisconsin
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Conservation of Energy
• Work-Energy Theorem:
•net W = DKE
• Conservative forces
•net W = -DPE
(total work done)
•-DPE= DKE
•DKE + DPE = 0
(no net change in energy)
• Conservation of Energy w/ only Conservative Forces:
•E = total energy = KE + PE (a constant)
•KEi + PEi = KEf + PEf
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Question 1
Imagine that you are comparing three different ways of having a ball move
down through the same height. In which case does the ball get to the
bottom first?
1. Dropping
correct
2. Slide on ramp (no friction)
3. Swinging down
4. All the same
1
ay=-g
2
|ax|<g
Free fall versus constrained fall
x
3
|ay(t)|<g
time
varying
The acceleration is different for the three cases
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Physics 103, Spring 2004, U. Wisconsin
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Question 2
Imagine that you are comparing three different ways of having a ball move
down through the same height. In which case does the ball reach the
bottom with the highest speed?
1.
2.
3.
4.
Dropping
Slide on ramp (no friction)
Swinging down
correct
All the same
1
2
3
In all three cases, the work done by the gravitational
force is the same since the change in vertical
distance is the same
1 2
mgh  mv f  v f  2gh
2
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Physics 103, Spring 2004, U. Wisconsin
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Non-conservative Forces

Work depends on the path
Friction
» Longer path


More area erased
Adds or removes mechanical
energy from a system
Open system
» Erasing results in heat
generated
» Dissipated to the paper +
air system
net W  Wnc  Wc  DKE
Wc  DPE
W nc  DKE  DPE
KE i  PEi  W nc  KE f  PE f
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Physics 103, Spring 2004, U. Wisconsin
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Open versus Closed System
Total energy is constant in any process. It may change forms. Energy
leaving the open system is transformed into other energy (OE) heat,
sound, deformation of the ground, …
KE i  PEi  W nc  OE i  KE f  PE f  OE f
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Physics 103, Spring 2004, U. Wisconsin
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Question 3
Suppose the initial kinetic and potential energies of a system are
200J and 100J respectively, and that the final kinetic and potential
energies of the same system are 100J and -100J respectively. How
much work was done on the system by non-conservative forces?
correct
1. -300 J
2. -200 J
3. -100 J
4. Work done must be positive
The change in kinetic energy plus
the change in potential energy
equals the work done on the system
by non-conservative forces
2/19/03
Wnc = Ef - Ei
= (KEf + PEf) - (KEi + PEi)
= (100J -100J) - (200J + 100J)
= 0J - 300J
= -300J
Physics 103, Spring 2004, U. Wisconsin
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Question 4
A stone is launched upward into the air. In addition to the force of
gravity, the stone is subject to a frictional force due to air
resistance. The time the stone takes to reach the top of its flight
path is
1. larger than
2. smaller than
3. equal to
Velocity is getting smaller
continuously because of
friction - average velocity
on the way down is smaller
than on the way up.
the time it takes to return from the top to its original position.
If there were no friction, the sum of PE+KE is constant, Emax
Due to friction, the energy at the top of the trajectory is Emax-fd
Due to friction, on the way down the total kinetic energy when it returns to
the bottom is Emax - fd - fd
It takes longer to go down because it has smaller average kinetic energy on
the way down.
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Physics 103, Spring 2004, U. Wisconsin
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Power
W Joules(J)
P ,
 Watts (W)
t second(s)
Power when running up stairs
W KE  PE 12 mv 2  mgh
P


t
t
t
m  60 kg, v  2 m/s, h  3 m, t  2.5 s
( 12 )(60)(2) 2  (60)(9.8)(3)
120  1794
P
W
W  754 W
2.5
2.5
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Physics 103, Spring 2004, U. Wisconsin
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Preflight Question 3 & 4
A sports car accelerates from zero to 30 mph in 1.5 s. How long does
it take for it to accelerate from zero to 60 mph, assuming the
power of the engine to be independent of velocity and neglecting
friction?
1. 2 s
2. 3s
3. 4.5 s
Pretty Sure
Not Quite Sure
Just Guessing
5. 9s
6. 12 s
v1  v 0 v1
d

(because v 0  0), v1  1
t1
t1
t1
v  v0 v2
d
a2  2

(because again v 0  0), v 2  2
t2
t2
t2
a1 
70
60
50
A
B
C
D
E
F
40
30
20
10
0
Preflight 9.3
2/19/03
4. 6 s
P
W1 F1d1 ma1d1
v
v2


 ma1v1  m 1 v1  m 1
t1
t1
t1
t1
t1
Power is constant,  P  m
t 2  1.5s
v12
v2
v2
 m 2  t 2  t1 22
t1
t2
v1
60  60
 1.5s  4  6s
30  30
Physics 103, Spring 2004, U. Wisconsin
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Preflight Question 5 & 6
A cart on an air track is moving at 0.5 m/s when the air is suddenly
turned off. The cart comes to rest after traveling 1 m. The
experiment is repeated, but now the cart is moving at 1 m/s when
the air is turned off. How far does the cart travel before coming
to rest?
1. 1 m
2. 2 m
3. 3 m
4. 4 m
5. 5 m
6. Impossible to determine
KE1  12 mv12 ; KE 2  12 mv22 
70
KE 2 v 22
v 22
  KE 2  KE1 2
KE1 v12
v1
60
KE1  Fd1 ; KE 2  Fd2  d2  d1
12
d2  1m 2  4m
0.5
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Pretty Sure
Not Quite Sure
Just Guessing
50
A
B
C
D
E
F
40
2
2
2
1
v
v
30
20
10
0
Preflight 9.5
Physics 103, Spring 2004, U. Wisconsin
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Efficiency
W out
Efficiency of getting work done : Eff 
E in
E
Efficiency of energy conversion : Eff  out
E in
P
Efficiency of power conversion : Eff  out
Pin
W out mgh
Eff 

E in
E in

Energy used by weight lifter
: 8 kcal = (8 kcal) (4186 J/kcal) J
Potential energy of the weight lifted
2705
Eff 
 0.0833  8.33%
33488
2/19/03
: mgh = (120 kg) (9.8 m/s 2 ) (2.3 m) J
Physics 103, Spring 2004, U. Wisconsin
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Preflight Question 7&8
Do you do work on the outside world when you rub your hands to
keep them warm?
1. No, very little work on outside world
2. Yes, a lot of work is done on the outside world
Due to friction, heat is generated
and your hands warm up
70
60
50
40
A
B
30
The heat dissipates to the rest of
your body. Very little goes to
warming up the environment.
20
10
0
Preflight 9.7
2/19/03
Pretty Sure
Not Quite Sure
Just Guessing
Physics 103, Spring 2004, U. Wisconsin
15
Preflight Question 9&10
What is the efficiency of the activity of rubbing hands to keep
warm?
1. Efficiency is very low
2. Efficiency is very high
Due to friction, heat is generated and
your hands warm up
The heat dissipates to the rest of
your body. Very little goes to
warming up the environment.
60
50
40
A
B
30
20
Therefore, efficiency is very high
10
0
Preflight 9.9
2/19/03
Pretty Sure
Not Quite Sure
Just Guessing
Physics 103, Spring 2004, U. Wisconsin
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