Physics 101: Lecture 10 Potential Energy

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Physics 101 Lecture 10Potential Energy
Energy Conservation

• Todays lecture will cover Textbook Sections 6.5
  - 6.8

• Hour Exam 1, Monday 700 pm
• Conflict exam 515
• Review Session Sunday, Sept. 30, 8 pm, 141
  Loomis, Spring 2005 exam
• Kelpers 3rd law?!

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Suggested Practice Problems

• Old hour exams http//online.physics.uiuc.edu/cou
  rses/phys101/fall07/practice/index.html
• (centripetal motion is on HE1 this semester!)
• Ch 2
• Examples 2.2, 2.5, 2.8, 2.12, 2.13, 2.14
• Problems 1, 5, 7, 11, 13, 17, 29, 49, 69
• Ch 3
• Examples 3.1, 3.2, 3.6, 3.9, 3.11, 3.13
• Problems 5, 13, 33, 47, 57, 65, 67
• Ch 4
• Examples 4.1, 4.6, 4.7, 4.9, 4.12, 4.14
• Problems 1, 3, 5, 9, 17, 19, 23, 25, 27, 35, 41,
  53, 55
• Ch 5
• Examples
• Problems 1,5,13,39,47

Interactive examples on projectile
motion http//research.physics.uiuc.edu/PER/ie_10
0.html
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Review

• Work Transfer of Energy by Force
• WF F d cos?
• Kinetic Energy (Energy of Motion)
• K 1/2 mv2
• Work-Kinetic Energy Theorem
• SW DK

Preview

• Potential (Stored) Energy U

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Work Done by Gravity 1

• Example 1 Drop ball

Wg F d cos? d h Wg mghcos(00)
mgh ?y yf-yi -h Wg -mg?y
d
mg
mg
y
y
x
x
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Work Done by Gravity 2

• Example 2 Toss ball up

Wg F d cos? Wg mgh cos(1800) -mgh ?y
yf-yi h Wg -mg?y
d
mg
y
x
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Work Done by Gravity 3

• Example 3 Slide block down incline

Wg F d cos? d h/cos? Wg
mg(h/cos?)cos? Wg mgh ?y yf-yi
-h Wg -mg?y
?
h
d
mg
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Work and Potential Energy

• Work done by gravity independent of path
• Wg - mgDy - mg (yf - yi)
• Define Ugmgy
• Works for any CONSERVATIVE force
• Modify Work-Energy theorem

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Conservation ACT

• Which of the following statements correctly
  define a Conservative Force
• 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.
• B. 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.
• C. Both of the above statements are correct.
• D. Neither of the above statements is correct.

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Skiing Example (no friction)
A skier goes down a 78 meter high hill with a
variety of slopes. What is the maximum speed she
can obtain if she starts from rest at the top?
Conservation of energy SWnc DK DU
Ki Ui Kf Uf ½ m vi2 m g yi ½ m
vf2 m g yf 0 g yi ½ vf2 g yf
vf2 2 g (yi-yf) vf ?( 2 g
(yi-yf)) vf ?( 2 ? 9.8 ? 78) 39 m/s 87 mph
0 Kf-Ki Uf - Ui
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Pendulum ACT

• As the pendulum falls, the work done by the
  string is
• 1) Positive 2) Zero 3) Negative
• How fast is the ball moving at the bottom of the
  path?

W F d cos q. But q 90 degrees so Work is
zero.
Conservation of Energy (Wnc0) SWnc DK D U 0
Kfinal - Kinitial Ufinal - Uinitial
Kinitial Uinitial Kfinal Ufinal 0 mgh
½ m v2final 0 vfinal ?(2 g h)
h
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Pendulum Demo

• With no regard for his own personal safety your
  physics professor will risk being smashed by a
  bowling ball pendulum! If released from a height
  h, how far will the bowling ball reach when it
  returns?

Conservation of Energy (Wnc0) SWnc DK D U 0
Kfinal - Kinitial Ufinal- Uinitial Kinitial
Uinitial KfinalUfinal 0 mghinitial 0
mghfinal hinitial hfinal
h
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Lecture 10, Preflight 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?
• A. DroppingB. Slide on ramp (no friction)C.
  Swinging downD. All the same

39 2 2 58
X and y directions are independent from each
other so time only depends on y direction.
They all reach the bottom at the same time
because work done by gravity is independent of
the path, and they all reach with the same speed
because they are all starting with the same
velocity and same distance away from the top.
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Lecture 10, Preflight 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. Dropping2. Slide on ramp (no friction)3.
  Swinging down4. All the same

17 9 18 56
Conservation of Energy (Wnc0) SWnc DK D
U Kinitial Uinitial KfinalUfinal 0 mgh ½
m v2final 0 vfinal ?(2gh)
demo
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Lecture 10, Preflight 4
I don't really understand the difference between
conservative and nonconservative forces. If
energy is neither created nor destroyed and is
always conserved, how can there be
nonconservative forces?
We know that potential energy is a conservative
force, but wouldn't kinetic energy be a
non-conservative force? If this is the case, how
can we plug kinetic energy into the equation
regarding work and potential energy?
The fact that mass and angle have no effect on
the speed is somewhat confusing. Although they
reach the bottom at different points, the final
speed is the same. It is somewhat confusing.
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Skiing w/ Friction
A 50 kg skier goes down a 78 meter high hill with
a variety of slopes. She finally stops at the
bottom of the hill. If friction is the force
responsible for her stopping, how much work does
it do?
Work Energy Theorem Wnc Kf - Ki Uf - Ui
½ m vf2 - ½ m vi2 m g yf m g
yi 0 0 0 - g yi m
9.8 ? 78 ? 50 Joules
38200 Joules
Friction always does negative work
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Galileos Pendulum ACT

• How high will the pendulum swing on the other
  side now?
• A) h1 gt h2 B) h1 h2 C) h1 lt h2

Conservation of Energy (Wnc0) SWnc DK D
U Kinitial Uinitial KfinalUfinal 0 mgh1
0 mgh2 h1 h2
m
h1
h2
demo
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Power (Rate of Work)

• P W / Dt
• Units Joules/Second Watt
• How much power does it take for a (70 kg) student
  to run up the stairs in 141 (5 meters) in 7
  seconds?

P W / t m g h / t (70 kg) (9.8
m/s2) (5 m) / 7 s 490 J/s or 490 Watts
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Summary

• Conservative Forces
• Work is independent of path
• Define Potential Energy U
• Ugravity m g y
• Uspring ½ k x2
• Work Energy Theorem
• Chapter 6, problems 27, 31, 35

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