Physics 121C Mechanics Lecture 15 Energy November 5, 2004

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Physics 121C - MechanicsLecture
15EnergyNovember 5, 2004

• John G. Cramer
• Professor of Physics
• B451 PAB
• cramer_at_phys.washington.edu

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Announcements

• Homework Assignment 5 is now posted on Tycho
  and is due on Wednesday, November 10.
• Exam 2 will be held on Friday, November 12 in
  this room.
• Exam seating assignments will be posted on Tycho
  several days before the exam. Please look up
  your seat assignment before arriving at the exam.
  You may request a special seat type
  (left-handed, right handed on an aisle, up front,
  table in back, etc.) by sending me E-mail in the
  next few days.

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Lecture Schedule (Part 2)
You are here!
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Money as a Conserved Quantity
Johns Observations
Johns Laws of Money
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Energy as a Conserved Quantity
The Laws of Energy
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Kinetic and Gravitational Energy
and
Þ
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Kinetic and Potential Energy
Energy units 1 joule 1 J 1 kg m2/s2 1 N m
Example A 0.5 kg mass at a height of 1 m moves
with a velocity of 4.0 m/s. What is its kinetic
energy? What is its gravitational potential
energy? K ½mv2 ½(0.5 kg)(4.0 m/s)2 4.0 kg
m2/s2 4.0 J Ug mgy (0.5 kg)(9.80 m/s2)(1
m) 4.9 J
Enet K Ug 8.9 J is a conserved quantity (K
Ug)f (K Ug)i
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Example Launching a Pebble
Bob uses a slingshot to shoot a 20 g pebble
straight up with a speed of 25 m/s. How high
does the pebble go?
The rise of the pebble converts kinetic
energy to gravitational potential energy, and at
maximum height, K0. K1 Ug1 K0 Ug0
(conservation of energy) ½mv12mgy1
½mv02mgy0 mgy1 ½mv02 y1 v02/2g y1 (25
m/s)2/(2x9.80 m/s2) 31.9 m (Note that we
could have used the kinematic equation v12 v02
- 2gy1)
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Clicker Question 1
Which inequality describes the relation of
the gravitational potential energies of the four
balls shown above?
c) E1E2E3E4
a) E1gtE2gtE3gtE4
e) E1ltE2ltE3ltE4
b) E1gtE2E4gtE3
d) E1ltE2E4ltE3
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Energy Bar Charts
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The Zero of Potential Energy
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ExampleThe Speed of a Falling Rock
A rock is released from rest. Use both
Bettys and Bills perspectives to calculate its
speed just before it hits the ground.
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Gravitational Potential Energy
Consider a block moving on a surface of arbitrary
shape
This is valid for any frictionless surface,
regardless of shape.
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Clicker Question 2
A small child slides down four frictionless
sliding boards. Which relation below describes
the relative sizes of her speeds at the bottom?
c) vAvBvCvD
a) vCgtvAgtvBgtvD
e) vCltvAltvBltvD
b) vAgtvBvCgtvD
d) vAltvBvCltvD
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Example The Speed of a Sled
Christine runs forward with her sled at 2.0
m/s. She hops onto the sled at the top of a 5.0
m high, very slippery slope. What is her
speed at the bottom?
K1 Ug1 K0 Ug0
½mv12mgy1 ½mv02mgy0 v1 v02 2gy1½
(2.0 m/s)22(9.80 m/s2)(5.0 m)½ 10.1 m/s
Notice that the steepness of the slope
and/or whether it has bumps and dips does not
matter in determining the answer. Only the
change in height and the initial speed are
relevant to the answer.
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Example Ballistic Pendulum
A 10 g bullet is fired into a 1.2 kg block
of wood that hangs from a 150 cm long string.
The bullet embeds itself in the block, and the
block swings out to an angle of 40o. What
was the initial speed of the bullet?
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Conservation ofMechanical Energy
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Strategy Conservationof Mechanical Energy

• MODEL Choose a system without friction or other
  losses of mechanical energy.
• VISUALIZE Draw a before-and-after pictorial
  representation. Define symbols that will be used
  in the problem, list known values, and identify
  what youre trying to find.
• SOLVE The mathematical representation is based
  on the law of conservation of mechanical energy.
• ASSESS Check that your result has the correct
  units, is reasonable, and answers the question.

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Basic Energy Model

• There are (at least) two kinds of energy, kinetic
  energy K associated with motion and potential
  energy U associated with the position of a
  particle.
• Kinetic energy can be transformed into potential
  energy, and potential energy can be transformed
  into kinetic energy.
• Under some circumstances, the mechanical energy
  Emech K U is a conserved quantity. Its value
  at the end of a process is the same as at the
  beginning. (Energy loss0)

Q1 Under what circumstances is Emech
conserved? Q2 What happens to the energy when
Emech is not conserved? Q3 How do you calculate
U for forces other than gravity?
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Clicker Question 3
A box slides alond a frictionless surface, as
shown in the figure. It is released from rest at
the position shown. What is the highest point h
that the box reaches on the other side?
d) hc
c) hb
b) ha
a) hlta
e) hgtc
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Elastic Solids andRestoring Forces
An elastic material is one that exhibits a
restoring force, a force that acts so that it
restores a system to an equilibrium position.
Examples are springs and rubber bands. An
elastic material stores potential energy when it
is deformed and restores it when it returns to
equilibrium. Microscopically, elastic solids
depend on the spring-like bonds that bind atoms
in a solid.
rubberband
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Stretching a Spring
The unloaded spring has a length L0. Hang a
weight of mass m on it and it stretches to a new
length L. Repeat the process and measure DsL-L0
vs. the applied force Fspmg. We find that
FspkDs, where k is the spring constant.
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Hookes Law
The linear proportionality between force and
displacement is found to be valid whether the
spring os stretched or compressed, and the force
and displacement are always in opposite
directions. Therefore, we write the
force-displacement relation as
This relation for the restoring force of a
spring is sometimes called Hookes Law, named
after Robert Hooke, a contemporary of Newton. It
is not really a law or nature, but rather a rule
of behavior for most springs.
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Example Dragging a Block (1)
A spring is attached to a 2 kg block. The
other end is pulled by a motorized toy train that
moves forward at 5.0 cm/s. The spring constant is
k50 N/m and the coefficient of static friction
between the block and the surface is ms0.6. The
spring is in equilibrium at t0 s when the train
starts to move. At what time does the block
start to slip?
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Example Dragging a Block (2)
This is an example of stick-slip motion, which
is common in nature. Example behavior of rocks
during seismic activity and earthquakes.
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Clicker Question 4
The force vs. displacement curves of three
springs are measured. Which spring has the
largest spring constant? a) Spring 1 b)
Spring 2 c) Spring 3 d) They are all the
same
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End of Lecture 15

• Before the next lecture, read Knight, Sections
  10.5 through 10.7.
• Homework Assignment 5 is posted on Tycho and is
  due on Wednesday, November 10.
• Exam 2 will be held on Friday, November 12 in
  this room.
• Exam seating assignments will be posted on Tycho
  several days before Exam 2. Please look up your
  seat assignment before arriving at the exam. You
  may request a special seat type (left-handed,
  right handed on an aisle, up front, table in
  back, etc.) by sending me E-mail before Monday.