Physics 121C Mechanics Lecture 17 Work November 15, 2004

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Physics 121C - MechanicsLecture
17WorkNovember 15, 2004

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

2
Announcements

• Exam 2 will (I hope) be graded and ready to
  return on Wednesday. The grades for the
  multiple-choice part of Exam 2 are already on
  Tycho.
• I plan to come to the area outside the main doors
  of the A102 Lecture Hall BEFORE 1020 on
  Wednesday (or on Friday, if necessary) and make
  the graded exam papers available, in order to
  avoid the mob scene we had in returning the last
  exam.
• Homework Assignment 6 should soon be posted on
  Tycho and will be due on Wednesday, November 24.

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Lecture Schedule (Part 3)
You are here!
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Our Basic Energy Model
Thermal Energy The thermal energy Eth of a
system is associated with the systems
temperature and with the vibration of atoms and
molecules within an object. Friction
converts mechanical energy into thermal energy.
Atwo-way street?
System Energy The system energy Esys is the sum
of the mechanical energy of all objects within
the system plus the thermal energy of the
objects Esys Emech Eth K U Eth
?
?
Energy Transformations kinetic and potential
energy can be easily transformed into thermal
energy, but it is very difficult to transform
thermal energy into mechanical or potential
energy. (Heat-engine needed)
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Heat and Work
A system is always surrounded by a larger
environment, with which there is the possibility
of exchanging energy. An energy exchange
within the system is called an energy
transformation. An energy exchange between
the system and the environment is called an
energy transfer.
The mechanical transfer of energy to or from
the system is called work, denoted by the symbol
W. The corresponding non-mechanical
(thermal) transfer to/from the system is called
heat.
The sign of W is interpreted as follows Wgt0
when the environment does work on the system,
increasing system energy. Wlt0 when the system
does work on the environment, decreasing system
energy.
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Work and Kinetic Energy
Definition of Work Work (W) is energy
transferred to or from a body or system by the
application of a force. But how much energy
does a given force transfer?
Þ
Here, Fs means that component of the force F
that is parallel to the direction of translation
s.
Work
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The Work-Kinetic-Energy Theorem
The work-kinetic-energy theorem When one or
more forces act on a particle as it is displaced
from an initial position to a final position, the
net work done on the particle by these forces
causes the particles kinetic energy to change by
DKWnet.
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Work and Impulse Theorems
Kinetic Energy to/from Momentum
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Calculating and Using Work (1)
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Calculating and Using Work (2)
Consider the work done in these situations
The same amount of work is done on each of
these particles.
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Example Pulling a Suitcase
A rope inclined upward at 45o pulls a
suitcase through the airport. The tension on the
rope is 20 N. How much work does the
tension do, if the suitcase is pulled 100 m?
Note that the same work could have been done
by a tension of just 14.1 N pulling in the
horizontal direction.
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Example Work and Kinetic Energy in a Rocket
Launch
A 150,000 kg rocket is launched straight up.
The rocket engine generates a thrust of 4.0 x
106 N. What is the rockets speed at a
height of 500 m? (Ignore air resistance and mass
loss due to burned fuel.)
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Perpendicular Force and Motion
A car is traveling on a curved highway. The
force due to friction fs points toward the center
of the circular path. How much work does the
frictional force do on the car? Zero!
General Result A force that is everywhere
perpendicular to the motion does no work. (If F
s, then Dvt0 and DK0.)
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Work and the Directionof a Constant Force
Force and Displacement
q
Work W
Sign
Energy Transfer

F(Dr)
0
Energy is transferred into the system. The
particle speeds up. K increases
lt 90

F(Dr)cos q
No energy is transferred. Speed and K are
constant.
0
0
90
-
F(Dr)cos q
gt 90
Energy is transferred out of the system. The
particle slows down. K decreases
-
-F(Dr)
180

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Example Pushing a Puck
A 500 g ice hockey puck slides across
frictionless ice with an initial speed of 2.0
m/s. A compressed air gun is used to exert a
continuous force of 1.0 N on the puck as it moves
50 m. The air gun is aimed at the front edge of
the puck, with the compressed air flow 30o below
the horizontal.
What is the pucks final speed?
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Multiplying Vectors(from Lecture 5)
Given two vectors
Dot Product (Scalar Product)
Cross Product (Vector Product)
AB is B times the projectionof A on B, or vice
versa.
(determinant)
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Scalar or Dot Product of Vectors
Unit Vectors
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ExamplesCalculating Dot Products
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ExampleWork from a Dot Product
A 60 kg skier is gliding at 2.0 m/s when he
starts down a very slippery 50 m long 100
slope. What is his speed at the bottom?
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Clicker Question 1
Which force does
the most work? (a) The 10 N force (b) The 8 N
force (c) The 6 N force (d) All are equal
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Work Done by a Variable Force
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ExampleUsing Work to Find Car Speed
A 1500 kg car accelerates from rest with a
net force that decreases linearly with position
from 10,000 N to zero, as shown. What is
the cars speed after traveling 200 m?
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ExampleWork-Kinetic-EnergyTheorem for a Spring
The pin-cube machine was an unsuccessful
predecessor of the pinball machine. A 100 cube
is launched by pulling a spring back 20 cm and
releasing it. The spring constant is k20 N/m
and the kinetic coefficient of friction is
mk0.10 What is the cubes launch speed, as
it leaves the spring?
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Work, Force, andPotential Energy
General Observation the work done by gravity is
independent of the path followed by the object
and depends only on Dy.
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Conservative Forces
Consider a more general case in which a
force F (similar to gravity) depends only on the
position along any path taken by a particle
moving from point A to point B. The potential
energy U also depends only on location UU(r ).

• Potential energy is an energy of position. The
  system has a unique value of potential energy
  when the object is at A, a different value when
  the object is at B, etc. Thus, the net change in
  potential energy is DUUB-UA, and is the same
  whether the object moves form A to B along Path 1
  or along Path 2.
• Potential energy is transformed to kinetic energy
  with DK-DU. If DU is independent of path, then
  DK must also be independent of path. In moving
  from A to B, the particle must arrive at B with
  the same kinetic energy, no matter which path is
  taken.
• The change in the particles kinetic energy is
  related to the amount of work done on the
  particle by force F. According to the
  work-kinetic-energy theorem, DKW. Because DK is
  independent of path, the work W done by the force
  in moving from A to B must also be independent of
  path.

A potential energy can be associated with any
conservative force.
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End of Lecture 17

• Before the next lecture, read Knight, Sections
  11.6 through 11.9.
• Homework Assignment 6 is posted on Tycho and is
  due on Wednesday, November 17.