Physics 114C Mechanics Lecture 16 Walker: Ch' 7'12 Work

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Physics 114C - MechanicsLecture 16 (Walker
Ch. 7.1-2)Work EnergyOctober 24, 2008

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

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Announcements

• Homework Assignment 5 is posted on Tycho and is
  due by 1159 PM on Thursday, October 30.
  Homework up to 24 hours late will receive 70
  credit.
• There are now 144/166 clicker registrations.
• My office hours are 130-220 PM on Tuesdays and
  330-420 PM on Thursdays, both in the 114 area
  of the Physics Study Center on the Mezzanine
  floor of PAB C (this building).
• If you have not yet picked up your Exam 1, you
  can get if from Susan Hong, C136 PAB. Regrade
  requests for Exam 1 should be turned in to Susan
  by noon Monday, October 27. See the 114C
  Syllabus for instructions on how to request a
  regrade.

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Lecture Schedule (Part 2)
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Work Done by a Constant Force
The definition of work, when the force is
parallel to the displacement
(7-1)
SI work unit newton-meter (Nm) joule, J
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Typical Work
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Work for Force at an Angle
If the force is at an angle to the displacement
(7-3)
Only the horizontal component of the force
does any work (horizontal displacement).
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Work Summary
Energy is transferred from person to spring
as the person stretches the spring. This is
work.
Work 0
SI Units for work 1 joule 1 J 1 Nm 1
electron-volt 1 eV 1.602 x 10-19 J
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Work Done by a Constant Force
The work can also be written as the dot
product of the force F and the displacement d
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Negative and Positive Work
The work done may be positive, zero, or
negative, depending on the angle between the
force and the displacement
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Perpendicular Force and Work
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.
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Work on a Systemwith Many Forces
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Work Done by a Constant Force
If there is more than one force acting on
an object, we can find the work done by each
force, and also the work done by the net force
(7-5)
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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 by pulling in the
horizontal direction.
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Gravitational Work
In lifting an object of weight mg by a
height h, the person doing the lifting does an
amount of work W mgh. If the object is
subsequently allowed to fall a distance h,
gravity does work W mgh on the object.
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Example Loading with a Crane
A 3,000 kg truck is to be loaded onto a ship
by a crane that exerts an upward force of 31 kN
on the truck. This force, which is large enough
to overcome the gravitational force and keep the
truck moving upward, is applied over a distance
of 2.0 m. (a) Find the work done on the truck by
the crane. (b) Find the work done on the truck
by gravity. (c) Find the net work done on the
truck.
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Positive NegativeGravitational Work
When positive work is done on an object,
its speed increases when negative work is done,
its speed decreases.
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Kinetic Energy The Work-Energy Theorem
After algebraic manipulations of the
equations of motion, we find
Therefore, we define the kinetic energy
(7-6)
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Kinetic Energy The Work-Energy Theorem
Work-Energy Theorem The total work done on an
object is equal to its change in kinetic energy.
(7-7)
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Clicker Question 1
Car 1 has twice the mass of Car 2, but they
both have the same kinetic energy. If the speed
of Car 1 is v, approximately what is the speed of
Car 2?
a) 0.50 v
e) 2.00 v
d) 1.414 v
c) v
b) 0.707 v
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Problem Solving Strategy
Picture The way you choose the y direction or
the x direction can help you to easily solve a
problem that involves work and kinetic
energy. Solve1. Draw the particle first at its
initial position and second at its final
position. For convenience, the object can be
represented as a dot or box. Label the initial
and final positions of the object.2. Put one or
more coordinate axes on the drawing.3. Draw
arrows for the initial and final velocities, and
label them appropriately.4. On the
initial-position drawing of the particle, place a
labeled vector for each force acting on it.5.
Calculate the total work done on the particle by
the forces and equate this total to the change in
the particles kinetic energy. Check Make sure
you pay attention to negative signs during your
calculations. For example, values for work done
can be positive or negative, depending on the
direction of the displacement relative to the
direction of the force. Kinetic energy values,
however, are always positive.
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Example A Dogsled Race
During your winter break, you enter a
dogsled race across a frozen lake, in which the
sleds are pulled by people instead of dogs. To
get started, you pull the sled (mass 80 kg) with
a force of 180 N at 40 above the horizontal.
The sled moves Dx 5.0 m, starting from rest.
Assume that there is no friction. (a) Find the
work you do. (b) Find the final speed of your
sled.
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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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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 to slow it
down as it moves 0.50 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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Example Work on an Electron
In a television picture tube, electrons are
acceleratedby an electron gun. The force that
accelerates theelectron is an electric force due
to the electric fieldin the gun. An electron is
accelerated from rest by anelectron gun to an
energy of 2.5 keV (2,500 eV) over a distanceof
2.5 cm. (1 eV 1.60 x 10-19 J) Find the
force on the electron, assuming that it is
constant and in the direction of the electrons
motion.
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End of Lecture 16

• Before Monday, read Walker Chapter 7.3-4
• Homework Assignments 5 should be submitted
  using the Tycho system by1159 PM on Thursday,
  Oct. 30.(24 hours late Þ 70 credit)
• Register your clicker, using the Clicker link
  on the Physics 114C Syllabus page.