Physics 114C Mechanics Lecture 17 Walker: Ch. 7.34 Work

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Physics 114C - MechanicsLecture 17 (Walker
Ch. 7.3-4)Work PowerFebruary 6, 2009

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

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Announcements

• HW5 is due at 1159 PM on Thursday, February 12.
  Homework up to 24 hours late will receive 70
  credit.
• As of today 186/205 clickers are registered. I
  recently sent an E-mail reminder to the
  unregistered students. Cumulative clicker scores
  (27 max) as of Tuesday, Feb. 3 are posted on
  Tycho under Lecture Score 4.
• My office hours are 1230-120 PM on Tuesdays and
  230-320 PM on Thursdays, both in the 114 area
  of the Physics Study Center on the Mezzanine
  floor of PAB C (this building).
• We will have Exam 2 on Friday, February 13. It
  will cover Chapters 5-8 and will be similar to
  Exam 1 in its structure. There will again be
  assigned seating. There are already too many
  requests for right-handed aisle seats and front
  row seats, but new requests will be accepted.

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Lecture Schedule (Part 2)
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Work and Area
If the force is constant, we can graphically
interpret the work done (W F d) as the area of
a rectangle F tall and d wide
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Work Done by a Variable Force
If the force takes on several successive
constant values we can add adjacent rectangles
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Work Done by a Variable Force
We can then approximate a continuously
varying force by a succession of constant values.
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ExampleWork Done by a Varying Force
A force varies with x as shown.
Find the work done by the force on a
particle as the particle moves from x 0.0 m to
x 6.0 m.
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Elastic Solids Restoring 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 is 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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Clicker Question 1
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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Work and Springs
The force needed to stretch a spring an
amount x is F kx.
Therefore, the work done in stretching the spring
is
(7-8)
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Hookes Law and Work
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Clicker Question 2
4.0 m/s
A spring-loaded gun shoots a plastic ball
with a speed of 4.0 m/s. If the spring is
compressed twice as far, what is the balls speed?
a) 2.0 m/s b) 4.0 m/s c) 8.0 m/s d)
16.0 m/s e) 32.0 m/s
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Example Work Doneon a Block by a Spring
A 4.0 kg block on a frictionless surface is
attached to a horizontal spring with k 400 N/m.
The spring is initially compressed to 5.0
cm. (a) Find the work done on the block by the
spring as the block moves from x x1 -5.0 cm
to its equilibrium position of x x2 0 cm. (b)
Find the speed of the block at x2 0 cm.
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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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Power
Power is a measure of the rate at which work
is done
(7-10)
SI power unit 1 J/s 1 watt 1 W 1
horsepower 1 hp 746 W
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Power
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Power and Velocity
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Power and Velocity
If an object is moving at a constant speed
in the presence of friction, gravity, air
resistance, and so forth, the power exerted by
the driving force can be written
(7-13)
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ExampleThe Power of a Motor
A small motor is used to operate a lift that
raises a load of bricks weighing 500 N to a
height of 10 m in 20 s at constant speed. The
lift weighs 300 N. What is the power output
of the motor?
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End of Lecture 17

• Before Monday, read Walker Chapter 8.1-2
• Homework Assignments 5 should be submitted
  using the Tycho system by 1159 PM on Thursday,
  Feb. 12. (24 hours late Þ 70 credit)
• We will have Exam 2 on Friday, February 13. It
  will cover Chapters 5-8 and will be similar to
  Exam 1 in its structure. There will again be
  assigned seating. There are already too many
  requests for right-handed aisle seats and front
  row seats, but new requests will be accepted.