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PHCC 141: Physics for Scientists and Engineers I - Fall 2007
6b. Work, Energy, and Power
Due at 11:59pm on Monday, October 1, 2007
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Number of answer attempts per question is:
5
You gain credit for:
correctly answering a question in a Part, or correctly answering a question in a Hint.
You lose credit for:
exhausting all attempts or requesting the answer to a question in a Part or Hint, or incorrectly answering a question in a Part.
Late submissions:
reduce your score by 100% over each day late.
Hints
are helpful clues or simpler questions that guide you to the answer. Hints are not available for all questions. There is
no penalty
for leaving questions in Hints unanswered.
Grading of
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For
Multiple-Choice
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True/False
questions, you lose
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/
(
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credit per incorrect answer.
For
any other
question, you lose 3% credit per incorrect answer.
Integrate Force to Find Work
Work Done by a Spring
Consider a spring, with spring constant
, one end of which is attached to a wall. The spring is initially unstretched, with the
unconstrained end of the spring at position
.
Part A
The spring is now compressed so that the unconstrained end moves from
to
. Using the work integral
,
find the work done
by
the spring as it is compressed.
Hint A.1
Spring force as a function of position
The spring force vector
as a function of displacement
from the spring's equilibrium position, is given by
where
is the spring constant and
is a unit vector in the direction of the displacement of the spring (in this case, towards the
right).
Part A.2
Integrand of the work integral
The work done by the spring is given by the integral of the dot product of the spring force and an infinitesimal displacement of
the end of the spring:
,
where the infinitesmal displacement vector
has been written as
. Write
in terms of given quantities, and then compute
the dot product to find an expression for the integrand. (Note,
.)
Express your answer in terms of
,
, and
.

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Work Energy Problems
Work-Energy Scaling
A particle of mass
moves along a straight line with initial speed
. A force of magnitude
pushes the particle a distance
along the direction of its motion.
Part A
Find
, the final speed of the particle after it has traveled a distance
.
Part A.1
Find the final kinetic energy
Find
, the final kinetic energy of the particle after it has been pushed a distance
.
Part A.1.a Find the final kinetic energy in terms of the work done
Assume that the work done by the pushing force is
. Find the final kinetic energy,
, of the particle after it has been pushed
a distance
.
Express your answer in terms of the particle's initial kinetic energy,

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