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PHCC 141: Physics for Scientists and Engineers I - Fall 2007
6a. Work, Energy, and Power
Due at 11:59pm on Thursday, September 27, 2007
Hide Grading Details
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
Incorrect Answers
For
Multiple-Choice
or
True/False
questions, you lose
100%
/
(
# of options - 1
)
credit per incorrect answer.
For
any other
question, you lose 3% credit per incorrect answer.
Work Energy Theorem and Exercises
The Work-Energy Theorem
Learning Goal:
To understand the meaning and possible applications of the work-energy theorem.
In this problem, you will use your prior knowledge to derive one of the most important relationships in mechanics: the
work-energy theorem. We will start with a special case: a particle of mass
moving in the
x
direction at constant acceleration
.
During a certain interval of time, the particle accelerates from
to
, undergoing displacement
given by
.
Part A
Find the acceleration
of the particle.
Hint A.1
Some helpful relationships from kinematics
By definition,
.
Furthermore, the average speed is
,
and the displacement is
.
Combine these relationships to eliminate
.
Express the acceleration in terms of
,
, and
.
ANSWER:
=
Part B
Find the net force
acting on the particle.
Hint B.1
Using Newton's laws
Hint not displayed
Express your answer in terms of
and
.
ANSWER:
=
Part C

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Find the net work
done on the particle by the external forces during the particle's motion.
Express your answer in terms of
and
.
ANSWER:
=
Part D
Substitute for
from Part B in the expression for work from Part C. Then substitute for
from the relation in Part A. This will
yield an expression for the net work
done on the particle by the external forces during the particle's motion in terms of mass
and the initial and final velocities. Give an expression for the work
in terms of those quantities.
Express your answer in terms of
,
, and
.
ANSWER:
=
The expression that you obtained can be rearranged as
The quantity
has the same units as work. It is called the
kinetic energy
of the moving particle and is denoted by
.
Therefore, we can write

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