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MasteringPhysics
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Introductory mechanics
Chapter 01  Units, Physical Quantities, And Vectors
Due at 11:59pm on Tuesday, September 9, 2008
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Scientific Notation
A number written in scientific notation has the form
, where
and
is an integer.
Part A
Consider the expression
. Determine the values of
and
when the value of this expression is written in
scientific notation.
Hint A.1
A walkthrough
Hint not displayed
Enter
and
, separated by commas.
ANSWER:
,
=
5,2
Vector ComponentsReview
Learning Goal:
To introduce you to vectors and the use of sine and cosine for a triangle when resolving components.
Vectors are an important part of the language of science, mathematics, and engineering. They are used to discuss multivariable
calculus, electrical circuits with oscillating currents, stress and strain in structures and materials, and flows of atmospheres and
fluids, and they have many other applications. Resolving a vector into components is a precursor to computing things with or
about a vector quantity. Because position, velocity, acceleration, force, momentum, and angular momentum are all vector
quantities, resolving vectors into components is
the most important skill
required in a mechanics course.
The figure shows the components of
,
and
, along the
x
and
y
axes of the coordinate system, respectively. The
components of a vector depend on the coordinate system's
orientation, the key being the angle between the vector and the
coordinate axes, often designated
.
Part A
The figure shows the standard way of measuring the angle.
is
measured
to
the vector
from
the
x
axis, and counterclockwise is
positive.
Express
and
in terms of the length of the vector
and
the angle
, with the components separated by a comma.
ANSWER:
,
=
In principle, you can determine the components of
any
vector with these expressions. If
lies in one of the other
quadrants of the plane,
will be an angle larger than 90 degrees (or
in radians) and
and
will have
the appropriate signs and values.
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MasteringPhysics
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Unfortunately this way of representing
, though mathematically correct, leads to equations that must be simplified
using trig identities such as
and
.
These must be used to reduce all trig functions present in your equations to either
or
. Unless you
perform this followup step flawlessly, you will fail to recoginze that
,
and your equations will not simplify so that you can progress further toward a solution. Therefore, it is best to express all
components in terms of either
or
, with
between 0 and 90 degrees (or 0 and
in radians), and
determine the signs of the trig functions by knowing in which quadrant the vector lies.
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 Spring '10
 IASHVILI
 Trigonometry, mechanics, Dot Product

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