A thin rod of length L and mass m has a linear density X(x) = Ax² where A is a constant and is the distance from the rod's left end. Locate the rod's center of mass (from x = = 0) in terms of its length by filling in the missing factor below.
A thin rod of length L and mass m has a linear density X(x) = Ax² where A is a constant and is the distance from the rod's left end. Locate the rod's center of mass (from x = = 0) in terms of its length by filling in the missing factor below.
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18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
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![Computation
A thin rod of length L and mass m has a linear density A(x) = Ax²
where A is a constant and is the distance from the rod's left end. Locate
the rod's center of mass (from x = 0) in terms of its length by filling in the
missing factor below.
L
Aq.
[Hint: In terms of A and L, the rod's mass is M = f . Evaluate that
integral and substitute into the denominator of the center of mass
The constant A will cancel and
definition: cm =
So x dm
0
Xcm
=
Sot dm
you'll be left with an answer proportional to L.]
L
S₁ x x(x) dx
So
M
Record your numerical answer below, assuming three significant figures.
Remember to include a "-" when necessary.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F047a7e6a-f025-4b5b-ab83-4ffe14f69253%2F558f2983-dfc5-4d28-85ca-77b50995b035%2F81gqbjh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Computation
A thin rod of length L and mass m has a linear density A(x) = Ax²
where A is a constant and is the distance from the rod's left end. Locate
the rod's center of mass (from x = 0) in terms of its length by filling in the
missing factor below.
L
Aq.
[Hint: In terms of A and L, the rod's mass is M = f . Evaluate that
integral and substitute into the denominator of the center of mass
The constant A will cancel and
definition: cm =
So x dm
0
Xcm
=
Sot dm
you'll be left with an answer proportional to L.]
L
S₁ x x(x) dx
So
M
Record your numerical answer below, assuming three significant figures.
Remember to include a "-" when necessary.
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ISBN:
9781938168277
Author:
William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:
OpenStax - Rice University