Part A In Section 8.5 we calculated the center of mass by considering objects composed of a finite number of point masses or objects that, by symmetry, could be represented by a finite number of point masses. For a solid object whose mass distribution does not allow for a simple determination of the center of mass by symmetry, the sums of If the density p= M/V of the object is uniform, perform the integration described above and find the x-coordinate of the center of mass of the rod. Express your answer in terms of some or all of the variables p. M. L, and A. Icm = > Yem = must be generalized to integrals from rod's end Icm = M Sx dm, Ym= Sydm Submit Request Answer where z and y are the coordinates of the small piece of the object that has mass dm. The integration is over the whole of the object. Consider a thin rod of length L, mass M, and cross-sectional area A. Let the origin of the coordinates be at the left end of the rod and the positive x-axis lie along the rod. Part B If the density of the object varies linearly with x-that is, p= ax, where a is a positive constant-calculate the x-coordinate of the rod's center of mas: Express your answer in terms of some or all of the variables p, M, L, and A. IB =
Part A In Section 8.5 we calculated the center of mass by considering objects composed of a finite number of point masses or objects that, by symmetry, could be represented by a finite number of point masses. For a solid object whose mass distribution does not allow for a simple determination of the center of mass by symmetry, the sums of If the density p= M/V of the object is uniform, perform the integration described above and find the x-coordinate of the center of mass of the rod. Express your answer in terms of some or all of the variables p. M. L, and A. Icm = > Yem = must be generalized to integrals from rod's end Icm = M Sx dm, Ym= Sydm Submit Request Answer where z and y are the coordinates of the small piece of the object that has mass dm. The integration is over the whole of the object. Consider a thin rod of length L, mass M, and cross-sectional area A. Let the origin of the coordinates be at the left end of the rod and the positive x-axis lie along the rod. Part B If the density of the object varies linearly with x-that is, p= ax, where a is a positive constant-calculate the x-coordinate of the rod's center of mas: Express your answer in terms of some or all of the variables p, M, L, and A. IB =
College Physics
11th Edition
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:Part A
In Section 8.5 we calculated the center of mass by considering
objects composed of a finite number of point masses or objects
that, by symmetry, could be represented by a finite number of
point masses. For a solid object whose mass distribution does
not allow for a simple determination of the center of mass by
symmetry, the sums of
If the density p = M/V of the object is uniform, perform the integration described above and find the x-coordinate of the center of mass of the rod.
Express your answer in terms of some or all of the variables p, M, L, and A.
Xcm =
> Ycm =
?
must be generalized to integrals
TA =
from rod's end
Xem = M Sx dm, Yem = M Sy dm
Submit
Request Answer
where x and y are the coordinates of the small piece of the
object that has mass dm. The integration is over the whole of
the object. Consider a thin rod of length L, mass M, and
cross-sectional area A. Let the origin of the coordinates be at
Part B
the left end of the rod and the positive x-axis lie along the rod.
If the density of the object varies linearly with x-that is, p= ax, where a is a positive constant-calculate the x-coordinate of the rod's center of mass.
Express your answer in terms of some or all of the variables p, M, L, and A.
IB =
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