Need help with the equations on this one Part AIn Section 8.5 we calculated the center of mass by consideringobjects composed of a finite number of point masses or objectsthat, by symmetry, could be represented by a finite number ofpoint masses. For a solid object whose mass distribution doesnot allow for a simple determination of the center of mass bysymmetry, the sums ofIf 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 integralsTA =from rod's endXem = M Sx dm, Yem = M Sy dmSubmitRequest Answerwhere x and y are the coordinates of the small piece of theobject that has mass dm. The integration is over the whole ofthe object. Consider a thin rod of length L, mass M, andcross-sectional area A. Let the origin of the coordinates be atPart Bthe 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 =

Answered: Image /qna-images/answer/5598c54d-7ad7-4723-be5c-e27ffc315ea1.jpg

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 =

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter1: Getting Started

Section: Chapter Questions

Problem 25PQ

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Question

Need help with the equations on this one

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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