In Section 8.5 we calculated the center of mass by considering objects composed of ajinite number of point masses or objects that, by symmetry, could be represented by a finite number of point masses....

1 answer below »

In Section 8.5 we calculated the center of mass by considering objects composed of ajinite 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 Eqs XXXXXXXXXXmust be generalized to integrals where x and y are the coordinates of the small piece of the object that has mass t/m 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.
(a) If the density p = M/V of the object is uniform, perform the integration described above to show that the x-coordinate of the center of mass of the rod is at its geometrical center.
(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 mass.

Answered Same Day Dec 24, 2021

Solution

David answered on Dec 24 2021

129 Votes

SOLUTION.PDF

In Section 8.5 we calculated the center of mass by considering objects composed of ajinite number of point masses or objects that, by symmetry, could be represented by a finite number of point masses....

Solution

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment