This is an integration problem, to calculate the center of mass (center of gravity) for a continuous distribution. Specifically, we need the horizontal component of the center of mass. The height varies from h to zero according to this function: y(x) = h ( – 1)´ . The constants h and e replace 1.00 m and 3.00 m. There is also a thickness t and a density p. You need two integrals, the total mass and the center of mass. Possibly surprisingly, you don't actually need the numbers t, h, and p.

This is an integration problem, to calculate the center of mass (center of gravity) for a continuous distribution. Specifically, we need the horizontal component of the center of mass. The height varies from h to zero according to this function: y(x) = h ( – 1)´ . The constants h and e replace 1.00 m and 3.00 m. There is also a thickness t and a density p. You need two integrals, the total mass and the center of mass. Possibly surprisingly, you don't actually need the numbers t, h, and p.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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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Question

This is an integration problem, to calculate the center of mass (center
of gravity) for a continuous distribution. Specifically, we need the horizontal component of the
center of mass.
The height varies from h to zero according to this function: y(x) = h ( – 1)´ . The constants h
and e replace 1.00 m and 3.00 m. There is also a thickness t and a density p. You need two
integrals, the total mass and the center of mass. Possibly surprisingly, you don't actually need the
numbers t, h, and p.
Ax
y(x)
The column at x has a mass Am = (density * volume) = y(x) p t Ax. You add all the Am values to get
%3D
the total mass M. The sum becomes an integral:
M :
= pt
У(x) dx
For the center of mass, you add each column's x Am, and divide by M:
pt
Xc =
M
х у(x) dx
Calculate xc. The only quantity you'll need is e = 2 m.

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