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 the total mass M. The sum becomes an integral: M = pt | y(x) dæ For the center of mass, you add each column's x Am, and divide by M: pt x y(x) dæ M Calculate xc. The only quantity you'll need is e = 3 m.
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 the total mass M. The sum becomes an integral: M = pt | y(x) dæ For the center of mass, you add each column's x Am, and divide by M: pt x y(x) dæ M Calculate xc. The only quantity you'll need is e = 3 m.
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Transcribed Image Text:. 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
2
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 the
total mass M. The sum becomes an integral:
М — pt
|
y(x) dæ
For the center of mass, you add each column's x Am,
and divide by M:
pt
x y(x) dx
Xc
M
Calculate xc. The only quantity you'll need is e = 3
%3D
m.
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