X 5. 416 REED'S APPLIED MECHANICS FOR ENGINEERS graving of 4. Working in cm, and taking moments about the centre of sheave arranged vertically: = y = Σ moments of areas Σ areas 0.7854 x 502 x00-7854 x 12.52 x 10 137:815 2 y = 0-10 42-1 = -10 15 = -0.667cm 0.7854 × 50²-0-7854 x 12.52 The minus sign means that the centre of gravity is in the opposite direction to the hole, from the centre of the sheave, . CG = 6.67 mm from centre. Ans. Alternatively, if moments are taken about the thin edge of the sheave, y from edge 50² 0.7854 × 502 ×(250-7854 x 12.52 15 0.7854 × 50²-0-7854 x 12-52 42 × 25-15 35mm 385 = 42 - 1 15 = 25.667 cm from edge = 6.67 mm from centre à 420mm- 20 -120mm 100ma. Ommy 70mm

International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
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Chapter1: Introduction To Statics
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Problem 1.12P: A differential equation encountered in the vibration of beams is d4ydx4=2D where x = distance...
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An eccentric sheave of uniform thickness is 500 mm diameter, the hole for the shaft is 125 mm diameter and its center is 100 mm from the center of the sheave. Calculate the position of the center of gravity of the sheave from its geometrical center.

Hi, I already have the answer but am confused one some steps. I'm wondering how they simplified the equation (where I wrote 1 and 2) and where the numbest came from that I have circled in the questions. Picture attached. Please explain and break it down for me. Thanks 

X
5.
416
REED'S APPLIED MECHANICS FOR ENGINEERS
graving of
4. Working in cm, and taking moments about the centre of sheave
arranged vertically:
=
y =
Σ moments of areas
Σ areas
0.7854 x 502 x00-7854 x 12.52 x 10
137:815
2
y =
0-10
42-1
=
-10
15
= -0.667cm
0.7854 × 50²-0-7854 x 12.52
The minus sign means that the centre of gravity is in the
opposite direction to the hole, from the centre of the sheave,
. CG = 6.67 mm from centre. Ans.
Alternatively, if moments are taken about the thin edge of the
sheave,
y from edge
50²
0.7854 × 502 ×(250-7854 x 12.52 15
0.7854 × 50²-0-7854 x 12-52
42 × 25-15
35mm
385
=
42 - 1
15
=
25.667 cm from edge
= 6.67 mm from centre
à
420mm-
20
-120mm
100ma.
Ommy
70mm
Transcribed Image Text:X 5. 416 REED'S APPLIED MECHANICS FOR ENGINEERS graving of 4. Working in cm, and taking moments about the centre of sheave arranged vertically: = y = Σ moments of areas Σ areas 0.7854 x 502 x00-7854 x 12.52 x 10 137:815 2 y = 0-10 42-1 = -10 15 = -0.667cm 0.7854 × 50²-0-7854 x 12.52 The minus sign means that the centre of gravity is in the opposite direction to the hole, from the centre of the sheave, . CG = 6.67 mm from centre. Ans. Alternatively, if moments are taken about the thin edge of the sheave, y from edge 50² 0.7854 × 502 ×(250-7854 x 12.52 15 0.7854 × 50²-0-7854 x 12-52 42 × 25-15 35mm 385 = 42 - 1 15 = 25.667 cm from edge = 6.67 mm from centre à 420mm- 20 -120mm 100ma. Ommy 70mm
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