can you help show me how to calculate all-in table proforma, please give me detail on how to get all values in the table?

International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:Andrew Pytel And Jaan Kiusalaas
Chapter5: Three-dimensional Equilibrium
Section: Chapter Questions
Problem 5.2P: Draw the FBD for the bar described in Prob. 5.1 if the bar is homogeneous of mass 50 kg. Count the...
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can you help show me how to calculate all-in table proforma, please give me detail on how to get all values in the table?

Question
A rotating shaft carries four masses, A, B, C and D, rigidly attached to it; the mass centers are
at 30mm, 36mm, 39mm and 33mm respectively from the axis of rotation; A, C and D are 7.5kg,
5kg and 4kg; the axial distance between A and B is 400mm and that between B and C is
500mm; the eccentricities of A and C are at 90° to one another.
Find, for complete balance,
(a)
the angle between A, B and D;
(b)
the axial distance between the planes of revolution of C and D; and
(c)
the mass B.
Solution
A
B.
D
D
90°
115
-0-4m->-0:5m->
xm->
(a)
(b)
Figure Q1
The plane of B, Figure Q1(a), is chosen as the reference plane since it contains one of the
unknown masses and distances measured to the right of it are regarded as positive. Using the
given data, the following table is complied.
Transcribed Image Text:Question A rotating shaft carries four masses, A, B, C and D, rigidly attached to it; the mass centers are at 30mm, 36mm, 39mm and 33mm respectively from the axis of rotation; A, C and D are 7.5kg, 5kg and 4kg; the axial distance between A and B is 400mm and that between B and C is 500mm; the eccentricities of A and C are at 90° to one another. Find, for complete balance, (a) the angle between A, B and D; (b) the axial distance between the planes of revolution of C and D; and (c) the mass B. Solution A B. D D 90° 115 -0-4m->-0:5m-> xm-> (a) (b) Figure Q1 The plane of B, Figure Q1(a), is chosen as the reference plane since it contains one of the unknown masses and distances measured to the right of it are regarded as positive. Using the given data, the following table is complied.
Select plane B since it contains one of the unknown masses and distance measured to the right
of it are regarded as positive.
Table proforma.
mr
mrl
Plane
((kg)
(mm)
(kg.mm)
(m)
(kg.mm.m)
A
7.5
30
225
-0.4
-90
B
m
36
36m
39
195
0.5
97.5
D
33
132
0.5 + X
66 + 132x
The couple polygon, Figure Q1(c), is constructed from the data in the mrl column, the direction
of the couple due to A being downwards since it is negative.
975
132
195
90
66+132 *
225.
36m
Figure Ql(c)
Figure Q1(d)
By measurement, the closing side, ad = 132-6 = 66 + 132z kg mm m
from which
z= 0-505 m
Also
0 = 474°
The force polygon, Figure Q1(d), is then constructed, using the data in mr column and the
known directions of the forces at A, C and D.
By measurement, the closing side, db = 330 = 36m kg mm
.. m= 9-16 kg
Also
$= 174°
from which the angle between B and D=115°
The relative positions of the masses are shown in Figure Q1(b)
Transcribed Image Text:Select plane B since it contains one of the unknown masses and distance measured to the right of it are regarded as positive. Table proforma. mr mrl Plane ((kg) (mm) (kg.mm) (m) (kg.mm.m) A 7.5 30 225 -0.4 -90 B m 36 36m 39 195 0.5 97.5 D 33 132 0.5 + X 66 + 132x The couple polygon, Figure Q1(c), is constructed from the data in the mrl column, the direction of the couple due to A being downwards since it is negative. 975 132 195 90 66+132 * 225. 36m Figure Ql(c) Figure Q1(d) By measurement, the closing side, ad = 132-6 = 66 + 132z kg mm m from which z= 0-505 m Also 0 = 474° The force polygon, Figure Q1(d), is then constructed, using the data in mr column and the known directions of the forces at A, C and D. By measurement, the closing side, db = 330 = 36m kg mm .. m= 9-16 kg Also $= 174° from which the angle between B and D=115° The relative positions of the masses are shown in Figure Q1(b)
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