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Unformatted text preview: 1 ' ‘ 4 u
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I 783‘ Determine all forces acting on member BCD of the _ linkage shown in Fig. 137—83.
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788“ A block with a mass of 150 kg is supported by a ca— ‘ ble which passes over a ISOmm diameter pulley that is at 
tached to a frame as shown in Fig P7 88. Determine ail forces acting on member BCD of the frame. a ’77, Cal.
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l . {3.2 .g g): .._/JD. 300—50 {$05,149. F133:  L; 798 Determine all forces acting on member ACE of the
frame shown in Fig. P798. The diameter of the pulley at E
" is 120 mm. The mass of body Wis 100 kg. ZIFV ‘ Ev "
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i . ' . The tractor boom supports the uniform mass of 500 Kg ’ in the‘bucket which has a center of mass at G. Determine
the force in cylinder ~ ' . .CD and the resultant force
at pin .F. The load is supported equally on each side
of the tractor by a similar mechanism. 2 i I A Gilkg cabinet is mounted on casters which can be locked to‘pre—
vent their rotation. The coeﬂicient of friction £59.30. If' it = 800 mm. determine
the magnitude of the force F required to move the cabinet to the right (a) if all
casters are locked, (b) if the casters at B are locked and the casters at A are free to rotate. ' 3. The coeﬂiclents of friction are p5 = 0.25 and pk = 0.20 between all
surfaces of contact. Determine the smallest force I? required to start block D
moving if (a) block C is restrained by cable AB as shown, (11) cable AB is removed. 4; ., The coefﬁcients of friction'between the block and the incline are
[15 = 0.30 and a}: = 0.2.5. Determine whether the block is in equilibrium and ﬁnd the magnitude and direction of the friction force when P ='150 N. 5. A hand brake is used to control the speed of a ﬂywheel as shown. The coefﬁcients of ﬁiction are as = 0.3 and pk = 0.25. What torque should be applied to the ﬂywheel to keep it
rotating clockwise at a constant speed when P = 10 lb? ME 224L—MECHANICS LAB WORKSHEET 9
Page 2 6. Find the centroid of the Cshaped area with
respect to the x and y axes shown. 7. Find the centroid of the plane area with respect
to the x and y axes shown. 8. Find the centroid of the'Fshaped area with
respect to the x and y axes shown. 9. Find the coordinates of the centroid of the
shaded area with respect to the x and y axes. 51B SHEEN?!
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ofthe tractor by a. similar machanism. .. — ., ' _ , 02m 1.25111
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@WEWEW _ Engineers Computation Pad :en t semcammmmm , Example 811 WWWWMWNWWWN;M%WWMW$W  mtt‘ilfmii Wm . , Examplesrlz SolutiOn Centroid of 0 Composite Area with a Hole Problem Statement Let the C—shaped area of Fig. E8103 be represented by two parts
(1 and 2) as shown in Fig. E811. Part 1 is a rectangular area without the hole, and part 2 is a square area corresponding to the hole. Determine the centroid of the C—shaped area by
considering parts 1 and 2. . Figure £8.11 From Fig. E831, we can tabulate the sums of the moments of the areas of parts 1 and 2
with respect to the x and y axes, as shown in Table 13.8.11. Note that the sums in Table E8.11 are the same as the sums in Table E810. Thus, the
centroid coordinates are, as in Example 8.10, F 25500 x— 1500 —17.0mm
__4osoo_
32—1500 “27.0mm The centroidal coordinates have the same signs as those in Example 8.10, relative to the
x and 3: reference axes. Also, the area of the hole (part 2 in Fig. E8.ll) is taken as nega
tive, and, therefore, the moments of that area are also negative {see Eq. (8.21)]. Table £8.11
Centroid soordinates of a composite area with a hole
AREA camnote DISTANCE MOMENT our AREA
PA RT [mmzl [mm] [m3]
_____—————*———‘—r———‘_"—‘_"_“
i A: xi Yr APT! Ar}:
1 2 400 20 3O 48 000 72 000
2 —900 25 35 —22 500 31 500
Sums 1 500 —— — 25 500 40 500 Centroid of the Cross Section
of 0 Structural Member Problem Statement Along, ﬂat sheet of steel, 0.5 in thick, is bent into the shape shown 1n crosssection in Fig. E8.12a. Determine the centroid coordinates (E, i) of the cross sec—
tion. SOLUTION Composite Pa rte. The plate 15 divided into three segments as shown
in Fig. 9—185. Here the area of the small rectangle © 15 considered ‘negative” since it must be subtracted from the larger one Q). Moment Arms. The centroid of each segment is located as indicated ' in the figure. Note that the 32' coordinates of ® and C3) are negative. Summertime. Taking the data from Fig. 948b, the calculations are
tabulated as follows: Segment A (1’12) §‘(ft) 37m) SEA (1‘?) 37A (ft3)
W
1 §(3)(3) = 4.5 1 1 4.5 4.5
2 (3)(3) = 9 —1.5 1.5 —13.5 13.5
3 —(2)(1) = —2 —2.5 2 s —4
M = 11.5 23m = 74 2331 = 14
H__mm—_n______
Thus,
BIA —4
X“  E—A'H m — —0. 348 ft Ans
— _ EM _ .21 _
y— E A 11' 5 — 122ft Ans. NOTE. If these results are plotted m Fig 9—18, the location of point C
seems reasonable. 9.3 COMPOSITE BODIES 481 (b) 92L 3.9,,— is; y; A“
a: :LS’ 2%‘2965 75: ‘29”
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 Summer '06
 Lipovetsky
 Statics

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