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Equivalent force systems_2 [compatibility mode]
1. Equivalent forces
Three cables attached to a disk exert on it the
forces shown.
(a) Replace the three forces with an equivalent
force-couple system at A.
(b) Determine the single force which is equivalent
to the force couple system obtained in part a,
and specify its point of application on a line
drawn through points A and D.
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2. Equivalent forces
-99i+99j 103.4i+37.6j
Y
(141,141)
(-100,173.2)
X
XB
(0,-200)
99i-99j
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3. Equivalent forces
-99i+99j 103.4i+37.6j
Y
(100,173.2)
(-100,173.2)
X
XB
(0,-200)
Equivalent
system
99i-99j
F
C
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4. Equivalent forces
-99i+99j
Y
(141,141)
(-100,173.2)
X
XB
(0,-200)
99i-99j
F 99i 99 j 103.4i 37.6 j 99i 99 j 103.4i 37.6 j
M (141i 141 j ) 103.4i 37.6 j
Z ,A
(0i 200 j ) 99i 99 j (100i 173.2 j ) 99i 99 j
5317 k 14526k 19800k 9900k 17147k
17838k
17838k
F
C 103.4i+37.6j
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5. Equivalent forces
-99i+99j 103.4i+37.6j
Y
(141,141)
(-100,173.2)
X
XB
(0,-200)
Equivalent
system
99i-99j
F
P (x,y)
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6. Equivalent forces
-99i+99j
Y
(141,141)
(-100,173.2)
X
XB
(0,-200)
99i-99j
F 99i 99 j 103.4i 37.6 j 99i 99 j 103.4i 37.6 j
M (141i 141 j ) 103.4i 37.6 j
Z ,A
(0i 200 j ) 99i 99 j (100i 173.2 j ) 99i 99 j
5317 k 14526k 19800k 9900k 17147 k
17838k
F
P (x,y)
F F i F j x y
M ( xi yj ) F i F j xF
Z ,A x y y
yFx k
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7. Equivalent forces
F
P (x,y)
Fx i Fy j 103.4i 37.6 j Fx 103.4,Fy 37.6
xFy yFx 17838 103.4 x 37.6 y 17838
Equation of line of action 103.4x-37.6y=17838
Equation of line AD x=0
37.6y=-17838 y=-474mm
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8. Equivalent forces
The steel plate shown will support six 50 mm
diameter idler rollers mounted on the plate as shown.
Two flat belts pass around the rollers, and rollers A
and D will be adjusted so that the tension in each belt
is 45 N. Determine
(a) the resultant couple acting on the plate if a = 0.2
m,
(b) The value of a so that the resultant couple acting
on the plate is 54 Nm clockwise.
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9. Equivalent forces
45 200i aj
40000 a 2
(2a+c,0) 45i+0j
X
c
(-200,-a)
c (2a,2a)
(-200+c,a+200)
-45i+0j Y
-31.82i+31.82j
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10. Equivalent forces
a=200mm
45 200i aj
31.82 i 31.82 j
40000 a 2 45i+0j
(2a+c,0)
X
c
(-200,-a)
c (2a,2a)
(-200+c,a+200)
-45i+0j Y
-31.82i+31.82j
45 200i aj
F 45i 0 j 45i 0 j 31.82i 31.82 j
40000 a 2
45 200i aj
31.82i 31.82 j
40000 a 2
0 for a = 200mm
M (0i 0 j ) (31.82i 31.82 j ) ( 400 c i 0 j ) 45i 0 j
c
( 200 c i 400 j ) 45i 0 j (2ai 2aj ) 31.82i 31.82 j
0k 0k 18000k 63.86ak 63.86ak 18000k 25544k
7544k
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11. Equivalent forces
45 200i aj
40000 a 2
45i+0j
(2a+c,0)
X
c
(-200,-a)
c (2a,2a)
(-200+c,2a)
-45i+0j Y
-31.82i+31.82j 200i aj
45
F 45i 0 j 45i 0 j 31.82i 31.82 j
40000 a 2
45 200i aj
31.82i 31.82 j
40000 a 2
45 200i aj
M c (0i 0 j ) 2a c i 0 j 45i 0 j
40000 a 2
200 c i 2aj 45i 0 j (2 ai 2aj ) 31.82i 31.82 j
0k 0k 90ak 63.86ak 63.86ak 90ak 127.72k
90ak 127.72k 54k
90a 73.72
a 0.82
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