© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–121.
Determine the angle between the two cables attached to
the pipe.
u
SOLUTION
z
60
F
2
25 lb
uF2=cos 135°i+cos 60°j+cos 60°k
© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
Ans:
FBA =187 N
2–123.
Determine the magnitude of the projected component of the
force F = {400i – 200j + 500k} N acting along the cable BA.
SOLUTION
z
B
C
D
3 m
1 m
2 m
1 m
Fu
© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
Ans:
FCA =162 N
*2–124.
Determine the magnitude of the projected component of the
force F = {400i – 200j + 500k} N acting along the cable CA.
z
B
C
D
3 m
1 m
2 m
1 m
Fu
© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–125.
Determine the magnitude of the projection of force
along the axis.uF =600 N
SOLUTION
Unit Vectors: The unit vectors and must be determined first.From Fig. a,
Thus, the force vectors is given by
Vector Dot Product: The magnitude of the projected component of along the
axis is
Ans.=246 N
=(–200)(sin30°) +400(cos 30°) +400(0)
Fu=F#uu=(–200i+400j+400k)#(sin30°i+cos 30°j)
uF
F=FuOA =600a– 1
3i–2
3j+2
3kb=5–200i+400j+400k6 N
F
uu=sin30°i+cos30°j
uOA =rOA
rOA
=(–2–0)i+(4 –0)j+(4 –0)k
3(–2–0)2+(4 –0)2+(4 –0)2
=-
1
3 i+2
3 j+2
3 k
uu
uOA
30
2 m
4 m
4 m
F 600 N
z
xu
O
y
A
2–126.
Determine the magnitude of the projected component of
the 100-lb force acting along the axis BC of the pipe.
z
y
D
3 ft
6 ft
4 ft
8 ft
A
B
u
x
© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–127.
Determine the angle
u
between pipe segments BA and BC.
z
y
D
3 ft
6 ft
4 ft
8 ft
A
B
2 ft
u
x
SOLUTION
^
2–130.
Determine the angles and made between the axes OA
of the flag pole and AB and AC, respectively, of each cable.
fu
4m
C
B
z
2m
1.5 m
152
2–131.
Determine the magnitudes of the components of acting
along and perpendicular to segment BC of the pipe
assembly.
F
SOLUTION
y
x
z
A
B
4 ft
2 ft
4 ft
3 ft
*2–132.
Determine the magnitude of the projected component of
along AC.Express this component as a Cartesian vector.
F
SOLUTION
y
x
z
A
B
4 ft
2 ft
4 ft
3 ft
© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–133.
Determine the angle between the pipe segments BA and BC.
u
SOLUTION
y
x
z
A
B
4 ft
2 ft
4 ft
3 ft
SOLUTION
2–134.
If the force F = 100 N lies in the plane DBEC, which is
parallel to the x–z plane, and makes an angle of 10
°
with the
extended line DB as shown, determine the angle that
F makes with the diagonal AB of the crate.
30
F
2
6 kN
0.5 m
F
B
C
A
x
y
E
0.2 m
15
z
z¿
15
10u
0.2 m
D
© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–135.
Determine the magnitudes of the components of force
acting parallel and perpendicular to diagonal AB
of the crate.
F=90 lb
SOLUTION
1 ft
60
45
F 90 lb
A
B
z
*2–136.
SOLUTION
Vector Dot Product: The magnitudes of the projected component of Falong the x
and yaxes are
The negative sign indicates that Fxis directed towards the negative xaxis.Thus
Ans.Fx=75 N,
Fy=260 N
=260 N
=-75(0) +259.81(1) +129.90(0)
F
y=F#j=
A
–75i+259.81j+129.90k
B
#j
=-75 N
=-75(1) +259.81(0) +129.90(0)
F
x=F#i=
A
–75i+259.81j+129.90k
B
#i
=[–75i+259.81j+129.90k] N
Determine the magnitudes of the projected components of
the force acting along the xand yaxes.F=300 N
z
A
300 mm
F300 N
30
30
2–137.
z
A
O
xy
300 mm
300 mm
300 mm
F300 N
30
30
Determine the magnitude of the projected component of
the force acting along line OA.F=300 N
SOLUTION
2–138.
Determine the angle
u
between the two cables.
z
B
C
y
4 ft
6 ft
10 ft
10 ft
8 ft
uFAB 12 lb
SOLUTION
#r
© 2016 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently
exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.
2–139.
Determine the projected component of the force
F = 12 lb acting in the direction of cable AC. Express the
result as a Cartesian vector.
z
B
C
y
4 ft
6 ft
10 ft
10 ft
8 ft
uFAB 12 lb
SOLUTION