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Unformatted text preview: Problem 298 The cable attached to the tractor at B cxerts force F on the framework. Express this force as a
Cartesian vector N Given:
F = 350 1b .
a = 35 ft ; A
b = 50 ft t;
6' = 20 deg ' 5‘ ‘ F
3 ‘ in
Solution: x
Find the position vector and then the force bsin(6)
rAB = bcos(0) Fv = F —a rAB
erBI Problem 2100 Determine the position (x, y, 0) for ﬁxing cable BA so that the resultant of the forces exerted on the
pole is directed along its axis, from B toward 0, and has magnitude F R. Also, what is the magnitude of force F 3? y
ﬁr Given:
F] = 500 N
F2 = 400 N
= 1000 N
a = 1m
[7 = 2 m
c = 2 m
d = 3 m
Solution: Initial Guesses
F3 = 1 N x = l m y = 1 In Given
—c F2 a F3 FR = 0 + — —b + —— y [cZF+d2] —d, [\Ia2+b2+d2] —d (x2+y2+d2] —d x 1.9
3=Find(,,F3xy) ()=(24)m F3=38ON
y . Problem 2107 Given the three vectors A, B, and D, show that A(B + D) = (A B) + (A. D). Solution:
Since the component of (B + D) is equal to the sum of the components of B and D, then A(B + D) = AB + AD (QED) Also, A~(B + D) = (Axi + ij + Azk)[(Bx + Dx)i + (By + Dy)!" + (Bz + Dz)k] Ax(Bx + Dx) + Ay(By + Dy) + AZ(BZ + DZ) 102 = (AxBx + AyBy + A2192) + (AxDx + AyDy + AzDz) II (A. B) + (A D) (QED) Problelh 2119 Deterrnine the projected component of the force F acting along the axis AB of the pipe. Given
F = 80 N
a = 4 m
b = 3 m
c = 12 m
d = 2 m
e = 6 in Solution: Find the force and the unit vector —e —6 ‘ —35.3
rA
rA= —a——b rA= —7 m FV=FIr I Fv= —41.2 N
d— c —10 A —58.8
—e —6 . —0.9
l'AB
rAB = —b rAB = —3 m “AB = '1‘ I “AB = —0.4
d 2 AB 0.3 Now ﬁnd the projection using the Dot product. FAB = Fv' “AB ...
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 Fall '06
 Kane

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