w=7 x=0 y=7 z=7 for both questions P2.76R The angle between spring AC and the po

Question

w=7
x=0
y=7
z=7
for both questions

P2.76R The angle between spring AC and the post AD is 32. Knowing that the tension in the spring is 5X lb, determine (a) the x, y, and z components of the force exerted on the circular plate at poimt C, (b) the angles e, 8, and Q, defining the direction of the force at C. In order to move a wrecked truck, two cables are attached at A and pulled by winches B and Cas shown. Knowing that the tension in cable AC is 1.Y kips, determine the x, y, and is ft z components of the force exerted at A by the cable 28 t

Explanation / Answer

P2. 88R
SO COORINDATES OF POINT A = (5X, 0,4Z)
B = (0,18,4Z + 32)
C = (0,28,0)

tension in AC = 1.Y kips
tension in BA = T
weight of the truck = W

so from force balance
1.Y(-5Xi 28j - 4zki) + T(-5Xi + 18j + 32k) = -g(sin(32)i + cos(32)j )

comparing coefficients
-5*1.Y*X - 5XT = - g*sin(32)
28*1.Y + 18T = -g*cos(32)
-4z*1.Y + 32T = 0
T = 0.125z*1.Y

28*1.Y = -2.25z*1.Y - 5.198
1.Y = -5.198/(28 + 2.25z)

w = 7
y = 7
z = 7
x = 0

so x compoennt of force = 1.Y(-5X) = -59.5 kips
y cpomponent of fore = 1.Y*28 = 47.6 kips
z conmonent of force = -1.y*4z = -47.6 kips

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