Posted: December 17th, 2014

A vector B has three dimensions along the xyz coordinates and can be exemplified by the vector sum of the three rectangular components. B=Tx +Ty+Tz =v (Tx)² +(Ty)²+ (Tz)² =v(30)² +(32)²+ (30)² : v2824 =53.14lb

Question 1
A vector B has three dimensions along the xyz coordinates and can be exemplified by the vector sum of the three rectangular components.
B=Tx +Ty+Tz
=v (Tx)² +(Ty)²+ (Tz)²
=v(30)² +(32)²+ (30)²
: v2824
=53.14lb

Question 2
When forces exerts on an object which is at rest are balanced, then the object is said to be in a state of static equilibrium. In such a case the following conditions

exists: The sum of the external forces on the resting object must equal zero.
Determine magnitude of F1 and F3.Let TL and TR represent the coordinates
?F=F1+F2+F3=0
?Fx =0=-FL cos 135°
?Fy=0-FR sin 45°
a)?Fx=Tl cos 135°+  Tr cos45°=0
b) ?Fy=Tl Sin 135°+  Tr Sin 45°-120N

a)?Fx=Tl cos 135°+  Tr cos45°=0
b) ?Fy=Tl Sin 135°+  Tr Sin 45°-18N

Question 3
Let the sum of moments at a reaction = (SM = 0) and distance 5m run from A to B., and C to D for 3m
SMb = 0=4(5)-Ay (8)
Ay=2.5kN
In the case of CD
SMc=0=32(3)-Ay (8)
Ay=12

Let the sum of moments at a reaction = (SM = 0)
SMB= 0= 50(5)-Ay (10)
Ay=10kN

Question 3(b)
Let the sum of moments at a reaction = (SM = 0)
SMB= 0= 40(3)-Ay (6)
Ay=20kN

Let the sum of moments at a reaction = (SM = 0)
SMc= 0= 150(3)-Ay (6)
Ay=75kN

References
Consumer, D. S., & Allen, J. H. (2010). Statics. John Wiley & Sons Canada, Limited.
Nelson, E. W., Best, C. L., McLean, W. G., & Nelson, E. W. (2010). Statics. New York: McGraw-Hill.

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