Q.3) Given the following system of three forces (a) express each vector in Cartesian vector notation (b) determine the magnitude and coordinate direction angles of the resultant force F2 = 300 lb 45° F = 170 lb %3D 60° 30° 120° 40° F3 = 240 lb

Structural Analysis
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ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
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can you please solve these two questions?

Q.3) Given the following system of three forces
(a) express each vector in Cartesian vector notation
(b) determine the magnitude and coordinate direction angles of the resultant force
F2 = 300 lb
45°
F = 170 lb
%3D
60°
- у
30°
120°
40°
F3 = 240 lb
%3D
Transcribed Image Text:Q.3) Given the following system of three forces (a) express each vector in Cartesian vector notation (b) determine the magnitude and coordinate direction angles of the resultant force F2 = 300 lb 45° F = 170 lb %3D 60° - у 30° 120° 40° F3 = 240 lb %3D
Expert Solution
Step 1

Given. 

F1 = 170 lb

F2 = 300 lb

F3 = 240 lb

Component of forces in X, Y, Z directions

F1x = 170*cos30° * cos 40° = 112.78 lb

F1y = -170*cos30° * sin 40° = 94.6339 lb

F1z = 170*sin30° = 85 lb

Cartesian vector of F1 = 112.78i -94.6339j +85k

F2x = 300*cos120° = -150 lb

F2y = 300*cos60° = 150 lb

F2z = 300*cos45° = 212.132 lb

Cartesian vector of FF2 = -150i +150j +212.132k

F3x = F3y = 0

F3z = -240lb

Cartesian vector of F3 = -240k

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