Resultant of Three or More Concurrent Forces

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Lecture 5

• Resultant of Three or More Concurrent Forces

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Concurrent Forces

• Application of the parallelogram law requires
  extensive geometric and trigonometric
  calculations.
• These problems are best solved using the
  rectangular component method.

3
Example
Use the sine law and the law of cosines to
resolve the forces in the u,v coordinate system
and the x,y coordinate system.
4
Example
Solution
u,v coordinates
Fu/sin60 Fv/sin30 120/sin90
Fu 120 sin60/sin90 103.9 kN
Fv 120sin30/sin90 60 kN
5
Example
x,y coordinates
Fx/sin30 Fy/sin60 120/sin90
120 kN
300
Fy
Fx 60 kN, Fy 103.9 kN
600
Fx
6
Example
Determine the magnitude of Fu and Fv
Fu
1500 kN
Fv
7
Example
Solution
1) Draw the force system
2) Since all angles are known use the sine law
Fu/sin400 Fv/sin300 1500/sin1100
Fu 1500sin400/sin1100 1026 kN
Fv 1500sin300/sin1100 796 kN
8
Example
3) Check solution by adding the components of Fu
and Fv along the line of action of the applied
force.
9
Example
Determine the magnitude of F2 and the angle ? to
maintain the boat along its line of action. The
force required to pull the boat is 500 kN.
F1
line of action
350
?
F2
10
Example
Solution
1) Draw force system
2) Apply law of cosines
11
Example
3) Apply law of sines
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Additional Material

• Read Section 2.4
• Problems Section 2
• 31,35,47,57