## Determine the resultant of force system, Mechanical Engineering

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Q: Determine the resultant of force system which is acting tangential to the circle of radius 1m as shown in the figure given below. Also find the direction of it and line of action

 Sol.: ∑H = 120 - 150 = -30N ...(i) ∑V = 50 - 80 = -30N ...(ii)

R = (  ∑H2  +  ∑V2)1/2

R = ((-30)2  + (-30)2)1/2

R = 42.43 N                                                                             .......ANS

tanθ   = -30/-30 = 45º                                                                                      .......ANS

Now for finding position of resultant let perpendicular distance of the resultant from center 'O' be'd'.

By applying varignon's theorem, taking moment about the point O.

R.d = -80 X 1 + 150 X 1 + 120 X 1 - 50 X 1

42.42 X d = -80 X 1 + 150 X 1 + 120 X 1 - 50 X 1

d = 3.3m                                                                                  .......ANS

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