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The resultant of two forces at right angle is 17N if the maximum resultant is 23N the greater force is

The resultant of two forces at right angle is 17N if the maximum resultant is 23N the greater force is

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2 Answers

Arun
25750 Points
5 years ago
If F1 and F2 are two forces with resultant "R'' and ∅ being angle between them
           R=(√F1²+F2²+2F1F2cos∅)
If  F1 and F2 are at 90°
   R=(√F1²+F2²+2F1F2cos90)
      =(√F1²+F2²)
If R is maximum ⇒⇒cos∅ is maximum
Maximum value of cos∅= 1
So,
 R=(√F1²+F2²+2F1F2cos0)=(√F1²+F2²+2F1F2)
~~~~~~~~~~~~~~~~~~~~~~~~~
According to question 
Resultant of F1 and F2 at right angle is 17N
 17=(√F1²+F2²)
  289=(F1²+F2²)
~~~~~~~~~~~~~~~~~~~
maximum resultant is 23N  
23= (√F1²+F2²+2F1F2)
 529=(F1²+F2²+2F1F2)
 289=(F1²+F2²)
 529=289+2F1F2
 529-289=2F1F2
 240=2F1F2
 120=F1F2
Now 
(F1+F2)²=F1²+F2²+2F1F2
F1+F2=√289+240
F1+F2=23
Similarly (F1-F2)²=F1²+F2²-2F1F2
F1-F2=√289-240
F1-F2=√289-240=√49=7
F1-F2=7
F1+F2=23
---------------
2F1=30
F1=15 F2=8
So greater force is 15N
Regards
Arun (askIITians forum expert)
Eshan
askIITians Faculty 2095 Points
5 years ago
Let the forces be\vec{F_1}and\vec{F_2}.
The resultant of two forces kept perpendicular is\sqrt{F_1^2+F_2^2}=17N
Maximum resultant is possible when the two forces at in the same direction.

Therefore,F_1+F_2=23N
HenceF_1=15N, F_2=8N

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