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2015-04-19T10:35:11+05:30

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Let the 2 forces be p1 and p2.
given:
p1-p2=10.....(1)
p1^2 + p2^2=50^2.....(2)
2 equations 2 unknowns. hence they can be solved.
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2015-04-22T14:56:55+05:30

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Resultant force when the forces are in opposite direction :
         F₁ - F₂ = 10 N    --- (1)

Resultant force Magnitude  when the forces are at right angles:
   F²  =  F₁² + F₂² + 2 F₁  F₂  Cos 90°
   50²  =  F₁² + F₂²    ---  (2)

       F₁² + ( F₁ - 10)²  = 2500
        F₁²  - 10 F₁ - 1200 = 0
       
         F₁ = [ 10 + -  √4900 ] / 2 = 40  or  -30 N

   F₂ =  30 N  or  - 40 N

The magnitudes of the two forces are :  30 N and 40 N.

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