The sum of the magnitude of two forces acting at a point is 18 and the magnitude of the resultant is 12.if the resultant is at 90 degree with the force of the smaller magnitude,what are the magnitudes of forces.

Asked by  | 9th Aug, 2011, 07:53: AM

Expert Answer:

Let P and Q be the forces and P is greater than Q, acting at a point O inclined at some angle with each other.
Here, P+Q = 18 ....(1)
and the resultant  R=12
Construct a parallelogram with sides with OA = Q, OB = P, with angle AOB as an obtuse angle and OA along the horizontal direction.
Draw the diagonal OC  to the parellelogram OACB  so that angle AOC =90o .
OC is the resultant  R which is perpendicular to the smaller force Q.  
Consider triangle AOC.
OA = Q
AC = OB  = P
and angle AOC =90o
Therefore, triangle AOC is a right angled triangle with AC = P as hypotenuse.
Then   P2  = Q2 + R2 
or, P2 - Q2 = R2 
or, (P+Q) (P - Q)  = R2  
or, P -Q  = R2/P+Q
or, P- Q  = 144/18 = 8  ...(2)  
Adding (1) and (2)  
2P = 26
or, P = 13
Then Q = 18-13=5

Answered by  | 10th Aug, 2011, 05:39: PM

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