The sum of magnitude of two forces acting at a point is 18N and the magnitude of the resultant force is 12N. If the resultant force is at 90 degree with the force of the smaller magnitude. What are magnitude of forces?

Asked by RIZWAN YASIN | 12th Apr, 2013, 04:14: PM

Expert Answer:

Let P and Q be the forces and P is greater than Q , acting at a point O inclined angle .

Here P+Q = 18 ....(1)

and the resultant R =12 N.

Construct a parallelogram with sides with OA = Q, OB = P, with angle AOB as an obtuse angle and OA along the x axis.

Draw the diagonal OC to the parellelogram OACB so that angle AOC =90 degree .

The diagonal OC = resultant R which is perpendicular to the s maller force Q . consider the triangle AOC , OA = P, AC = OB = P, and angle AOC =90degree.

That is 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

that is, P- Q = 144/18 = 8 ...(2)

Adding (1) and (2) ,

2P = 26

or P = 13 N .

Then Q = 5 N.

Answered by  | 13th Apr, 2013, 10:33: AM

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