Question

the sum of the magnitudes of two forces acting at a point is 18 Newton and the magnitude of their resultant is 12 Newton if the resultant makes angle of 90 degree with the force of smaller magnitude what are the magnitude of the two forces ​

Answer 1

Answer:

13N and 5N

Explanation:

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 P^ 2 = Q^2 +R^2 or P^2 - Q^2 = R^2 or (P+Q) (P - Q) = R^2 or P -Q = R^2/P+Q that is P- Q = 144/18 = 8 ...(2) Adding (1) and (2)

2P = 26 or P = 13 N . Then Q = 5 N.

Answer 2

Answer:

Answer is given above.