The sum of two forces acting at a point is 16 Newton If the resultant force is 8 Newton and its direction is perpendicular to minimum force then the forces are?

Answer 1

Let y+x=16n (sum of two forces)

r=8n (resultant of forces)

suppose x

then,

r² =y² -x²

r² =(y-x)(y+x)

as y+x=16

r²/16=(y-x)

as r=8n

(8)² /16=y-x

64/16=y-x

4=y-x________ equation 1

now,

16=y+x_________equation 2

soving equation 1 & 2

y-x=4

y+x=16

_______

2y=20

y=10

now put y=10 in equation 1 or 2 ( here i will put in 2)

16=10+x

16-10=x

6=x

from this the forces will be 10n & 6n for better understanding see diagram:

Answer 2

The two forces are 8 Newton each, acting in perpendicular directions. The minimum force creates a right triangle with the resultant force, such that the square of the minimum force plus the square of 8 Newton force equals the square of 16 Newton (by using Pythagoras theorem).