B determine the magnitude and point of application of the si

B) determine the magnitude and point of application of the single force equivalent to given system.

>> All Forces acting on the system are:

1). F1 = 5 kN, at point A = (5,0,0)

2). F2 = 4 kN, at point B = (5,7.5,0)

3). F3 = 3 kN, at point C = (0,5,0)

>> Let, Fr = Resultant Force

>> So, Fr = F1 + F2 + F3

=> Fr = 5 + 4 + 3 = 12 kN

=> Resultant Force = 12 kN

>> Now, Moment at O, Mo = [ (5 i ) X ( - 5 k) ] + [ (5 i + 7.5 j ) X ( - 4 k ) ] + [ (5 j ) X ( - 3 k ) ]

=> Mo = 25 j + 20 j - 30 i - 15 i

=> Mo = - 45 i + 45 j .......ANSWER......

>> Let, The Resulatnt Force is Acting at a point P, whose Coordinates are (x,y,0)

As, Resultant Force, Fr = 12 kN

So, Mo = - 45 i + 45 j = (x i + y j ) X (- 12 k )

=> -45i + 45 j = 12*x j - 12*y i

Equating COefficients both sides,

x = y = 3.75 m

>> So, Point at wich Net Force , 12 kN is acting has coordinates (3.75,3.75,0)