Question

The forces F 1, F 2, ..., F n acting at the same point P are said to be in equilibrium if the resultant force is zero, that is, if F 1 + F 2 + ... + F n = 0.



F 1 = i + j, F 2 = i – j, F 3 = 9 i + 2 j

Find the additional force required for the forces to be in equilibrium P.

Answer 1

F1 =<1, 1> in this case, consider F1 as u = <u1,u2>=<1,1>
F2= <1,-1>
F2 as v = <v1,v2>= <1,-1>
F3= <9,2>
F3 as w =<w1,w2>=<9,2>
F4 = <x, y> such that x + u1+v1+w1 =0
or x = -u1-v1-w1
so F4 = <11,2>
x + u1+ v1 + w1 =0 or x = - u1 -v1-w1 = -1-1-9 =-11
so its -11,-2
hope this helps

Answer 2

For the forces to be in equilibrium:
F 1 + F 2 + F 3 + F 4 = 0
i + j + i - j + 9 i + 2 j + F 4 = 0
11 i + 2 j + F 4 = 0
F 4 = - 11 i + 2 j
F 4 = ( -11, - 2 )