Physics Resultant Force

There are 3 forces involved F1, F2 and F.
Assume the forces are drawn on the x and y co-ordinates system, one unit represents a force of 1 Newton.
The point where the force F1 and F meet is the origin (0, 0) of co-ordinates system.
The line joining the points (0, 0) and (-2, 2) is force F1
The line joining the points (0, 0) (2, 5) is The resultant force F
This Force is the same as the line joining (0, 0) and (-2, -5).
They both have same magnitude and same direction.
Assuming all 3 forces involved acting on the same point (0, 0)
Resolve all the forces in x (horizontal) and y (vertical) directions.
Along the x-axis,
Force F1x = -2N (towards West)
Resultant force Fx = -2N (towards West)
F2x = unknown
Fx = F1x + F2x
-2N = -2N +F2x
F2x = +2N - 2N
F2x = 0 N

Along the y-axis,
Force F1y = +2N (towards North or upwards)
Resultant force Fy = -5 N (towards South, or downwards)
F2y = unknown
Fy = F1y + F2y
- 5N = + 2N + F2y
F2y = -5N –2N
F2y = - 7N
Negative sign indicates towards South, or downwards
(F2)^2 = (F2x)^2 + (F2y)^2
(F2)^2 = (0)^2 + (-7N)^2
(F2)^2 = (0 + 49) Newton^2
F2 = = - [square root of 49) N, direction pointing South
F2 = - 7N pointing South (i.e. downwards)
This force F2 is perpendicular to x-axis

Hence force F2 is 7 Newton downward. This force acts along the y-axis on the diagram. The arrow is downwards.


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