Find the resultant of the following forces: 
(i) 10 N along the x-axis 
(ii) 6 N along the y-axis and 
(iii) 4 N along the negative x-axis. 
Ans. (8.5 N making 45° with x-axis)


Given:  

F1  = 10 N along the x-axis 
F2  = 6 N along the y-axis
F3  = 4 N along the negative x-axis

To Find:
Resultant force  = F =  ? 

Solution:  

1. Select the suitable Scale 

let  1 cm = 2 N, So, 

F1  = 10 N along x-axis = 5cm

F2  = 6 N along y-axis =3 cm

F3  = 4 N along negative x-axis = 2cm




2. Arrange these forces F1, F2, and F3 according to head-to-tail rules such that the tail of force F2 coincides with the head of force F1 at point B as shown in the figure, similarly the tail of force F3 coincides with the head of force F2 at point C.

3. Join point A, the tail of the force F1, and point D, the head of force F3. Let AD represent force F. According to head to tail rule, force F represents the resultant force.

4. Measure AD and multiply it by 2 N cm⁻¹ , the scale to find the magnitude of the resultant force F. So, line segment AD = F = 4.25 cm ｘ2 N cm⁻¹ = 8.5 N

5. Using a protractor measure the angle ∠DAB which the force F makes with x-axis. This gives the direction of the resultant force. Hence ∠DAB = 45°

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