Forces F1, F2 and F3 are applied in the directions shown. F2 and F3 are vertical

Question

Forces F1, F2 and F3 are applied in the directions shown. F2 and F3 are vertical and horizontal,

respectively. Determine the magnitude of the smallest force F1 that can be applied, and the angle

?, such that the resultant force due to the three forces is directed along dotted line marked as

Forces F1, F2 and F3 are applied in the directions shown. F2 and F3 are vertical and horizontal, respectively. Determine the magnitude of the smallest force F1 that can be applied, and the angle ?, such that the resultant force due to the three forces is directed along dotted line marked as 'a'.

Explanation / Answer

F1 should be such that forces along inclined = 0

=> F1Sin(30 + A) + 200Cos60 = 400Cos30

=> F1Sin(30+ A) = 246.41

=> Sin(30 + A)= 246.41/F1

Now, Sin lies between (0,1) for this equation,

=> 0 < 246.41 < F1

=> Minimum F1 = 246.41

for this Sin(30 + A) = 1

=> 30 + A = 90

=> A = 60

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