Question

Determine magnitude of resultant force of the force system shown in the figure 1.​

Answer 1

Explanation:

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Answer 2

Answer:

The resultant force is 21.1002 kN in the northeast direction.

Explanation:

Force is divided into two components, Fcosθ towards the x-axis and Fsinθ towards the y-axis, when θ is given towards the x-axis.

All the forces are broken into components -

1. 10 kN - 10cos60° towards the east and 10sin60°towards the north
2. 5 kN - 5cos30° towards the east and 5sin30° towards the north
3. 12 kN - 12cos40° towards the east and 12sin40° towards the south

• Total force towards the east direction - 10cos60° + 5cos30° + 12cos40° = 5 + 4.330 + 9.192 = 18.5220 kN
• Total force towards the north direction - 10sin60° + 5sin30° - 12sin40° = 8.660 + 2.5 - 7.7136 = 3.4464 kN

The Resultant Force =  $\sqrt{18.5220^{2} + 3.4464^{2} + 2(18.5220)(3.4464)cos45 }$

$= 21.1002$ kN

The resultant force is 21.1002 kN in the northeast direction.

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