Let us determine the magnitude & direction of the resultant of coplanar concurrent forces as shown below.
As you can observe in the above drawing, there are 5 forces acting at a given angle. Let us split those inclined forces into horizontal & vertical components as shown below.
Points to remember:
The component of a force opposite to the angleθ is taken as sinθ & remaining components are taken as cosθ, where θ is the angle of a particular force.
Let us now resolve the forces into ΣFx & ΣFy,
Where,
ΣFx 👉 whatever the forces acting in the X-direction.
ΣFy 👉 whatever the forces acting in the Y-direction.
Note:
One more thing you should know before proceeding further 👇
The direction of the horizontal component (along the X-axis)
Moving towards the right direction 👉 +ve.
Moving towards the left direction 👉 -ve.
The direction of the vertical component (along the Y-axis)
Moving towards the upward direction 👉 +ve.
Moving towards the downward direction 👉 -ve.
Now,
ΣFx = [150cos55° - 200sin35° - 60sin60° - 130cos40°]
= [86.036 - 114.71 - 51.96 - 99.585]
ΣFx = - 180.219 N ( ← )
As ΣFx is -ve, it is moving in the left-hand side direction.
ΣFy = [150sin55° + 200cos35° - 60cos60° +130sin40° + 50]
=[ 122.87 + 163.83 - 30 + 83.562 +50]
ΣFy = + 390.262 N ( ↑ )
As ΣFy is +ve, it is moving in the upward direction.
1. Resultant of coplanar forces:
R = √ (ΣFx)² + (ΣFy)²
= √ (- 180.219)² + (390.262)²
= √ 119,825.54
R = 346.158 N
Resultant of coplanar concurrent forces = R = 346.158N.
2. Direction of forces ( θ):
tanθ = [ΣFy ÷ ΣFx]
= [390.262 ÷ 180.219]
= 2.165
θ = tan⁻¹(2.165)
θ = 65.21°
The direction of resultant force = θ = 65.21°
As you can observe in the above drawing, the resultant is lying in the 4th quadrant at a direction of 65.21° from the X-axis.
Thank you for going through these calculation steps❤. Have a good day 😄.
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