Lecture Notes: Analyzing Forces and Components

Forces

• There are three forces: Force A, B, and C.
• Force A
  • Direction: Upwards and to the right.
  • Components:
    • AX: Horizontal component, upwards and to the right.
    • AY: Vertical component, upwards.
• Force B
  • Direction: Upwards and to the left.
  • Components:
    • BX: Horizontal component, upwards and to the left.
    • BY: Vertical component, upwards.
• Force C
  • Direction: Downwards and to the right.
  • Components:
    • CX: Horizontal component, to the right.
    • CY: Vertical component, downwards.

Solving the Components

Force A

• AX
  • Formula: ( A \cdot \cos(45^\circ) )
  • Result: ( +70.711 ) kN (to the right)
• AY
  • Formula: ( A \cdot \sin(45^\circ) )
  • Result: ( 70.711 ) kN (upwards)

Force B

• BX
  • Formula: ( B \cdot \cos(30^\circ) )
  • Result: ( -129.904 ) kN (to the left)
• BY
  • Formula: ( B \cdot \sin(30^\circ) )
  • Result: ( 75 ) kN (upwards)

Force C

• CX
  • Formula: ( C \cdot \cos(\theta_x) )
  • Result: ( +89.443 ) kN (to the right)
• CY
  • Formula: ( C \cdot \sin(\theta_x) )
  • Result: ( -178.885 ) kN (downwards)

Conclusion

• Simple process of solving force components.
• Positive results indicate directions to the right or upwards, while negative results indicate to the left or downwards.

End of Problem Number 1

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