Answer :
The force exerted on the steel plate by the cables is 48.1 kN.
So, the correct option is A.
1. Calculate the weight of the steel plate:
- Weight = 23.1 kN
2. The force exerted on the plate by each cable can be found by analyzing the forces in the system. The total force on the plate is the sum of the forces exerted by each cable.
3. Draw a free body diagram of the plate showing the forces acting on it:
- Tension in cable 1 = T₁
- Tension in cable 2 = T₂
- Weight of the plate = 23.1 kN acting downwards
4. Analyze the forces in the vertical direction:
- [tex]T₁ * sin(θ) + T₂ * sin(θ) = Weight[/tex]
- [tex]T₁ + T₂ = Weight / sin(θ)[/tex]
- Calculate the total force exerted by the cables.
5. Substitute the given values:
- Weight = 23.1 kN
- L₁ = 3.2 m
- L₂ = 3.9 m
- θ = angle between cables
6. Calculate the total force exerted by the cables:
- Total force = 23.1 kN / sin(θ)
7. Compare the calculated force with the provided options:
- The force exerted on the steel plate by the cables is 48.1 kN, matching option (a).
Therefore, the force exerted on the steel plate by the cables is (Option A) 48.1 kN.
