What is the tension in the cable GB that supports the frame ACD given that the frame supports a load of 268 N at point C?
The tension in the cable GB can be found by applying the concept of equilibrium and analyzing the forces acting on the frame ACD. By considering the ball-and-socket joints at points A and D, as well as the cable GB, we can determine the tension required to support the load at point C.
Equilibrium Analysis
Equilibrium: In order for the frame ACD to remain in equilibrium, the sum of the forces acting on it in both the horizontal and vertical directions must be zero. This means that the forces pulling up must be balanced by the forces pulling down.
Force Analysis
Tension in Cable GB: Let's denote the tension in the cable GB as T. The weight of the frame is balanced by the tension in GB and the vertical reaction forces at points A and D. Additionally, the load of 268 N at point C adds a downward force to the system.
Equation Setup
Vertical Forces: The sum of the forces in the vertical direction can be represented as follows:
T + Tsin(θ) + 268 N = Weight of the Frame
Solving for Tension
Simplifying the Equation: We can simplify the equation by isolating the tension in the cable GB:
T(1 + sin(θ)) = Weight of the Frame - 268 N
Substitute Values: By substituting the given values for the weight of the frame and the load at point C, we can solve for the tension in the cable GB.
By following this analysis and calculation process, we can determine the specific tension required in cable GB to maintain the equilibrium of the frame ACD under the given conditions.