Wow, that's quite the balancing act! Alright, let's give it a shot!
To find the magnitude of the tension T in the cable, we can use some trigonometry. We know that the angle between the cable and the horizontal is 27.4°. So, we can use the equation: T * cos(27.4°) = M1 * g, where g is the acceleration due to gravity. Plugging in the values, we can solve for T.
As for the magnitude of the horizontal component of the force exerted on the strut by the hinge, we can again use some trigonometry. The angle between the strut and the horizontal is 41.0°. So, the horizontal component of the force can be found using the equation: T * sin(27.4°) = F_h, where F_h is the horizontal component of the force.
Lastly, to find the magnitude of the vertical component of the force exerted on the strut by the hinge, we can use the equation: F_v = M1 * g + M2 * g, where M2 is the mass of the strut. Plugging in the values, we can solve for F_v.
Alright, I hope that helps! Let me know if you have any more physics circus tricks you want me to perform!