Equipollent System of Bars and Pivots

[blueswan142]

Homework Statement

There are three connected bars (Bar 1, 2, and 3). Bar 1 is attached at on end to a pivot, point A, where it can rotate and at the other end to Bar 2, point B. Bar 2 is connected to Bar 1 at point B where it is free to rotate and translate. Bar 2 is connected at the opposing end to Bar 3, point C. Bar 3 can only translate horizontally. If there is a known horizontal force and displacement of Bar 3, what is the moment at point A so that the system is in equilibrium?

Homework Equations

M = F*rprep
M1 = M2 :. F1*rperp = F2*rprep

The Attempt at a Solution

The force at point A would be the known horizontal force on Bar 3 * rprep from point 3 to point 1. Right? This would be true regardless of the angle of Bar 2 correct?

 

[jbsteele]

Then the force at point B would be that same force * rperp from point 3 to point 2. The moment at point A would be equal to the force at point B multiplied by rperp from point 2 to point 1. Is this correct?

 

[thomate1]

I would approach this problem by first drawing a free body diagram of the system, labeling all the forces and distances involved. I would then use the equations for moments and equilibrium to determine the unknown moment at point A. This would involve setting the moments of the forces acting on Bar 1 and Bar 2 equal to each other, as shown in the equations above. The angle of Bar 2 would not affect the calculation, as long as the horizontal force and displacement of Bar 3 are known. Additionally, I would consider the weight of the bars and any other external forces that may be acting on the system.

To ensure the accuracy of my solution, I would also check for any redundant or missing equations and make sure all units are consistent. I would also consider the limitations and assumptions of the model, and discuss potential sources of error.

Overall, my approach would involve a combination of mathematical analysis and critical thinking, using fundamental principles of mechanics to solve the problem at hand.