Solid mechanics problem (pretty much a static problem)

[DyslexicHobo]

Homework Statement

A pin-jointed truss ACE is part of a cable-hoist system that is used to lift cargo boxes, as shown in Fig P1.4-5. The cable from the lift motor to the cargo sling passes over a 6-in pulley that is supported by a frictionless pin at C. The weight of the cargo box being lifted is 1500 b. Neglecting the weight of the cables, determine the reactions at the pin supports at A and E, and determine the axial force in each of the following members: F1 (in member AB), F2(in member AD), and F3 (in member DE). Explain the answer you got for the value of F2.

Homework Equations

Pretty much all the basic statics equilibrium equations. (Sum of F_x=0, F_y=0, M_z=0)

The Attempt at a Solution

I drew up a picture, but the main problem I'm having is how to deal with the sum of the moments. It's been a while since I've done any statics problems, so I'm unsure of how to incorporate the moment that the tension in the cable causes. I think I can find out everything else the question asks once I get past this small hurdle.

 

[nvn]

DyslexicHobo: Preferably reverse the direction of reaction force Ft in your diagram, if you wish. You know the magnitude of Ft is equal to the cable tension, right? And you know the direction of Ft. Resolve Ft into components Ftx and Fty. You know reaction force Fe is collinear with member DE, right? Resolve Fe into components Fex and Fey. Now sum moments about any point you wish.

 

[thomate1]

I would approach this problem by first identifying and defining all the variables involved, such as the weight of the cargo box, the lengths and angles of the truss members, and the forces acting on each member. I would then use the basic statics equilibrium equations to set up a system of equations and solve for the unknown variables. In this case, the sum of the moments equation would involve the tension in the cable, which can be calculated using the weight of the cargo box and the angle of the cable over the pulley. From there, I would use the equations to solve for the reactions at A and E, as well as the axial forces in each member.

For F2, the axial force in member AD, I would expect it to be zero since it is a zero-force member. This means that it does not contribute to the stability or equilibrium of the truss and can be removed without affecting the overall structure. This is because the forces acting on this member are parallel and equal in magnitude, resulting in a net force of zero.

Overall, the solution to this problem would involve using a combination of equations, calculations, and logical reasoning to determine the reactions and forces in the truss. It is important to carefully consider all the forces acting on each member and how they contribute to the overall equilibrium of the system.