We also don't know at what angles the pushrods A and B are acting at.
I always tell my students that doing problems with variables is just like doing problems with numbers...all the manipulations are the same. However it does get to a point where you have so many variables that it becomes not only a tedious problem, but extremely messy and prone to errors.
The more information you can provide, the more likely we will be able to help you with this.
-Dan
You have left the problem with 17 unknown variables, 6 of which need to be determined in terms of the others to find the two forces you are looking for in part 1. And I'm not sure the other two parts can even be done with the information given, even if I decided to do an internet search on the amount of stress a tubular bar of Aluminum can withstand before it deforms.
You either need to go to your professor and demand more information about the problem, or if this is a project you are constructing you need to come up with some more design constraints before you can reasonably expect to get an answer.
-Dan
The answer is...maybe. The problem with this is that we need six linearly independent equations. We have Newton's Laws in two dimensions, then we need 4 torque equations. Typically (but not generally) if we pick an axis of rotation that has one or more of the unknown forces acting upon it, we get a linearly independent equation. But not always, so the system needs to be checked before you can say it will generate a solution. We have 5 points where unknown forces act, so it may be possible. But given the amount of effort it is going to take to generate a torque equation coupled with the number of "known unknowns" in the system, linear independence is going to be hard to verify. It might even be faster simply to try and solve the system which, if you are doing it by hand, is going to take a while.
So not impossible to do, just difficult.
-Dan
First the "known" unknowns (the ones that we supposedly know, but weren't given to us in the problem):
The mass of both bars
The angle each pushrod makes with each respective bar
The angle the two bars make with each other
The angle the bottom bar makes with the table (or whatever surface its attached to)
The length of the bottom bar
The positions of the point of contact between the bottom bar and both pushrods
(Total number of known unknowns: 10)
Now for the unknowns:
The force each pushrod is exerting on the respective bar
The two components of the reaction force on the pivot between the two bars**
The two components of the reaction force on the pivot between the bottom bar and the table
(Total number of unknowns: 7)
** Typically we resolve the reaction force on a pivot into perpendicular components which gives 2 unknowns for each pivot. (If we don't do this then the size and direction of this force are 2 unknowns anyway.) If we are lucky we don't have to solve for these, but in this case with two pivots we can't eliminate them from the equations so they have to be found.
This gives a total list of 17 variables. There are actually only 16 independent variables here: pushrod A exerts the same amount of force on the bottom bar as it does the top by a Newton's 3rd Law argument.
(This whole argument relies on frictionless pivots. If you need to include this factor as well then we've got 18 independent variables.)
-Dan
Something just occurred to me. For the other two problems, we are given neither the outer nor the inner radius of the aluminum bar. These have to be taken into account in order to calculate the total stress the bar can take. So there's another two known unknowns in the problem.