Ends A and B of the 5-kg rigid bar are attached by lightweight collars that may slide over the smooth fixed rods shown in the figure.
The center of mass of the bar is at its midpoint. The length of the bar is 1.5 m. Determine the horizontal force F applied to
collar A that will result in static equilibrium as a function of the distance, d (0.5 ≤ d ≤ 1.5 cm).
sum of forces and moments are zero
Point A only has resisting forces in i and k directions
Point B only has resisting forces in i and j directions
The Attempt at a Solution
This is where I run into trouble. In another version of this problem that my class is supposed to do, we have to figure out the 'limit' of d in terms of L which is 1 meter in this problem setup. Looking at the figure, I really don't seem to have enough information to say what an acceptable limit of d would be. The problem I have pasted into this post gives d a limit at (0.5 ≤ d ≤ 1.5 cm), but I do not know how that limit is logical.
The problem my class has to solve:
Ends A and B of the 5-kg rigid bar are attached by lightweight collars that slide over the smooth fixed rods as shown in the figure. The center of mass of the bar is at its midpoint. The length of the bar is 1.5m.
1. Consider the geometry of the system.
a. For L = 1 m, what is the limit of d?
b. For L = 0.5 m, what is the limit for d?
c. Show your work & explain the limits on d physically as it relates to the system.
Another student from this class and I worked at it for an couple hours and it just isnt clear what we can and can't assume about the geometry of this system. When considering a limit of d when L is a value, should we assume that by limit of d, it means that the absolute highest and lowest d can be when point A moves on its rod? Being a statics problem, we just arent sure if this is a safe assumption. Force F keeps the rod in its current location afterall (because statics!)
This said, when tearing it apart into triangles, we can't seem to solve for either d in terms of l, or even the distance point A is away from point B (in the x direction). There's bound to be a way to simplify this problem, but we havent been assigned problems like this ever before in this class, so have no confidence in having a correct solution for this problem.
Once I can get a good conception of what this problem really is, i am sure i can figure the rest out on my own. Any hints would be very much appreciated!
I believe the context of the problem is Internal Forces and Machines.