Kinematics problem: sliding bar.

[jasc15]

I have been wrestling with this problem for a few days and it is really frustrating me. The image below shows a bar of length l whose endpoints are constrained to move along the lines shown. Point A moves at a constant velocity to the right and I want to find the angle theta as a function of x_A.

I dusted off my dynamics textbook, and there are many examples of this set up in the kinematics chapter, but the only analytical solution shown has the angular acceleration of the bar as a function of theta, alpha and x_A.

http://img411.imageshack.us/img411/2960/slidingbarqd2.png

 

[MikeLizzi]

http://mysite.verizon.net/mikelizzi/physicsForumSolution.htm

 

[jasc15]

Great, thanks! and here i thought no one was looking at this. I apprecate your work. I guess now it's a problem of related rates to find the angular velocity and angular acceleration of the bar about point A given dx/dt.

Edit: I just noticed an error. in your expression $$cos\theta=\dfrac{x_{A}-x_{B}}{l}$$ you rearranged it to show that $$x_{B}=-\dfrac{l\cdot cos\theta}{x_{A}}$$ where it should be $$x_{B}=x_{A}-l\cdot cos\theta$$. It's still a bit ugly to play with the algebra and trig, but I'm messing with that now.

Thanks again!