Find the angle theta at which the ladder leaves the wall

[HiPPiE]

A uniform ladder of length L leans against a smooth (no friction) wall. The floor is also smooth (no friction) and the ladder makes an angle of Theta-0 with the floor when the ladder is installed at rest.

a) Before the ladder leaves the wall, express the equations of motion of the ladder in terms of a single generalized coordinate.

b) Find a constant of the motion.

c) Find the angel theta at which the ladder leaves the wall.

EDIT:
By the way, the idea is that the ladder accumulates some momentum in the horizontal, the way its motion is, and because of that it detaches from the wall rather than sliding all the way down against it.

 

[Nenad]

A uniform ladder of length L leans against a smooth (no friction) wall. The floor is also smooth (no friction) and the ladder makes an angle of Theta-0 with the floor when the ladder is installed at rest.

a) Before the ladder leaves the wall, express the equations of motion of the ladder in terms of a single generalized coordinate.

b) Find a constant of the motion.

c) Find the angel theta at which the ladder leaves the wall.

EDIT:
By the way, the idea is that the ladder accumulates some momentum in the horizontal, the way its motion is, and because of that it detaches from the wall rather than sliding all the way down against it.

Nobody is going to solve your problems for you, try telling us what you are stuck with.

Regards,

Nenad

 

[HiPPiE]

You guys are bitter. It's not my homework or anything, I just thought it was a good problem because it was hard and I don't know how to do it. It was on a test my dad was proctoring.

 

[Nenad]

You guys are bitter. It's not my homework or anything, I just thought it was a good problem because it was hard and I don't know how to do it. It was on a test my dad was proctoring.

We are not here to solve arbitrary problems, if you want to know how to approach th problem, draw the free body diagram, label all of your axis, create your force equations and work form there. Try doing this first, if you get stuck, come and ask.

Regards,

Nenad

 

[HiPPiE]

OK... this is what I have so far:

Free body diagram: What are the relationships between the normal forces and the gravity?

Motion of center of mass: this works... but we now need to find the acceleration along this path and such... hmmm

 

[NateTG]

Well, this is a classic problem.
As I recall, the sly way to do this is to use energy.

 

[whozum]

Your pictures don't make sense. How can the center of mass move in the fashion demonstrated?

 

[HiPPiE]

I sort of derived why the equation of motion is x^2 + y^2 = 1/4 L^2.
That's the equation of a circle, if you didn't know. Again though, this is only if the ladder stays against the wall, which, in theory, it wouldn't.

As for understanding the motion, though, you can see it pretty easily:
Take a piece of paper, draw the wall and floor. Then draw many of the same-length ladder in different positions against the wall. Completely upright, completely laying down, and many positions in between. Then draw a dot at the middle of each ladder and connect the dots :)

 

[whozum]

First off, your center of mass particle draws out a complete quarter circle, which isn't possible considering its motion is not along the entire ladder (from wlal to floor). Second, you have drawn the CM moving to the right and then concave downward, but the force pulling the ladder is directed downwards. It should be starting down and then concave right as the ladder bottom is pulled out.