Collision involving blocks and pulley

[Chestermiller]

You are right. Sorry for my English. A body can have acceleration while its velocity is steel zero.
But this problem is more complicate because the "radius" of A movement is not constant.

Thank you for finally acknowledging that mass A can be accelerating upward even though its initial upward velocity is zero.

All works with assumption about "circular" movement with radius l probably are basically wrong.

Excuse me, but my analysis does not assume that the movement of mass A is circular with radius l, and it does take into account the fact that the radial distance of mass A from the pulley is not constant. The equations that I presented in post #62 give the actual trajectory of mass A at short times, where x is the distance mass A moves to the left, and y is the distance mass A moves upward. If we eliminate time t from these equations, we obtain:
$$y=\frac{x^2}{4l}$$
This is consistent with a radius of curvature of the circular arc of mass A of 2l, rather than l. So mass A does execute a circular arc at short times, but, as a result of the increasing radial distance of mass A from the pulley, it is initially traveling along an arc of radius 2l rather than l.

Chet

 

[ehild]

Theodoros inspired me to do the Lagrangian method. I have to admit that TSny and Chet were right, the upward acceleration of B is v₀²/(2L) at t=0, just after the collision .

@theodoros.mihos : I see, you considered upward positive for y, so the sign is OK in the constraint.
But why did you write that the potential energy of A is $\frac{gy_A^2}{\sqrt{x_A^2+y_A^2}}$ instead of gy_A?

 

[theodoros.mihos]

@ehild you are right. This mistake comes for a previous look about the direct force.
@chet. I see match more works except yours. Nothing personal.
Now all differs.

 

[Chestermiller]

@ehild you are right. This mistake comes for a previous look about the direct force.
@chet. I see match more works except yours. Nothing personal.
Now all differs.

I have no idea what you are saying. But I can tell you that I am totally thrilled that ehild, TSny, and I are now in total agreement.

Now that full consensus has been reached, I am closing this thread.

Chet