Solve an Unusual Pulley Problem: Finding the Timing of Two Weights in Motion

[z_particle]

I came across this problem recently. It's a pulley problem, albeit a slightly unusual one.

The situation is sort of hard to explain without a diagram, but I'll do my best.

There's a pulley on the edge of a table, and there's a string that's stretched across it. The string has two weights attached to its two ends - of equal mass M. A length L of the string stretches on either side of the pulley, and initially the masses are held so that the string is horizontal (i. e. one mass is kept at rest on the table, and the other which is outside the table is supported so that the string remains horizontal, and just touching the pulley). From this position, the system is released. Two things happen - the mass outside the table swings down to hit the wall, and the mass on the table slides forward to hit the pulley. There is no friction involved.

The question is, which happens earlier? And how do we find that out rigorously?

I can't get the hang of it because:

1. I can't figure out if the tension remains constant throughout the duration of the fall of the outside block.

2. The length of the string outside the table also varies during the fall, so I can't apply anything related to circular motion on this block.

Can someone please help me out?

Many thanks in advance,

Z

 

[Doc Al]

Hint: Consider and compare the vertical and horizontal forces acting on each mass.