One of Boris Korunsky's brain twisters

[Salamon]

Homework Statement

Two identical blocks are attached by a massless string running over a pulley. The rope initially runs over the pulley at the rope's midpoint, and the surface that block 1 rests on is frictionless. Blocks 1 and 2 are initially at rest when block 2 is released with the string taut and horizontal. Will block 1 hit the pulley before or after block 2 hits the wall? (Assume that the initial distance from block 1 to the pulley is the same as the initial distance from block 2 to the wall.) See Attached Figure

Homework Equations

Fnet = ma
Fg = mg
Fc = mv^2/r

The Attempt at a Solution

I know that block 1 hits the pulley first. But Korunsky says that the solution is very simple.

I am not sure if I am right.

I can draw a freebody diagram showing that tension acts on block 1 and is equal to the net force.
I can also draw a freebody diagram showing that Tension - mgcosΘ is equal to the net force. Would this mean that the acceleration of the second block is less than the acceleration of the first block? Is this why block 1 hits the pulley first?

 

[TSny]

What determines the horizontal component of acceleration of block 2?

 

[Salamon]

TsinΘ?

 

[TSny]

You have the right idea. I'm not sure how you're defining the angle Θ (from vertical or from horizontal).

Anyway, how does the horizontal force acting on block 1 compare with the horizontal force acting on block 2?

 

[Salamon]

Ok, well if Θ is with respect to the horizontal, then TcosΘ is the horizontal force on block 2 which is less than the horizontal force on block 1 which is T.

Is that it?

 

[TSny]

Ok, well if Θ is with respect to the horizontal, then TcosΘ is the horizontal force on block 2 which is less than the horizontal force on block 1 which is T.

Yes.

Is that it?

What can you say about the horizontal components of acceleration of each block?

Which block (if either) has to travel more horizontal distance?

Which block should arrive at the wall first?

 

[Salamon]

So the horizontal acceleration of block 2 is less.

They both have the same horizontal distance to travel.

Therefore, block 1 strikes first.

Correct?

 

[TSny]

Yes. Sounds good.