One of Boris Korunsky's brain twisters

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Homework Help Overview

The problem involves two identical blocks connected by a massless string over a pulley, with one block on a frictionless surface and the other hanging. The scenario questions whether block 1 will hit the pulley before or after block 2 hits a wall, given that both blocks start from rest and are initially equidistant from their respective endpoints.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the forces acting on each block, including tension and gravitational components. There are inquiries about how the angle Θ affects the forces and accelerations of the blocks. Some participants explore the relationship between the horizontal forces and accelerations of the blocks.

Discussion Status

The discussion is active, with participants validating each other's reasoning about the forces and accelerations. There is an exploration of the implications of the forces on the motion of the blocks, and some participants express confidence in their conclusions regarding which block will reach its endpoint first.

Contextual Notes

Participants are working under the assumption that the blocks are identical and that the surface for block 1 is frictionless. The angle Θ's definition is also under discussion, which may affect the analysis of forces.

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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?
 

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What determines the horizontal component of acceleration of block 2?
 
TsinΘ?
 
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?
 
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?
 
Salamon said:
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?
 
So the horizontal acceleration of block 2 is less.

They both have the same horizontal distance to travel.

Therefore, block 1 strikes first.

Correct?
 
Yes. Sounds good.
 

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