Which Block Hits First, Block 1 or Block 2?

[Himanshu]

A tale of two blocks. "HELP!"

Homework Statement

The system shown below consists of two identical blocks of mass M connected by a massless, flexible string of length 2L. The string passes through a massless pulley which is fixed to the corner of the
supporting table. The string and the masses move with no friction, and gravity acts downward as usual. The system is allowed to move freely from the position shown in the figure.
Which happens first: (i) Block 1 hits the pulley, or (2) Block 2 hits the wall?

C:\Documents and Settings\a\My Documents\My Pictures\untitled1





The attempt at a solution

Frankly I really don't have ane any idea. I considered the tension in the string which is responsible for the motion of the first ball. I understand that the tension does not remain constant and therefore the force on block 1 is variable.

On block 2 tension and gravity are acting. I think that the time it would take to hit the table would depend upon the angular acceleration. angular acceleration would further depend upon the angle between the non horizontal part and the vertical.I am not able to manipulate these ideas into equations. Please help!.

I have posted the picture in the next post.

 

[Himanshu]

View attachment untitled1.bmp

 

[ogb p]

Hello,

It seems like you are struggling with this problem. Let's break it down and see if we can come up with a solution together.

First, let's look at the forces acting on each block. As you mentioned, block 1 has tension in the string and gravity acting on it. Block 2 also has tension and gravity acting on it, but it also has the added force of the wall pushing against it.

Next, let's consider the motion of each block. Block 1 will move downwards due to the tension in the string, while block 2 will move towards the wall due to the combined forces acting on it.

Now, to determine which block will hit first, we need to look at their respective velocities. Block 1 will have a constant downward velocity due to the tension, while block 2 will have an increasing velocity towards the wall due to the combined forces acting on it.

Based on this, we can conclude that block 1 will hit the pulley first, as it has a constant velocity and a shorter distance to travel compared to block 2.

I hope this helps. Let me know if you have any further questions or need clarification. Keep up the good work!