Question about Tension 100 identical blocks

[sona1177]

Each of 100 identical blocks sitting in a frictionless surface is connected to the next block by a massless string. The first block is pulled with a force 100 N.

a) what is the tension in the string connecting block 100 to block 99

B) what is the tension in the string connecting block 50 to 51?

I don't know how to do this. The only equation I got was T2-T1=ma for box 99 where T2 is the tension string attaching to box 98 and T1 is the tension in the string attached to 100. Also for box 100 I got -T=ma and plugged this into the equation -100 + T=ma and got T=50 N but this is wrong for part A and is supposed
To be the answer for part B but I don't see why. Can you please explain how to do this?

 

[hotvette]

Assuming the string doesn't stretch, all the masses will have the same acceleration. So, think of the entire set of blocks as a single mass being pulled and solve for the acceleration. Then you can determine the string tension between any of the blocks by considering all blocks upstream to be a single mass and all blocks downstream to be a single mass, thereby having a two block system.

 

[pgardn]

Does this picture make it any easier? All the blocks accelerate the same but you can combine blocks.

oops, edit, someone answered whilst I was drawing.

 

[Sandy_221]

So if there were a coefficient of friction of say 0.1 in this problem, then the 99 blocks together would produce a friction force of 0.1 x 99M x g and the one block to the right would produce a friction force of 0.1 x M x g.
And each of these two friction forces would be the amount that is added to its corresponding equation. Right?