Find the Acceleration of blocks A, B and C, and tensions in the strings. All the blocks are of equal masses of 10kg. Also F = 60N.

three black blocks which are horizontal to the surface. The first block on the left is connected to the middle and middle to Right with the help of a String. Also, there is a string attached to the Rightmost block which is pulled with Force F towards the Right Direction

Let's name the leftmost block as A, middle one as B and Rightmost as C

As we can see that the Question has 2 parts:

  1. To find the Acceleration of each Block.
  2. To find the tensions of the string ($T_1$ and $T_2$).

How I tried to solve the Problem:

For A:

$F - T = 10 a_1 \Rightarrow 60 - T_1 = 10a_1$ -------(1)

For B:

$T_1 - T_2 = ma_2 \Rightarrow 60 - 10a_1 - T_2 = 10a_2 $ (from (1) )

For C:

$T_2 = ma_3 \Rightarrow 6 = a_1 + a_2 + a_3$ (from last eqn. and further simplifying)

But, this is certainly not any closer to the 1st part which asks for acceleration of 3 Blocks. I don't have a single idea how to deal here with 3 acceleration variables ($a_1 , a_2$ and $a_3$) and 3 tension Variables ($T_1 , T_2$ and $T_3$) and use those here. I'm missing something here and I don't know how to proceed with the equations further.

For the second part, I can make a wild guess that tensions should be equal everywhere in the string, but as explained earlier due to the problem with equations I don't have enough idea to prove it as I've explained earlier that I had problems with the equation.

Note: My assumptions about the second part that tensions should be equal everywhere can be wrong as it's just a mere guess, I've not proved it.

Any help/hint is appreciated,

Best Regards :)


closed as off-topic by Aaron Stevens, Jon Custer, user191954, John Rennie, Kyle Kanos Oct 17 '18 at 10:11

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – Aaron Stevens, Jon Custer, Community, John Rennie, Kyle Kanos
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  • $\begingroup$ Hint: What would happen to the system if the blocks were not all accelerating at the same rate...? $\endgroup$ – Garf Oct 16 '18 at 15:49
  • $\begingroup$ @Garf If there is uneven acceleration then they'd either collide with each other or they'd try to go apart which is certainly not the possible case according to the question :P :) $\endgroup$ – Abhas Kumar Sinha Oct 16 '18 at 15:53
  • $\begingroup$ Please note that this site is not a place to obtain solutions to worked problems. Please see this Meta post on asking homework-like questions and this Meta post for "check my work problems". $\endgroup$ – Kyle Kanos Oct 17 '18 at 10:11
  • $\begingroup$ @KyleKanos I appreciate that you gave your time to help me. Can you help me further by giving examples of how should I post these kinds of questions? So that I can edit it and make it useful for the community members? $\endgroup$ – Abhas Kumar Sinha Oct 17 '18 at 15:30
  • $\begingroup$ @AbhasKumarSinha the first of the links I give should help. Basically don't ask us to do your work, ask us about the specific physics concept that is preventing you from understanding the problem $\endgroup$ – Kyle Kanos Oct 17 '18 at 15:53

We are not considering any friction,hence acceleration of the 3 blocks will be the same . Put a1=a2=a3=a and solve the equation you will get the required acceleration of the blocks and also the tensions from there.

  • $\begingroup$ I appreciate your answer but it'd be great if you'd consider why the accleration'd be equal? $\endgroup$ – Abhas Kumar Sinha Oct 16 '18 at 15:54
  • $\begingroup$ If we take our system to be comprising of all the three blocks ,then only force acting on it is F(due to absence of friction).From here we get acceleration of centre of mass of the system to be equal to a.Since the strings are inextensible we can consider this entire system to be moving together and hence acceleration of any part of it will be equal to a. $\endgroup$ – Sagnik Oct 16 '18 at 16:00

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