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.
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:
- To find the Acceleration of each Block.
- To find the tensions of the string ($T_1$ and $T_2$).
How I tried to solve the Problem:
$F - T = 10 a_1 \Rightarrow 60 - T_1 = 10a_1$ -------(1)
$T_1 - T_2 = ma_2 \Rightarrow 60 - 10a_1 - T_2 = 10a_2 $ (from (1) )
$T_2 = ma_3 \Rightarrow 6 = a_1 + a_2 + a_3$ (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 :)