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I actually don’t know how to begin in the first place. The first thought that went through mu head was to consider the 2kg and 3kg and the pulley as a singular system, but that isn’t possible because they’d have different accelerations. I could have written a constraint equation, but that isn’t right or very useful because there are three separate strings. Nonetheless here is the what I wrong (it’s probably wrong)

$a_1-2a_2-2a_3=0$

How should I i approach this question?

Aditya
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1 Answers1

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Let me write $m_{1}=1$ kg, $m_{2}=2$ kg and $m_{3}=3$ kg.If you draw the forces on each block, you will find the equations (I'm assuming the system is frictionless) $$m_{3}g - T_{1} = m_{3}a \hspace{1cm} (1) $$ $$T_{1}-m_{2}g=m_{2}a \hspace{1cm} (2)$$ and $$2T_{2} = T_{1} = m_{1}a \hspace{1cm} (3)$$ Equations (1) and (2) together become $$a = \frac{(m_{3}-m_{2})g}{m_{3}+m_{2}} \hspace{1cm} (4)$$ So you can solve it by substituting (4) into (3).

IamWill
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  • But shouldn’t a pseudo force act on the masses, as the pulley holding it is also accelerating downwards? – Aditya Nov 07 '19 at 13:22
  • And why is $T_2=2T_1$? (Please ignore whatever is written with the pencil, it’s a part of the question) – Aditya Nov 07 '19 at 13:23
  • There are basically two types of pulley: the fixed one and the movable one. The movable one (which is the case in the exercise) divides the tension in two equal parts, so this is why $T_{2} = 2 T_{1}$. – IamWill Nov 07 '19 at 14:11
  • Pseudo forces are used when you are in a non-inertial reference frame, where the Newton's laws do not apply and you have to "correct" them using some sort of mathematical equivalence. Here, there is no need to use pseudo forces. – IamWill Nov 07 '19 at 14:12
  • There are two movable pulleys. Which one are you talking about? – Aditya Nov 07 '19 at 14:17
  • The answer given is $T_1=T_2=120/11$ – Aditya Nov 07 '19 at 14:24
  • Look the drawing on this website https://www.topperlearning.com/answer/a-pulley-system-comprises-two-pulleys-one-fixed-and-the-other-movable-i-draw-a-labelled-diagram-of-the-arrangement-and-show-clearly-the-directions-of-/pi2xehsrr – IamWill Nov 07 '19 at 14:45
  • The name movable is not because it's moving, it is because it is not fixed. – IamWill Nov 07 '19 at 14:46
  • Okay that makes sense. But this still doesn’t explain $T_1=T_2$ – Aditya Nov 07 '19 at 15:54