# What will be the direction in which these masses accelerate and move?

I've worked out the accelerations of each of the masses, as asked in the question, but I'm struggling with the intuition of it all. I understand that mass C will move down, and so the pulley will move with the same acceleration towards the edge of the table. My confusion relates to the following:

If the tension in the string, and therefore the net force, is the same for both mass A and mass B, they must have different accelerations. So, I gather that the lighter mass of the two will move faster towards the pulley, and the heavier one will move slower. However, surely this would cause rotation in the pulley, which would cause the heavier mass to also move away from the pulley.

I am very confused as to how this will affect the acceleration of that heavier mass. Its acceleration must be only due to the tension in the string, so how can it possibly move away from the pulley while also accelerating towards it?

– Gert
Dec 30, 2020 at 17:26
• @Sunaabh Trivedi why do you think that the extra acceleration in lighter will affect the massive one . Isn't it possible that the rope becomes loose or get bended ? Dec 30, 2020 at 18:08

The larger mass does not move away from the pulley, imagine what would happen if it had infinite mass, or if it were nailed to the table. In such case the pulley will rotate, but it also moves towards the edge, in such a way that the large mass will not move at all. The same happens if the large mass is smaller and moves, even if the pulley rotates. There is relationship between both accelerations: $$a_B=a_C-a'$$ and $$a_A=a_C+a'$$, where $$a'$$ is the acceleration of the top masses relative to the pulley's center, if one gets closer the other gets farther because the rope has fixed length.(the answer is for the drawing on the left, I leave the other one up to you)

• Hi, thank you for your answer. So does that mean that neither of the two masses on the table will move, because the acceleration will be cancelled by the rotation of the pulley? Dec 30, 2020 at 19:14
• No, the masses will move as a whole with the pulley, plus they will move relative to each other with a relative acceleration given by 2a'
– user65081
Dec 30, 2020 at 19:17
• If you are standing on the pulley you will see mB moving away and Ma towards, but from the table point of view you need to add to both masses the acceleration of the pulley itself relative to the table
– user65081
Dec 30, 2020 at 19:19
• So if Mb is moving away from the pulley, is it still accelerating towards the pulley? (since the tension force is still directed towards the pulley) Dec 30, 2020 at 19:36
• It is accelerated in the same direction as the pulley, but less than the pulley (so they get farther apart), the other mass is also accelerated in the same direction but faster, thus getting closer to the pulley. The pulley accelerates at a_c, and the two other masses as stated in the answer
– user65081
Dec 30, 2020 at 20:18