Double pulley Atwood machine (with 3 masses)

[ehild]

Pull out g, it is nicer.
You get the result expected. m3 does not accelerate. It can be in rest, but then the hanging pulley is in rest, too, and your system is equivalent with a single pulley-two mass system. The "driving force" is the difference of the weights, the total mass is m1+m2.
I go to sleep...

 

[Sho Kano]

Thanks haruspex, and ehild!

 

[Sho Kano]

No, a3=A

On second thought, why is a3 = A?
a3 is down, while A is upwards

 

[haruspex]

On second thought, why is a3 = A?
a3 is down, while A is upwards

Depends on conventions! If all accelerations are positive up then a3 and A will have opposite signs, but if A is positive up and a3 is positive down they will have the same sign.

 

[Sho Kano]

Depends on conventions! If all accelerations are positive up then a3 and A will have opposite signs, but if A is positive up and a3 is positive down they will have the same sign.

So because originally, I specified downwards as positive, that's why a3 is positive.

 

[ehild]

On second thought, why is a3 = A?
a3 is down, while A is upwards

Look at the figure in Post # 56, 'A' was how the rope around the upper pulley accelerated along its length. It was said that the pulleys move clockwise. The rope moves with the pulley, so the right piece of it moves downward, and the left piece moves upward. The rope must keep its length! A is the magnitude of acceleration of all points of the rope.
The block m3 is attached to the right end of the rope, which moves downward, so the acceleration of m3 is equal to A. The hanging pulley is connected to the other end, so it accelerates upward, so its acceleration with respect to the ground is -A.
When ropes are involved in a problem, we can speak of the acceleration along their length .

 

[Anjum S Khan]

What are the answers ?

 

[Sho Kano]

What are the answers ?

See post 70, a1 = -A-B, a2 = B-A, a3 = A

These are the answers to part 1