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I was given the following example for an atwood machine: enter image description here

We should calculate the accelaration of the masses.

The given solution to this problem was the same as like there is just one pulley: $$a=\frac{m1*g}{m1+m2}$$

Can anyone give me a hint or a reason why we can ignore the system of pulleys?

The actual force that is necessary to accelarate m2 should be divided by 2, while the way of the string doubles -> Does this effect balance out any change and it is just the same process as there would be only one pulley?

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    $\begingroup$ Because there is only one point of contact to mass m1, to get the pulley effect you need to attach a pulley to m1 so that it would have 2 (or more) tensions on it. $\endgroup$ – PhysicsDave Mar 15 at 15:00
  • $\begingroup$ Seems like I have totally misunderstood how pulleys work in the first place ^^ So in this case the tension is not changed at all but only put in another direction ? $\endgroup$ – LurioTabasco Mar 15 at 15:46
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    $\begingroup$ Yes, Good article on pulleys here. wired.com/2017/01/physics-of-a-compound-pulley $\endgroup$ – PhysicsDave Mar 15 at 17:38
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A light, fixed, frictionless pulley (one that cannot translate at all during the operation) has only one effect, and that is to change the direction of the force/tension of the rope.

If the pulley is not considered "light", but has mass/moment of inertia, then it will also affect the acceleration of the system, much like any other mass would.

If a pulley is not fixed but can move, then it can change the relative acceleration rates of each end of the rope.

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