mth174
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When considering an Atwood pulley system, one in which it just has a pulley with two masses connected by a string of negligible friction, will this be appropriate for finding the acceleration:
We have two masses (m1 and m2), will the size in masses make a difference in the tensile force acting on the system? (This just occurred to me as I was writing it.)
But I made two free-body diagrams, the forcing acting upwards is tension, and downwards is m1g, and then on the other we have the tension acting upwards and m2g for the force of gravity. If you want to find the acceleration, can you take the fact that T=m1g and T=m2g and add then together: m1g+m2g=(m1+m2)a and result in a=(m1*g+ m2+g)/ (m1+m2)...
If you wanted to find tension, would it still be the same concept?
The direction of motion of this system is not simply 'up' or 'down', since one mass is rising while the other is falling. Part of the system is going up and part is going down.
To specify a positive direction you can choose either the direction in which one object or the other is as sending or descending, as you choose. For example you can choose as the positive direction that in which m1 is descending (in which case m2 would be ascending), or the direction in which m2 is descending (in which case m1 would been ascending).
Suppose we choose as the positive direction that in which m1 is descending. Then m1 g is a positive force acting on the system, while m2 g tends to accelerate the system in the negative direction, relative to the chosen positive direction. The net force is therefore m2 g - m1 , and the acceleration is
a = F_net / m = (m2 g - m1 g) / (m1 + m2).
To find the tension you have to isolate each mass. The free-body diagrams for m1 along has m1 g acting downward and the tension T acting upward. The net force on m1 is m1 * a. We have an expression for a, and from the free-body diagrams we can get an expression for F_net in terms of m1, g and T. Only T is regarded as unknown so we can easily solve for T.
We can do the same for m2, getting an independent expression for T. This expression should be identical to the one obtained from the free-body diagrams for m1.