00:01
So we have an outlet machine here, which is just two masses, tied to a string of a rope, strung over a pulley.
00:08
We have all the important information about the machine, and we need to answer three questions.
00:14
The first of which is, why is the tension t2 greater than the tension t1? and that's simply that t2 is the tensile force in rope 2, and rope 2 is attached to a larger mass than the mass attached to t2.
00:30
To row one so since it has a larger mass experience is a larger force unless the tensile force is greater now part two is to find the magnitude of the acceleration and to do that we make use of these three free body diagrams and we solved them for the tension of t1 with free body diagram one t2 with free body diagram two and we solve for the difference of the two tensions with free body diagram three so starting with equation one here look at the free body diagram we see the two forces acting on the mass are the force of tension and i'm not going to write the the arrow above all of these just to save some time from now on but just know that the tensions are vectors and from uh that's positive and the force of gravity is negative and that equals mass times the acceleration.
01:36
You can solve that for m1m1a minus m1g.
01:46
And moving on to equation two.
01:50
This one we see that the acceleration is negative and it's going in the negative direction.
01:55
So while the tension is positive, the acceleration is going to be negative.
02:03
So you get the tension minus the gravity equals negative m2a or t2 equals m2g minus m2a and for three we have to solve the sum of the torques and that equals the difference in the tensions times the radius of the pulley and equals the moment of inertia of the pulley times the angular acceleration.
02:42
And for this particular pulley, that equals m r squared over two times the angular acceleration...