Pulley problems are common in physics, and in this example you will learn how to draw FBD with different coordinate systems that work with each drawing individually.
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I re-recorded the algebraic simplification so it is easier to follow. Let me know if you still have questions. 🙂
The answer given for the acceleration (3.6 m/s^2) didn’t seem intuitively correct to us, since M is more than twice m, which should yield an acceleration of more than half that expected under normal gravity for a single body (i.e., > 4.9 m/s^2). We also didn’t follow the algebra, where -m(g+a)+Mg=ma was simplified to a=[(M-m)/(M+m)]g.
If we just plug the values directly into the first formula from the previous sentence, we get -1.3(9.81+a)+(2.8 * 9.81)=1.3a -> -12.75 + 1.3a + 27.47 = 1.3a -> 14.74 = 2.6a -> a=5.66 m/s^2. This answer seems intuitively correct, and unless there’s an error in our math, correctly derived from the “pre-simplification” version of the equation.