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AP Physics 1 Essentials question: Dynamics


Page 80, question #4.12 in the book...


I'm not understanding the worked out solutions, especially why the tensions were subtracted. Explanations would be appreciated 

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Draw separate free body diagrams for each of the objects, showing the direction of the forces on each object.  For example, for the (2m) mass, you would have a dot with an arrow to the left (T3), and an arrow to the right (T2).  The up and down arrows (forces Fn up and mg down) are balanced, so we'll focus on the x-direction.  Writing Newton's 2nd Law in the x-direction, since T2 is in the positive direction, we'll leave it as positive, and since T3 is in the -x direction, it will be negative.  Therefore T2-T3 = (2m)a.




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