From my understanding, in this atwood machine, one mass is on a horizontal surface, and the other is hung off a pulley and left to freefall. Pictured below:
If only the hanging mass affects the acceleration of the entire system, why does the tension in m1 equal (m1*a)?
Trying to work through this myself: I may have misinterpreted that (m1*a) was mass times gravity, which isn't the case. However, that's still confusing. The acceleration is equal throughout the string, so the acceleration is equal to the force of gravity on m2. That makes sense to me algebraically and conceptually, but why does the TENSION equal (m1 * a)?
Best Answer
Cut the string to the right of M1. You need to replace it with the force that the string exerted to the right on M1. That force is the tension in the string. Since there are no other forces acting on M1 horizontally (assumes frictionless table), the acceleration of M1 must be $\frac{T}{M_1}$.
Hope this helps.