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## Homework Statement

Consider now the case where the string of length l has mass per length λ ̸= 0. Show that the instantaneous acceleration of m2 is given by a2 = (m

_{1}−m

_{2})+2x

_{0}λg/(M + m

_{1}+ m

_{2})

where M = λ l is the total mass of the string and find the tension in both ends of the string. (please see picture!)

## Homework Equations

I have the solution and it starts off with three equations

T

_{2}- m

_{2}g = m

_{2}a

T

_{1}- m

_{1}g = -m

_{1}a

T

_{1}+ 2x

_{0}λg - T

_{2}= Ma

_{2}

Although i completely understand where the first two come from I'm a little confused my the last one. Although i get that it is supposed to show the force on the string, I can't figure out how the left hand side is true. IF someone could please explain where this equation came from that would be much appreciated.

Also when i was attempting this problem before seeing the solution i came up with two equations:

T

_{1}- m

_{1}g - (l/2 + x

_{0})λg = m

_{1}a and the equivalent for the second mass. Would these also be correct?