 #1
 50
 0
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?
The Attempt at a Solution
Attachments

8.8 KB Views: 366