We saw in Example 7.3 (page 255) that the acceleration of

QUESTION:

We saw in Example 7.3 (page 255) that the acceleration of the Atwood machine is x = (m m2)g/(mi+ m2). It is sometimes claimed that this result is "obvious" because, it is said, the effective force on the system is (m1 m2)g and the effective mass is (m1 + m2). This is not, perhaps, all that obvious, but it does emerge very naturally in the Lagrangian approach. Recall that Lagrange's equation can be thought of as [Equation (7.17)] (generalized force) = (rate of change of generalized momentum). Show that for the Atwood machine the generalized force is (m1 m2)g and the generalized momentum (mi m2).i. Comment.