Question

The figure below shows Atwood's machine, in which two containers are connected by a cord (of negligible mass) passing over a frictionless pulley (also of negligible mass). At time t = 0, container 1 has mass 1.30 kg and container 2 has mass 2.40 kg, but container 1 is losing mass (through a leak) at the constant rate of 0.170 kg/s.

When does the acceleration reach its maximum value?

Answer 1

0.170 a+ m da/dt = -g dm/dt + .170 a
da/dt = 0.170 g /m

You can see from m da/dt = -g dm/dt that the acceleration is increasing with time until dm/dt = 0. So the maximum acceleration is reached when the container is empty.