'If I have an hour to solve a problem, I'd spend 55 minutes thinking about the problem and 5 minutes thinking about the solution' (Albert Einstein) Are we sure we are working on the right problem? Are ...

This is a classic introductory physics problem. Basically, you have a cart on a frictionless track (call this m 1) with a string that runs over a pulley to another mass hanging below (call this m 2).