I have this really simple rope tension problem that can be solved for seconds using simple logic. I know what the answer is, I know why it is, but I cannot write it down and explain it mathematically.
The problem is the following: An object with mass 6 kg hangs from a rope. The rope is pulled with acceleration of 1 m/s*s. What is the tension in the rope?
Clearly the answer is 66 N, but I fail when try to explain it. If I choose downward for positive then tension T = 60 N - 6 N = 54 N. Where am I wrong? How is actually tension in a rope measured?