# Simple rope tension problem

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?

• Please do not use tags of which you don't know the meaning of. the sem tensor is a totally different thing. It made this came in the related column: Formulation of general relativity . Also, don't use the cm tag if a more specific tag applies. Finally, the hw tag applies even if it's inot real hw. By the way, these hw questions must ask about a conceptrual douts. – Abhimanyu Pallavi Sudhir Sep 14 '13 at 12:05

Think what the tension does. At every point of the (massless) rope, there are two forces acting: gravity pulling down and you pulling up. Then tension is the difference of these forces $$T = F_p - F_G$$ Since you're pulling upwards with an acc. of 1m/s^2 $F_p = +60N$ which we arbitrarily count positive. But $F_G = -6N$ necessarily points the other way, so $T = (60 - (-6) )N = 66N$