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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?

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  • $\begingroup$ 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. $\endgroup$ – Abhimanyu Pallavi Sudhir Sep 14 '13 at 12:05
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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 $T = (60 - (-6) )N = 66N$

Think that the rope needs to excert a force of 66N on the weight in order for the weight to accelerate at 1m/s^2.

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6*10 - T = 6*-1 You can take the body to be a single system and draw it's free body diagram. When you do that, you can see that there is acceleration due to gravity acting on the body, so g= 10 m/ss. As the mass and acceleration of the body is already given as 6 kg and -1 m/ss ( in downward direction ) respectively we can easily find out the Tension. The formula we use here is W - T = ma. ( W = mg ) So, since we know m = 6 kg, a = -1 m/ss, g = 10 m/ss Therefore, W - T ma =) 6 * 10 - T = 6 * (-1) =) 60 - T = -6 =) 60 + 6 = T =) 66 = T So tension on the rope is 66 N.

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    $\begingroup$ Note that this site has MathJax enabled, which means you can use Latex-like syntax to add in equations for readability. $\endgroup$ – Kyle Kanos Aug 6 '15 at 18:30

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