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Old Apr 21st 2015, 12:06 PM   #1
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Question Simple explanation needed

Hi everybody out there. I have a simple problem one which I in fact solved fairly easily with a few assumptions. However looking back on it I find that I do not fully understand one facet of the problem and I am asking if anyone can give me a simple explanation to clear my confusion.
The problem is a simple problem in Newton's First Law.
Scenario - We have two 25 Newton blocks at each end of a rope. The rope is suspended via a friction-less pulley which is attached by a chain to the ceiling.
We can ignore the mass of the chain , pulley and rope.

a) What is the tension in the rope ?
b) What is the tension in the chain ?... (I told you it was simple)

I don't want an explanation on how to solve this problem, I have already done that. I would like a simple explanation on why the tension in the rope is equal to 25 Newtons and not 50 Newtons (25x2). Now I know the answer is 25 Newtons but when I try to rationalize it I just get confused I cannot get the thing straight in my mind.
Any help would be appreciated. Thanks
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Old Apr 21st 2015, 01:27 PM   #2
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Newton's 2nd law says that the acceleration of the block is equal to the sum of forces acting on the block. You know this system is in equilibrium, and hence acceleration = 0 and the rope must pull up on each block with a force of 25N to precisely counteract the force of gravity acting on the block. It doesn't matter that there are two blocks balancing each other - If the rope actually had 50N of tension then each block would "feel" 50 N pulling upwards, and both blocks would accelerate upward.

This is actually a classic puzzle that often foils first year physics students. I remember being asked a similar problem: suppose you have a rope with a breaking strength of 100N. You tie one end of the rope to a horse thatccan pull with 90N of force, and tie the other end to a tree. Does the rope break? No, because the tension will be 90N, which is below the breaking strength. Now untie the rope from the tree and tie it to a second horse who will pull in the opposite direction of the first horse with 90 N of force. Does the rope break? The answer is no because the tension on the rope is still 90N.
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Old Apr 21st 2015, 03:32 PM   #3
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Because unless you go in for impulsive snatching forces (crane drivers would tell you about these) a mass cannot exert a greater force than its own weight under gravity. This is why you cannot sit on a chair and lift yourself bodily off the floor, but you can lift more than your own weight by pushing against something like the floor.

In order to have any tension at all a string or chain must be pulled from both ends.
So each 25kg mass exerts a force of 25g N when hanging down.

Last edited by studiot; Apr 22nd 2015 at 08:39 AM. Reason: spelling
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Old Apr 22nd 2015, 08:01 AM   #4
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Just a little thank you note to the two who answered my post. Thanks a lot, your answers have cleared up any confusion I had about the concept of the value 'tension' in the the particular problem (and in general) which is exactly what I was looking for.
Thank you for taking the time to answer my question.
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