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Question
If two ends of a rope are pulled with forces of equal magnitude and opposite direction, the tension at the center of the rope must be zero. True or false?

The answer is false. I chose true though and I'm not understanding why. Forces act at the center of mass of the object, so if there are two forces of equal and opposite magnitude, then they should cancel out resulting in zero tension, no?

Answer
Hello sam,

It looks like your logic goes like this:
Newton's 2nd Law says that if net force, Fnet, is zero (due to there being two forces of equal and opposite magnitude) then acceleration is zero (the formula being Fnet = m*a). Then that should also apply to tension. But that is not a proper application of Newton's Law. Newton's Law tells you that the center of the rope would not accelerate right or left, but tension is a different concept.

Imagine this: cut that rope in the middle and tie each half to a rubber band (you might call it a rubber binder) (just to be clear - so the rope is now longer by the length of the rubber band minus the amount of rope used in the knots). Now apply those 2 forces in the same way as before. The rubber band would have to stretch, right? The stretch is a response to the amount of tension in the rope.

Another question just for fun: What would the magnitude of the tension be? Twice the magnitude of either of the 2 forces? No just the magnitude of one of the forces. Those 2 forces could be developed by hanging a mass from a hook on the ceiling. The weight of the mass is a force pulling down. The hook pulls up with a force in the opposite direction.

I hope this helps,
Steve

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Steve Johnson

Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

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I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

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BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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