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B Tension is causing me to be tensed

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  1. May 5, 2016 #1
    There's two questions about tension(the force), that no matter how much I try to find answers to and understand since the past few days, I'm simply not able to. Any help in this matter would be highly appreciated.

    1) If person A and person B are holding a rope, and person A applies 100N of force, he would get a reaction of 100N and the tension in the rope would be 100N. Fair enough. Now, if person B pulls with 100N too, person B would be pulled not only by the reaction force of 100N, but also by the force exerted by person B. In this case, shouldn't the tension be = 200N?

    Related sub-question: If a block of 10 kg is hanging from the ceiling, It would be exerting 100N downwards and get a reaction from the rope of 100N, and the ceiling would pull it with 100N too. So shouldn't the tension be 200N?

    2) If person A is pulling the string with 100N and person B with 200N, why is the tension in the rope 100N?
    I've read somewhere that in a string with negligible mass, this would result in the string slipping off the hands of person A, which makes sense. But why wouldn't that be the case with a string with mass too?
     
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  3. May 5, 2016 #2

    CWatters

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    Hold it right there. In the first situation how does A "get a reaction force" if B doesn't also apply 100N to the rope?
     
  4. May 5, 2016 #3
    1. It's the same force, not additional forces. Think about the rope. There's 100N of tension in the rope. Person A is pulling with 100N force. If person B didn't pull with an equal force the rope would move. If you imagine cutting the rope at any point and putting scales on the cut ends they would both read 100N. If you put one scale in the rope at any point it would read 100N.
    2. If person A is pulling with 100N force and person B pulls with 200N force then the tension in the rope would not be 100N. Person A would accelerate in the direction of person B, the magnitude of the acceleration would be (200N - 100N)/(mass of person A). The force would be (acceleration) X (mass of person A).
     
  5. May 5, 2016 #4

    jbriggs444

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    Agreed, completely.

    We cannot know the acceleration of person A because we do not know all the forces to which person A is subject. In any case, the acceleration of person A will be the net force on person A divided by the mass of person A. That net force will not, in general, happen to match the discrepancy in tension between the two ends of the rope.

    We do know the all the relevant horizontal forces on the rope. If there is a 200N force on one end and a 100N force oppositely directed on the other end then the net force on the rope is 100 N. The acceleration of the rope is then given by 100N divided by the mass of the rope.

    A rope with a small mass subject to a large net force will accelerate quickly. That explains why trying to pull on one end of a rope can result in a collision between the ground and one's posterior. The rope will move.
     
  6. May 5, 2016 #5
    We know that person A is in equilibrium pulling 100N against person B pulling 100N. If person B starts pulling 200N (all other things remaining the same) then my statements work just fine for the purposes of this thought experiment.
     
  7. May 5, 2016 #6

    jbriggs444

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    No. They do not. We have no information about the stability of the supposed equilibrium in the face of disturbances.

    Edit: Nor do we have an assurance that an equilibrium exists. We know only the force between A and the rope, not whether A is already accelerating under the unknown net force upon him.
     
  8. May 5, 2016 #7
    If I'm in space, and I pull a rope with 100N that is just freely floating or even attached to another person, the rope will exert a 100N force on me
     
  9. May 5, 2016 #8

    CWatters

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    Correct but only if B accelerates at the same rate as the rope so he doesn't also apply a force to it. Did you mean to make it that complicated?

    How does that differ from a situation where A pulls one end with 100N and the other end is fixed to a pole? The pole also exerts 100N on the rope.

    In this situation the rope isn't accelerating so does the rope still provide the reaction force you mention? or is it provided by B or the pole?
     
  10. May 5, 2016 #9
    I was trying to stay as basic as possible without adding any unknown scenarios, taking the question as stated.
    Quoting from above:
    "2) If person A is pulling the string with 100N and person B with 200N, why is the tension in the rope 100N?
    I've read somewhere that in a string with negligible mass, this would result in the string slipping off the hands of person A, which makes sense. But why wouldn't that be the case with a string with mass too?[/QUOTE]"

    Note that this is physically impossible. You can't have two different tension forces on a simple straight piece of rope. If the end points aren't fixed then one will move, and my equations are correct in this context. If the end points are fixed then the tension throughout the rope must be the same.

    No, we don't. But let's assume for the purposes of this experiment that the facts are as stated, and not conditions at some undefined instantaneous moment in time. I am sure that there are many scenarios that are not part of the stated problem that could be imagined. .
     
  11. May 5, 2016 #10
    So is the reaction provided by the pole or the rope? It could be the rope since in space when it is unattached to something, that's what it does.
    Also, what would be the tension in the case that the rope is fixed to another person while being pulled?
     
  12. May 5, 2016 #11
    The reaction is due to the pole. If the rope were unattached there would be no tension, unless you were accelerating hard enough while holding the rope that (mass of rope) X (rate of acceleration) = 100N.
     
  13. May 5, 2016 #12

    CWatters

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    +1

    If the rope is tied to a fixed pole that means the rope isn't accelerating. Therefore the inertia of the rope can't be providing a reaction force. Therefore the reaction force must be provided by the pole.
     
  14. May 5, 2016 #13
    If you pull on the rope with your hand, the reaction, if any, on the hand, can be provided only by the rope. Your hand is not interacting with anything else but the rope.
    The Newton third law pair involving your hand regards the rope and the hand.
    The interaction between the rope and the pole is a different interaction, characterized by a different pair of forces. Even if the magnitudes of the forces in the two pair may be equal, these are different forces.
    If the rope is not attached, both your force and the reaction of the rope may be very small (zero if the rope is considered massless). But you should realize that not only the "reaction" is zero, your force is zero as well. Both forces in the pair are zero. Or actually small.

    Attaching the other end of the rope to a pole you introduce another pair of forces, at the pole end.
    This time you can pull the rope with a larger force and the rope will pull you with the same larger force.
    So the effect of the pole is to allow you to increase the forces at your end. However this is not the same as saying that the pole produces the reaction force at your hand.
     
  15. May 5, 2016 #14
    Oh, so the rope in this case only serves the purpose of "transfering" the force to the pole, and the pole provides a reaction which is "transfered" back to the person holding the rope. Is this correct?
     
  16. May 5, 2016 #15
    This is the part that confused me. Introduce a new pair of forces at the pole end?
    aa.png
    Could you make a free body diagram on this including these new set of forces?
     
  17. May 5, 2016 #16

    jbriggs444

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    What body do you want to focus your attention on? The person, the rope, the pole or the Earth?
     
  18. May 5, 2016 #17
    The person and the pole
     
  19. May 5, 2016 #18

    jbriggs444

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    That's two bodies.
     
  20. May 5, 2016 #19
    There's enough space. Or maybe make two separate fbd's
     
  21. May 6, 2016 #20

    Dale

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    What forces act on the person?

    What forces act on the pole?
     
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