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Two spring scales holding a hanging mass, what're the readings on both scales?

  1. Sep 21, 2014 #1
    Having trouble with this tricky physics problem, anyone have an idea of what the answer would be?


    1. The problem statement, all variables and given/known data


    A 20-kg fish is weighed with two spring scales, each of negligible weight. What will be the readings on the scales?

    A. Each scale will read 10 kg
    B. Each scale will read 20 kg
    C. The top scale will read 20 kg, and the bottom scale will read 0 kg
    D. The bottom scale will read 20 kg, and the top scale will read 0 kg
    E. Each scale will show a reading greater than 0 kg and less than 20 kg, but the sum of the two readings will be 20 kg



    2. Relevant equations

    Fnet = ma = Fg + Fsp1 + Fsp2 (+ T??)



    3. The attempt at a solution

    I'm going to be honest, I'm stumped on this one. I feel like the both spring forces will balance out the downward weight (w = mg). I think A makes the most sense, but I don't really know how to prove this is the correct answer using the formulas or a free-body diagram. I did draw the question out on MS Paint but I don't really know what else to add. Does the tension of the string play a key role in finding the answer? If anyone knows the answer and an explanation, it would be so helpful.

    Thanks!
    https://s.yimg.com/hd/answers/i/8fa9348e4cd54bf5b1fec3a8fbf55378_A.png?a=answers&mr=0&x=1411356970&s=78c197df753cb35bcf57e84d0ec4c158 [Broken]
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Sep 21, 2014 #2

    Simon Bridge

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    Do you know the springs are one after the other like that?
    If there were no springs - what would be the tension in the wire holding the fish up?
    If there were one spring, what would be the tension in the wire holding the spring up?

    Still stumped:
    Draw a free body diagram for each spring, and the fish.
     
  4. Sep 21, 2014 #3
    Yes, there are two spring scales, arranged like that. Our physics professor gave us a practice exam and that was what the picture looked like.

    If there were no springs, then:
    Fnet = T + -Fg = ma = 0
    T - Fg = 0
    T = Fg
    T = (20kg)(9.8m/s2)
    T = 196 N

    For that free-body diagram, I drew a dot representing the fish, an upward arrow labeled T, and a downward arrow labeled Fg.

    The springs are what are confusing me. When drawing a free-body diagram for the spring, would I have the spring be the mass? Would I draw Fspring and T upward, and Fg downward? Would T change due to the spring? I am pretty confused obviously, haha. Thanks for helping me though!
     
  5. Sep 22, 2014 #4

    Simon Bridge

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    No - the problem statement says springs have negligible mass.
    Make them a dot with tensions up and down from them.

    Note: if a spring balance is pulled in opposite directions by the same force F, what force does the balance show?
     
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