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Clock Torque Question

  1. Mar 4, 2013 #1
    I have attempted this a few times, I got these answers--- 655.44N and 345.144N
    If anyone can solve this for me it would be appreciated


    The hour and minute hands of the clock in
    the famous Parliament Clock Tower in London are 1.7 m and 3.4 m long and have masses
    of 89 kg and 60 kg, respectively
    Calculate the magnitude of the torque
    around the center of the clock due to the
    weight of these hands indicating 3 h and
    1 min; i.e., 3:1 o’clock. Assume the clock
    hands can be modeled as uniform thin rods
    and at 3:00 o’clock, the hour hand is precisely
    90◦
    from the vertical. The acceleration of
    gravity is 9.81 m/s
    2
    .
    Answer in units of N · m
     
  2. jcsd
  3. Mar 4, 2013 #2
    I got 1482.74N*m and 208.97N*m. How did you solve these?
     
  4. Mar 4, 2013 #3
    (360 deg/rev) / [12hr * 60 min/hr/rev] = 0.5° / min

    Th = mg(l/2)cosθ
    Th = 60(9.81)(1.7/2)cos(-0.5)
    Th =500 Nm

    360 deg/rev / 60 min/rev = 6 degrees/min
    90 - 6 = 84° from horizontal

    Tm = mg(l/2)cosθ
    Tm = 89(9.81)(3.4/2)cos84

    Tm = 155 Nm
     
  5. Mar 4, 2013 #4
    155+ 500 =650Nm 600-144 = 345Nm thats how i got those answers
     
  6. Mar 4, 2013 #5
    My answers were the torques for the hour hand and minute hand. I messed up the one for the Tm though but i fixed it and had the same answer as you also i forgot to divide my answers by 2 so the Th I had is 741.37. Torque is force multiplied by the perpendicular distance so for Th you just had to do mg(L/2).
    Where did the 600-144 come from?
     
  7. Mar 4, 2013 #6
    Actually my Th was wrong too. Sorry I mixed up the masses. so I got 500 also for that one
     
  8. Mar 4, 2013 #7
    So what would I do with the 500 and 155? I added them together and it was wrong do it take 500-155 or 155-500?
     
  9. Mar 5, 2013 #8
    Counter-clockwise moments (or torques in the English speaking world?) are positive and clockwise moments are negative so all you have to do is to think which direction would the hands of the clock swing due to gravity if they could swing freely. The hour hand would swing clockwise due to gravity and the minute hand would swing counter-clockwise because of gravity pulling it. Did my explanation make sense to you?
     
    Last edited: Mar 5, 2013
  10. Mar 5, 2013 #9
    I put in -345 , 655 and 345 and all of them were wrong so far
     
  11. Mar 5, 2013 #10

    NascentOxygen

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    Staff: Mentor

    Hi lep11. It sounds like you live in a fascinating land. Contrast your experience with this: at 3:01 the hands of plain old English speaking clocks are located on the same side of the vertical, and both exert clockwise torque on their shaft. :smile:
     
  12. Mar 5, 2013 #11

    NascentOxygen

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    Staff: Mentor

    That looks right.

    What's the torque for the minute hand?
     
  13. Mar 5, 2013 #12
    Yes, it may sound like that because I mistakenly thought the time was 2:59 instead of 3:01, sorry. :redface:
     
  14. Mar 5, 2013 #13

    CWatters

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    Science Advisor
    Homework Helper

    I got the slightly different figure of 742.13 N.m and 104.59 N.m. Might make a difference to the rounding.
     
  15. Mar 5, 2013 #14
    In the end I ended up getting those torques, thank you to everyone for your help and input!
     
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