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Centripetal Force of a linear spring

  1. Sep 1, 2016 #1
    • Member warned that the homework template must be used
    I was given a question relating centripetal force to solve
    A linear spring of negligible mass requires a force of 18.0 N to cause its length to increase by 1.0 cm.
    A sphere of mass 75.0 g is attached to one end of the spring. The distance between the centre of the sphere M and the other end P of the unstretched spring is 25.0 cm
    The sphere is rotated at constant speed in a horizontal circle with centre P. The distance PM increases to 26.5 cm.

    My main problem is how you find the radius of the sphere, (if you can, can you tell me how in a step by step process if you can ) and also answering the question

    Kind Regards
     
  2. jcsd
  3. Sep 2, 2016 #2
    I think in your question the radius of the sphere is not important(? Maybe it just regards the sphere as a point, and just use the centripetal force to find its speed?
     
  4. Sep 2, 2016 #3

    Andrew Mason

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    You are not given enough information to determine the radius of the sphere. The radius of the sphere is immaterial if the question is: what is the angular speed of the sphere?
    AM
     
  5. Sep 2, 2016 #4

    haruspex

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    Quite so. Christopher, if you find that surprising, consider that once the system is rotating constantly then that includes the rotation of the sphere about its own axis. There is no centripetal force that need be applied to a sphere externally to maintain that aspect of its rotation.
     
  6. Sep 2, 2016 #5
    Also the question was to determine the speed of the sphere: my attempt of this was to try use the formula f=mv^2/r, however I cant seem to find the radius, I have uploaded a picture of the question as well. View attachment 105425

    Kind Regards
     

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    Last edited: Sep 2, 2016
  7. Sep 2, 2016 #6

    haruspex

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    As has already been explained to you, if you are only asked to find the speed of the sphere then you will not need to find its radius and cannot do so.
    One approach is to say "let the radius be r", write out all the equations, and gasp in astonishment as r disappears during the subsequent algebra.
     
  8. Sep 2, 2016 #7
    Oh, which equation should I use to find the speed of the sphere?

    Kind Regards
     
  9. Sep 2, 2016 #8

    haruspex

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    I suspect that you already have all the equations you need but became blocked by the belief that you needed to find the radius.
    Post the equations that you have, and any other standard equations that you feel may be relevant.
     
  10. Sep 3, 2016 #9
    Sorry I was not able to reply early, I was at school, however I was able to figure out how to do the question, I realised that the radius of for the centripetal is 0.265 ( not the sphere, my bad...) then I made the equation mv^2/r equal to 27 ( since the string increased by 1.5 cm ), after that I solved it given that m= 0.75 and r= 0.265. Thank you for helping me guys :)

    Kind Regards
     
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