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Power found from Trimmer

  1. Mar 20, 2014 #1
    1. The problem statement, all variables and given/known data
    The head of a grass string trimmer has 100 g of cord wound in a light, cylindrical spool with inside diameter 3.00 cm and outside diameter 18.0 cm as shown in the figure below. The cord has a linear density of 10.0 g/m. A single strand of the cord extends 16.0 cm from the outer edge of the spool.

    http://www.webassign.net/pse/p10-50.gif

    When switched on, the trimmer speeds up from 0 to 2 300 rev/min in 0.210 s. What average power is delivered to the head by the trimmer motor while it is accelerating?


    2. Relevant equations
    I = Icm + MD^2
    1/2 m (R1^2 + R2^2)

    P = 1/2 I ωf^2


    3. The attempt at a solution

    can't figure out a exact one :(

    please help explain the work you did to find the answer because I can't get this one at all
     
  2. jcsd
  3. Mar 20, 2014 #2

    Simon Bridge

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    The average power is the total work done divided by the time it took.
     
  4. Mar 20, 2014 #3
    that is true but this is the formula i derived but i hope its right

    I = m*[L^2/12 + (R2 + L/2)^2]

    then plug that into power formula

    P = 1/2* I * ωf^2/ Δt

    the issue is what should L in both parts of the I equation? I know R2 is 0.17 m / 2 to get .085 radius
     
  5. Mar 20, 2014 #4

    Simon Bridge

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    The equations are meaningless without the reasoning.

    What is R2 supposed to represent. What is L supposed to represent?
    Some radius and some angular momentum sure - but of what? Or is L some length?

    It helps to troubleshoot your equations if you are clear about what each of the letters means.
    It's a good discipline for you when you troubleshoot yourself too and it is worth marks in an exam.

    Lets see... You will certainly need the moment of inertia of the trimmer-head...
    How are you modelling that? You've not said.

    Guessing: Looks like you are modelling it as just a rod length L - rotating about a pivot displaced from com by the outer radius of the hoop and half the length of the rod. Is that all there is to the trimmer head?
     
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