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Use differentials to estimate the change in tension of yo-yo string

  1. Oct 12, 2012 #1
    . The problem statement, all variables and given/known data

    The tension T in the string of the yo-yo is given by:

    T=(mgR)/(2r^2+R^2)

    where m is the mass of the yo-yo and g is the acceleration due to gravity. Use differentials to estimate the change in tension if R is increased from 3cm to 3.1cm and r is increased from 0.7cm to 0.8cm. Does the tension increase or decrease?

    2. Relevant equations

    I assume you'd need

    dT=∂T/∂r*dr + ∂T/∂R*dR

    3. The attempt at a solution

    I'm not completely sure how to approach this problem. My guess is that you need to find the partials, and then use the values to which r and R increase somehow, maybe as dr and dR values...but I'm not sure how to go about that.
    Any help would be greatly appreciated :)
     
  2. jcsd
  3. Oct 12, 2012 #2

    Mark44

    Staff: Mentor

    This is a good start. In place of dr and dR, approximate them with Δr = .1 (cm) and ΔR = .1 (cm). Evaluate your two partials using r = .7 cm and R = 3 cm.
     
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