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Walking speed of a dinosaur

  1. Feb 5, 2012 #1
    1. The problem statement, all variables and given/known data

    All walking animals, including humans, have a natural walking pace, a number of steps per minute that is more comfortable than a faster or slower pace. Suppose this natural pace is equal to the period of the leg, viewed as a uniform rod pivoted at the hip joint. A) How does the natural walking pace depend on the length L of the leg, measured from hip to foot? B) Fossil evidence shows that Tyrannosaurus rex, a two-legged dinosaur that lived about 65 million years ago at the end of the Cretaceous period, had a leg length L = 3.1 m and a stride length (the distance from one foot-print to the next print of the same foot ) S = 4.0 m. Estimate the walking speed of Tyrannosaurus rex.


    2. Relevant equations

    I=(m*L^2)/3
    T=2*pi/w


    3. The attempt at a solution

    T=2*pi/w=2*pi/sqrt(Lmg/I)

    I=(m*L^2)/3

    T=pi*sqrt(4L/3g)=2.04s

    v=s/T=4m/2.04s=1.96m/s

    But the answer says that T=2pi*sqrt(2L/3g)=2.88s
    v=s/T=4m/2.88s=1.4m/s
     
  2. jcsd
  3. Feb 5, 2012 #2
  4. Feb 5, 2012 #3

    BruceW

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    Homework Helper

    you've said, you've seen the answer is T=2pi*sqrt(2L/3g), But you have used: T=2pi*sqrt(L/3g), so this is where the problem is. I guess the problem stems from the first line, where you seemed to use w=sqrt(Lmg/I), but this is not true (which is why you end up with an incorrect answer for the period of the motion).
     
  5. Feb 5, 2012 #4
    Why is w=sqrt(Lmg/I) incorrect?
     
  6. Feb 6, 2012 #5

    BruceW

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    Homework Helper

    That equation for the angular frequency is correct for a pendulum where there is a small bob on the end of a light, inextensible string. But in this question, the pendulum is a uniform rod. So that equation for the angular frequency is not correct.

    Are you meant to derive the equation for the angular frequency of a pendulum made of a uniform rod? If not, you can guess what it is, since you've seen the answer. The rest of your working is correct, its just the angular frequency which was wrong.
     
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