ps2 - Biology 427 Problem Set 2 Here are some interesting...

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Unformatted text preview: Biology 427 Problem Set 2 Here are some interesting and useful data for this second problem set. You may not need all of this stuff. As usual, we have also provided you with another article for your insightful commentary. Raw data Peak human running speed (sprinter): Human mass: Human leg length: T. rex leg length g = earth's gravitational acceleration: 11 m/s 70 kg 1m 2m ~10 m/s2 Terrestrial Froude Number: Fr = V2/(g l) (where l is the leg length and U is the forward speed). Power equations for "step-n-hop" locomotion model (from Lecture 5): P = (1 + ) M g2 b/ 8 V + m V3/2(a+b) with an optimum "jumpiness" (j = b/a) j = (2 V2 (m/M)1/2/(a g)) - 1 Ballistic walker V M stride length which is derived from an argument about power demands for this mode of locomotion and a kinematic relationship between the vertical excursions of the body mass (h+d) and the horizontal excursions (a+b): h + d = (a + b) g b /8 V2 "a" is commonly about equal to the leg length. 1. Two biomechanics students competed in a ballistic walking race. One was a female whose leg length was 0.8 m and the other was a male whose leg length was 1.2 m. For a 5 m distance they both scored an identical time of 2.4 s (these by the way are real data!). (a) Is this greater of less than the maximum predicted speed for rigid limb (ballistic) walking (b) Explain what factors could contribute to the proportionately greater speed attained by the female biomechanics student. 2. Tyrannosaurus rex was a large theropod who had a body mass of approximately 7000 kg. Recent fossil evidence showed that this mass was supported by a leg that was approximately 2 m long (from the tarsus to the femoral-pelvic joint). Moreover, there is other fossil evidence that indicates a stride length (that is the distance between two successive footprints of the same foot) of about 6 meters. a. If T. rex followed the rules of ballistic walking, what peak velocity would you predict? How much greater is that than the peak velocity you can achieve by this method (estimate your leg length). b. Assume that the effective foot mass of T. rex is about 5% of the total body mass. Further assume that there is no storage of elastic strain energy in the tendons of this creature ( = 1). With those assumptions and your computation for the jumpiness of this creature (take leg length = a and figure what you think the quantity b/a is), what velocity and stride frequency would you predict? c. Given your estimate of the stride frequency, calculate the total rate of energy expenditure -- that means you compute the changes in potential energy in each stride and divide that energy by the time that the foot is on the ground. ...
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