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To account for the walking speed of a bipedal or quadrupedal ani- mal, model a leg that is not con- tacting the ground as a uniform rod of length €, swinging as a physical pendulum through one-half of a cycle, in resonance. Let 0mas represent its amplitude. (a) Show that the animal's speed is given by the expression Võgtsin 0 max if 0m is sufficiently small that the motion is nearly simple harmonic. An empirical relationship that is based on the same model and applies over a wider range of angles is Vögl cos (0ma/2) sin 0 max (b) Evaluate the walking speed of a human with leg length 0.850 m and leg-swing amplitude 28.0°. (c) What leg length would give twice the speed for the same angular amplitude?

To account for the walking speed of a bipedal or quadrupedal ani- mal, model a leg that is not con- tacting the ground as a uniform rod of length €, swinging as a physical pendulum through one-half of a cycle, in resonance. Let 0mas represent its amplitude. (a) Show that the animal's speed is given by the expression Võgtsin 0 max if 0m is sufficiently small that the motion is nearly simple harmonic. An empirical relationship that is based on the same model and applies over a wider range of angles is Vögl cos (0ma/2) sin 0 max (b) Evaluate the walking speed of a human with leg length 0.850 m and leg-swing amplitude 28.0°. (c) What leg length would give twice the speed for the same angular amplitude?

Classical Dynamics of Particles and Systems
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter11: Dynamics Of Rigid Bodies
Section: Chapter Questions
Problem 11.15P
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To account for the walking speed of a bipedal or quadrupedal ani- mal, model a leg that is not con- tacting the ground as a uniform rod of length €, swinging as a physical pendulum through one-half of a cycle, in resonance. Let 0mas represent its amplitude. (a) Show that the animal's speed is given by the expression Võgtsin 0 max if 0m is sufficiently small that the motion is nearly simple harmonic. An empirical relationship that is based on the same model and applies over a wider range of angles is Vögl cos (0ma/2) sin 0 max (b) Evaluate the walking speed of a human with leg length 0.850 m and leg-swing amplitude 28.0°. (c) What leg length would give twice the speed for the same angular amplitude?
Transcribed Image Text:To account for the walking speed of a bipedal or quadrupedal ani- mal, model a leg that is not con- tacting the ground as a uniform rod of length €, swinging as a physical pendulum through one-half of a cycle, in resonance. Let 0mas represent its amplitude. (a) Show that the animal's speed is given by the expression Võgtsin 0 max if 0m is sufficiently small that the motion is nearly simple harmonic. An empirical relationship that is based on the same model and applies over a wider range of angles is Vögl cos (0ma/2) sin 0 max (b) Evaluate the walking speed of a human with leg length 0.850 m and leg-swing amplitude 28.0°. (c) What leg length would give twice the speed for the same angular amplitude?
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