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Solved: BIO Downward-Facing Dog. The yoga exercise
Chapter 11, Problem 67P(choose chapter or problem)
BIO Downward Facing Dog. One yoga exercise, known as the “Downward-Facing Dog,” requires stretching your hands straight out above your head and bending down to lean against the floor. This exercise is performed by a 750-N person, as shown in Fig. P11.67. When he bends his body at the hip to a \(90^{\circ}\) angle between his legs and trunk, his legs, trunk, head, and arms have the dimensions indicated. Furthermore, his legs and feet weigh a total of 277 N, and their center of mass is \(41 \mathrm{~cm}\) from his hip, measured along his legs. The person’s trunk, head, and arms weigh 473 N, and their center of gravity is
\(65 \mathrm{~cm}\) from his hip, measured along the upper body. (a) Find the normal force that the floor exerts on each foot and on each hand, assuming that the person does not favor either hand or either foot. (b) Find the friction force on each foot and on each hand, assuming that it is the same on both feet and on both hands (but not necessarily the same on the feet as on the hands). [: First treat his entire body as a system; then isolate his legs (or his upper body).]
Equation Transcription:
°
Text Transcription:
90^\circ
41 cm
65 cm
90 cm
75 cm
60 cm
Questions & Answers
QUESTION:
BIO Downward Facing Dog. One yoga exercise, known as the “Downward-Facing Dog,” requires stretching your hands straight out above your head and bending down to lean against the floor. This exercise is performed by a 750-N person, as shown in Fig. P11.67. When he bends his body at the hip to a \(90^{\circ}\) angle between his legs and trunk, his legs, trunk, head, and arms have the dimensions indicated. Furthermore, his legs and feet weigh a total of 277 N, and their center of mass is \(41 \mathrm{~cm}\) from his hip, measured along his legs. The person’s trunk, head, and arms weigh 473 N, and their center of gravity is
\(65 \mathrm{~cm}\) from his hip, measured along the upper body. (a) Find the normal force that the floor exerts on each foot and on each hand, assuming that the person does not favor either hand or either foot. (b) Find the friction force on each foot and on each hand, assuming that it is the same on both feet and on both hands (but not necessarily the same on the feet as on the hands). [: First treat his entire body as a system; then isolate his legs (or his upper body).]
Equation Transcription:
°
Text Transcription:
90^\circ
41 cm
65 cm
90 cm
75 cm
60 cm
ANSWER:
Solution 67P
Here, we need to consider the person’s legs and upper body separately and then find the moments of the weight about those portions center of gravity.
Let us have a look at the simplified figure below.
Now, applying Pythagoras theorem, we can calculate the distance between his feet and hands.
Let, be the distance.