Problem 5.7 Consider a person standing on tiptoe on one foot. For this position, the forces...

  

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Problem 5.7 Consider a person standing on tiptoe on one foot. For this position, the forces acting on the foot are shown in Fig. 5.45. Point A is the point of attachment of the Achilles tendon through which a force is exerted by the gastrocnemius and soleus muscles on the calcaneus. Point B designates the center of the ankle joint and C is the point of application of the ground reaction force. For this system assume that the weight of the foot can be ignored as it is relatively small when compared to the weight of the entire body of the person. For this position of the foot, it is estimated that the lines of action of the tensile force in the Achilles tendon and the reaction force (F₁) of the ankle joint make an angle 0 = 49° and ß= 65° with the hori- zontal, respectively. Furthermore, for this position of the foot, it is also estimated that the magnitude of force exerted by www.TechnicalBooksPDF.com Applications of Statics to Biomechanics the gastrocnemius and soleus muscles on the calcaneus is FM = 1275.4 N. (a) Determine the entire weight (W) of the person. (b) Determine the magnitude of the reaction force (F₁) of the ankle joint. Answers: (a) W = 831.8 N; (b) F₁ = 1980.3 N 139 FJ B B C FM W Fig. 5.45 Forces acting on the foot form a concurrent system of forces Problem 5.7 Consider a person standing on tiptoe on one foot. For this position, the forces acting on the foot are shown in Fig. 5.45. Point A is the point of attachment of the Achilles tendon through which a force is exerted by the gastrocnemius and soleus muscles on the calcaneus. Point B designates the center of the ankle joint and C is the point of application of the ground reaction force. For this system assume that the weight of the foot can be ignored as it is relatively small when compared to the weight of the entire body of the person. For this position of the foot, it is estimated that the lines of action of the tensile force in the Achilles tendon and the reaction force (F₁) of the ankle joint make an angle 0 = 49° and ß= 65° with the hori- zontal, respectively. Furthermore, for this position of the foot, it is also estimated that the magnitude of force exerted by www.TechnicalBooksPDF.com Applications of Statics to Biomechanics the gastrocnemius and soleus muscles on the calcaneus is FM = 1275.4 N. (a) Determine the entire weight (W) of the person. (b) Determine the magnitude of the reaction force (F₁) of the ankle joint. Answers: (a) W = 831.8 N; (b) F₁ = 1980.3 N 139 FJ B B C FM W Fig. 5.45 Forces acting on the foot form a concurrent system of forces

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