Standing Tiptoe

1. Standing Tiptoe Consider the following model of the forces acting on the foot when a person stands on their tiptoe on a horizontal surface. Below, the first image is an anatomical sketch of a foot showing the musculoskeletal structure, emphasizing the location of the tibia and Achilles tendon, and the second is a simplified model of the foot as a single rigid body showing the location and axis along which the forces from the floor, tibia, and Achilles tendon act upon the foot when a person stands tiptoe. Assume the person stands on a single foot and that the acceleration due to gravity is 102 LIGAMENTS OF THE ANKLE JOINT Flexor digiforum longus Plantaris tendon Superficial peroneal n Achilles tendon D Tibialis posterior Soleus Soleus Long saphenous v. -Sural n. Peroneus tertius Sural nerve- -Post tibial Achilles Ext. digitorum Tibia tendon - longus FLhallucis Plantoris -longus -Tibialis anterior 150 tendon -Ext. hallucis longus Ant. tibial n. and a. Tibia Plantar ad Anterior inferior Fibula tibiofibular lig. fibular lig. Deltoid lig and lat plantar nn Ant talofibular lig. -Interosseous -Tibialis posterior talocalcanean ligament Abductor hallucis -Bifurcate lig Ext. hallucis longus Extensor Dorsalis c : Calcaneus digitorum brevis pedis a. cu* Cuboid m . Medial tubercle Extensor digitorum longus of talus -25 cm n . Navicular p.b. Peroneus brevis p.I.* Peroneus longus 18 cm .t. . Subtalar joint * : Talus Dissected by Dr. J.M. Odiorne "U.Br.Columbia - Drawing Ligaments of ankle joint - English labels" by Department of Anatomy, University of British Columbia, UBC and J.M. Odiorne, UBC, license: CC BY-NC-SA. Created for: Department of Anatomy (now Department of Cellular and Physiological Sciences) at the University of British Columbia. Source: website Clinical Anatomy, http://www.clinicalanatomy.ca a. Using the simplified model above, make a complete and properly labeled force diagram for the foot. Ignore the mass of the foot. b. Briefly explain your choice of direction for the action of the forces exerted by the Achilles tendon and the tibia on the foot. . Suppose that the normal force on the foot from the floor is 700 N (effectively supporting the entire weight of the individual), verify that the Newton's 2nd law for the forces and torques on the foot are given by the below expressions. Briefly explain the chosen location of the pivot based on these expressions. EF : NET sin 150 - NFA sin 0 = 0 EFy : (700 N) + NFA COS 0 - NFT COS 150 = 0 ET : NFA (7.00 cm) - (700 N)(18.0 cm) cos 0 = 0. d. Solve for the angle 0. (hint: there is some tough algebra here, use the trig identity sin 0 + cos 0 = 1 to write everything in terms of either cos 0 or sin 0) e. Solve for the magnitude of the forces from the tibia and Achilles tendon