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A person of mass m is standing on his tiptoes on both feet. The situation is pictured on the right. Assume that the Achilles' tendon is vertical and that both feet make the same angle with the horizontal. Take d₁ = 5 cm and d₂ = 15 cm. Our goal is to find the force that the tibia exerts on the foot and the force that the Achilles' tendon exerts on the foot (in terms of the mass of the person, m). Step 1: Draw all the forces acting on the foot. Identify which forces are known and which are unknown (on diagram). Important: At the point of contact between the tibia and the foot (point between d₁ and d₂) the tibia is exerting a downward force on the foot. This force is not equal to the weight or the weight divided by 2. The normal force (contact force between floor and foot) is equal to half the weight due to the person standing on both tiptoes. Step 2: Based on the knowns and unknowns, choose a point of rotation for which to write Tnet = 0 which will eliminate all but one unknown. Write that equation and solve for the unknown. Calf muscle Achille's tendon a a Step 3: Use Fnet,x = 0 and Fnet,y = 0 to solve for any other unknown forces. Important: Find the angle that the cable makes with the horizontal direction. This is a different angle than the one you used above. You will need this angle to find the x component of the force in the cable.

A person of mass m is standing on his tiptoes on both feet. The situation is pictured on the right. Assume that the Achilles' tendon is vertical and that both feet make the same angle with the horizontal. Take d₁ = 5 cm and d₂ = 15 cm. Our goal is to find the force that the tibia exerts on the foot and the force that the Achilles' tendon exerts on the foot (in terms of the mass of the person, m). Step 1: Draw all the forces acting on the foot. Identify which forces are known and which are unknown (on diagram). Important: At the point of contact between the tibia and the foot (point between d₁ and d₂) the tibia is exerting a downward force on the foot. This force is not equal to the weight or the weight divided by 2. The normal force (contact force between floor and foot) is equal to half the weight due to the person standing on both tiptoes. Step 2: Based on the knowns and unknowns, choose a point of rotation for which to write Tnet = 0 which will eliminate all but one unknown. Write that equation and solve for the unknown. Calf muscle Achille's tendon a a Step 3: Use Fnet,x = 0 and Fnet,y = 0 to solve for any other unknown forces. Important: Find the angle that the cable makes with the horizontal direction. This is a different angle than the one you used above. You will need this angle to find the x component of the force in the cable.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Problem C:** A person of mass \( m \) is standing on his tiptoes on **both feet**. The situation is pictured on the right. Assume that the Achilles’ tendon is vertical and that both feet make the same angle \( \theta \) with the horizontal. Take \( d_1 = 5 \) cm and \( d_2 = 15 \) cm. Our goal is to find the force that the tibia exerts on the foot and the force that the Achilles’ tendon exerts on the foot (in terms of the mass of the person, \( m \)). **Step 1:** Draw all the forces acting on the foot. Identify which forces are known and which are unknown (on diagram). **Important:** At the point of contact between the tibia and the foot (point between \( d_1 \) and \( d_2 \)) the tibia is exerting a downward force on the foot. This force is *not* equal to the weight or the weight divided by 2. The normal force (contact force between floor and foot) is equal to half the weight due to the person standing on both tiptoes. **Step 2:** Based on the knowns and unknowns, choose a point of rotation for which to write \( \tau_{\text{net}} = 0 \) which will eliminate all but one unknown. Write that equation and solve for the unknown. **Step 3:** Use \( F_{\text{net},x} = 0 \) and \( F_{\text{net},y} = 0 \) to solve for any other unknown forces. **Important:** Find the angle that the cable makes with the horizontal direction. This is a different angle than the one you used above. You will need this angle to find the x component of the force in the cable. **Diagram Explanation:** The diagram shows a side view of a foot standing on tiptoes. It includes: - The **Calf muscle** attaching to the **Achilles tendon**, which is drawn vertically. - The **Tibia**, positioned above the foot. - Distances \( d_1 \) and \( d_2 \) are marked from the ankle joint where the foot meets the tibia and where the Achilles tendon attaches to the heel, respectively. The diagram assists in visualizing forces and angles relevant to the problem of balancing moments and forces.
Transcribed Image Text:**Problem C:** A person of mass \( m \) is standing on his tiptoes on **both feet**. The situation is pictured on the right. Assume that the Achilles’ tendon is vertical and that both feet make the same angle \( \theta \) with the horizontal. Take \( d_1 = 5 \) cm and \( d_2 = 15 \) cm. Our goal is to find the force that the tibia exerts on the foot and the force that the Achilles’ tendon exerts on the foot (in terms of the mass of the person, \( m \)). **Step 1:** Draw all the forces acting on the foot. Identify which forces are known and which are unknown (on diagram). **Important:** At the point of contact between the tibia and the foot (point between \( d_1 \) and \( d_2 \)) the tibia is exerting a downward force on the foot. This force is *not* equal to the weight or the weight divided by 2. The normal force (contact force between floor and foot) is equal to half the weight due to the person standing on both tiptoes. **Step 2:** Based on the knowns and unknowns, choose a point of rotation for which to write \( \tau_{\text{net}} = 0 \) which will eliminate all but one unknown. Write that equation and solve for the unknown. **Step 3:** Use \( F_{\text{net},x} = 0 \) and \( F_{\text{net},y} = 0 \) to solve for any other unknown forces. **Important:** Find the angle that the cable makes with the horizontal direction. This is a different angle than the one you used above. You will need this angle to find the x component of the force in the cable. **Diagram Explanation:** The diagram shows a side view of a foot standing on tiptoes. It includes: - The **Calf muscle** attaching to the **Achilles tendon**, which is drawn vertically. - The **Tibia**, positioned above the foot. - Distances \( d_1 \) and \( d_2 \) are marked from the ankle joint where the foot meets the tibia and where the Achilles tendon attaches to the heel, respectively. The diagram assists in visualizing forces and angles relevant to the problem of balancing moments and forces.
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