College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Can you check my homework? Im sure I got the right answer, would the force of the tibia be -2984N instaead of positive? thank you
![### Educational Content on Foot Biomechanics
#### Problem Statement
A person stands on the ball of one foot. The normal force due to the ground pushing up on the ball of the foot has a magnitude of 750 N. Ignore the weight of the foot itself. The other significant forces acting on the foot are the tension in the Achilles tendon pulling up and the force of the tibia pushing down on the ankle joint.
#### Diagram Explanation
The accompanying diagram illustrates the forces acting on the foot:
- **Achilles Tendon**: The diagram shows the Achilles tendon exerting an upward force shown by an arrow labeled \( F_{\text{Achilles}} \).
- **Tibia**: An arrow labeled \( F_{\text{tibia}} \) is depicted exerting a downward force on the ankle joint.
- **Normal Force**: An arrow labeled \( N \) indicates the normal force exerted by the ground, pointing upward.
- **Anatomy of Foot**:
- **Tibia**: Bone labeled in the upper part of the leg.
- **Calcaneus (heel bone)**: Depicted at the bottom of the foot, where the normal force \( N \) acts.
- **Gastrocnemius-soleus muscles**: Shown connected to the Achilles tendon.
#### Question
If the tension in the Achilles tendon is 2234 N, what is the force exerted on the foot by the tibia? If the force is upward, enter a positive value. If the force is downward, enter a negative value.
**Calculation:**
Given:
- Tension in the Achilles tendon \( T_{\text{Achilles}} \) = 2234 N (upward)
- Normal force \( N \) = 750 N (upward)
To find the force exerted by the tibia \( F_{\text{tibia}} \), we use the equilibrium condition. For vertical forces to balance:
\[ F_{\text{tibia}} + T_{\text{Achilles}} - N = 0 \]
\[ F_{\text{tibia}} + 2234 - 750 = 0 \]
\[ F_{\text{tibia}} = 750 - 2234 \]
\[ F_{\text{tibia}} = -1484 \]
So, the force exerted on the foot by the tibia is **-1484 N (downward)**.
However,](https://content.bartleby.com/qna-images/question/ff7f72a6-27ca-4fc6-a195-84c52d046220/17c1afcd-f628-4e9c-a67a-46c612d3914c/eunsio3_processed.jpeg)
Transcribed Image Text:### Educational Content on Foot Biomechanics
#### Problem Statement
A person stands on the ball of one foot. The normal force due to the ground pushing up on the ball of the foot has a magnitude of 750 N. Ignore the weight of the foot itself. The other significant forces acting on the foot are the tension in the Achilles tendon pulling up and the force of the tibia pushing down on the ankle joint.
#### Diagram Explanation
The accompanying diagram illustrates the forces acting on the foot:
- **Achilles Tendon**: The diagram shows the Achilles tendon exerting an upward force shown by an arrow labeled \( F_{\text{Achilles}} \).
- **Tibia**: An arrow labeled \( F_{\text{tibia}} \) is depicted exerting a downward force on the ankle joint.
- **Normal Force**: An arrow labeled \( N \) indicates the normal force exerted by the ground, pointing upward.
- **Anatomy of Foot**:
- **Tibia**: Bone labeled in the upper part of the leg.
- **Calcaneus (heel bone)**: Depicted at the bottom of the foot, where the normal force \( N \) acts.
- **Gastrocnemius-soleus muscles**: Shown connected to the Achilles tendon.
#### Question
If the tension in the Achilles tendon is 2234 N, what is the force exerted on the foot by the tibia? If the force is upward, enter a positive value. If the force is downward, enter a negative value.
**Calculation:**
Given:
- Tension in the Achilles tendon \( T_{\text{Achilles}} \) = 2234 N (upward)
- Normal force \( N \) = 750 N (upward)
To find the force exerted by the tibia \( F_{\text{tibia}} \), we use the equilibrium condition. For vertical forces to balance:
\[ F_{\text{tibia}} + T_{\text{Achilles}} - N = 0 \]
\[ F_{\text{tibia}} + 2234 - 750 = 0 \]
\[ F_{\text{tibia}} = 750 - 2234 \]
\[ F_{\text{tibia}} = -1484 \]
So, the force exerted on the foot by the tibia is **-1484 N (downward)**.
However,
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