Goal Apply the equilibrium conditions to the human body. Humerus Problem A W = 47.3 N (11 lb) weight is held in a person's hand with the forearm horizontal, as in Figure 8.11. The biceps muscle is attached d = 0.0302 m from the joint, and the weight is / = 0.351 m from the joint. Find the upward force F exerted by the biceps on the forearm (the ulna) and the downward force R exerted by the humerus on the forearm, acting at the joint. Neglect the weight of the forearm. W - Biceps Ulna (a) (ь) Figure 8.11 (a) A weight held with the forearm horizontal. (b) The mechanical model for the system.
Goal Apply the equilibrium conditions to the human body. Humerus Problem A W = 47.3 N (11 lb) weight is held in a person's hand with the forearm horizontal, as in Figure 8.11. The biceps muscle is attached d = 0.0302 m from the joint, and the weight is / = 0.351 m from the joint. Find the upward force F exerted by the biceps on the forearm (the ulna) and the downward force R exerted by the humerus on the forearm, acting at the joint. Neglect the weight of the forearm. W - Biceps Ulna (a) (ь) Figure 8.11 (a) A weight held with the forearm horizontal. (b) The mechanical model for the system.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![**Example 8.6 A Weighted Forearm**
**Goal:** Apply the equilibrium conditions to the human body.
**Problem:** A weight \( W = 47.3 \, \text{N} \) (11 lb) is held in a person's hand with the forearm horizontal, as shown in Figure 8.11. The biceps muscle is attached \( d = 0.0302 \, \text{m} \) from the joint, and the weight is \( l = 0.351 \, \text{m} \) from the joint. Find the upward force \( \vec{F} \) exerted by the biceps on the forearm (the ulna) and the downward force \( \vec{R} \) exerted by the humerus on the forearm, acting at the joint. Neglect the weight of the forearm.
**Figure 8.11:**
- *(a)* A diagram showing a weight held with the forearm horizontal.
- *(b)* The mechanical model for the system. This includes a lever representing the forearm, with distances \( d \) and \( l \) marked. The forces \( \vec{F} \) and \( \vec{R} \) are shown at the appropriate points.
**Strategy:** The forces acting on the forearm are equivalent to those acting on a bar of length 0.351 m, as shown in Figure 8.11b. Choose the usual x- and y-coordinates as shown and the axis \( O \) on the left end. Use the conditions of equilibrium to generate equations for the unknowns and solve.
**Solution:**
1. **Apply the second condition for equilibrium (step 3).**
\[
\sum \tau_i = \tau_R + \tau_F + \tau_{BB} = 0
\]
\[
R(0) + F(0.0302 \, \text{m}) - (47.3 \, \text{N})(0.351 \, \text{m}) = 0
\]
\[
F = \_\_\_\_ \, \text{N}
\]
**Guidance:** Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully.
\[
F = \_\_\_\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a74cc31-62f4-4982-89c3-ce8d7d2cfbb2%2Fcc253050-3a80-4bbb-93da-db459f6ded44%2F84xgkg_processed.png&w=3840&q=75)
Transcribed Image Text:**Example 8.6 A Weighted Forearm**
**Goal:** Apply the equilibrium conditions to the human body.
**Problem:** A weight \( W = 47.3 \, \text{N} \) (11 lb) is held in a person's hand with the forearm horizontal, as shown in Figure 8.11. The biceps muscle is attached \( d = 0.0302 \, \text{m} \) from the joint, and the weight is \( l = 0.351 \, \text{m} \) from the joint. Find the upward force \( \vec{F} \) exerted by the biceps on the forearm (the ulna) and the downward force \( \vec{R} \) exerted by the humerus on the forearm, acting at the joint. Neglect the weight of the forearm.
**Figure 8.11:**
- *(a)* A diagram showing a weight held with the forearm horizontal.
- *(b)* The mechanical model for the system. This includes a lever representing the forearm, with distances \( d \) and \( l \) marked. The forces \( \vec{F} \) and \( \vec{R} \) are shown at the appropriate points.
**Strategy:** The forces acting on the forearm are equivalent to those acting on a bar of length 0.351 m, as shown in Figure 8.11b. Choose the usual x- and y-coordinates as shown and the axis \( O \) on the left end. Use the conditions of equilibrium to generate equations for the unknowns and solve.
**Solution:**
1. **Apply the second condition for equilibrium (step 3).**
\[
\sum \tau_i = \tau_R + \tau_F + \tau_{BB} = 0
\]
\[
R(0) + F(0.0302 \, \text{m}) - (47.3 \, \text{N})(0.351 \, \text{m}) = 0
\]
\[
F = \_\_\_\_ \, \text{N}
\]
**Guidance:** Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully.
\[
F = \_\_\_\
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