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To solve this problem, we can apply the principle of torque equilibrium. For the biceps force to hold the baseball without the arm rotating, the clockwise torque (due to the weight of the baseball) must equal the counterclockwise torque (due to the force of the biceps).

Here's how to approach it:

1. **Torques Calculation:**
   - **Clockwise torque** due to the baseball is given by:
     \[
     \tau_{\text{baseball}} = F_{\text{baseball}} \times r_{\text{baseball}}
     \]
     where \( F_{\text{baseball}} = 1.421 \, \text{N} \) is the force (weight of the baseball) and \( r_{\text{baseball}} = 17 \, \text{cm} = 0.17 \, \text{m} \) is the distance from the elbow to where the force acts (the palm of the hand).

   - **Counterclockwise torque** due to the biceps is given by:
     \[
     \tau_{\text{biceps}} = F_{\text{biceps}} \times r_{\text{biceps}}
     \]
     where \( F_{\text{biceps}} = 12.6 \, \text{N} \) is the biceps force and \( r_{\text{biceps}} = 2.75 \, \text{cm} = 0.0275 \, \text{m} \) is the distance from the elbow to where the biceps attaches.

2. **Equilibrium Condition:**
   In static equilibrium, the torques must balance:
   \[
   \tau_{\text{biceps}} = \tau_{\text{baseball}}
   \]
   So:
   \[
   F_{\text{biceps}} \times r_{\text{biceps}} = F_{\text{baseball}} \times r_{\text{baseball}}
   \]

3. **Substitute Known Values:**
   \[
   12.6 \, \text{N} \times 0.0275 \, \text{m} = 1.421 \, \text{N} \times 0.17 \, \text{m}
   \]

4. **Calculate:**

Let me compute whether this equation holds true.The counterclockwise torque due to the biceps is \( 0.3465 \, \text{Nm} \), while the clockwise torque due to the baseball is \( 0.24157 \, \text{Nm} \).

Since the torque generated by the biceps is greater than the torque required to hold the baseball, the 12.6 N of biceps force is sufficient to hold the baseball in the palm of the hand.

Would you like any further details or clarifications?

Here are 5 related questions:
1. How would the required biceps force change if the weight of the baseball increased?
2. What would happen if the distance from the elbow to the hand was longer?
3. How does the angle at which the biceps pulls affect the torque?
4. How could we calculate the biceps force if we include the weight of the forearm?
5. What role does friction play in stabilizing the baseball?

**Tip:** When analyzing torque problems, always ensure that the forces and their distances from the pivot point are correctly accounted for.

Is 12.6 N of Biceps force sufficient to hold a baseball that weighs 1.421 N on the palm of your hand? Neglect the weight of the forearm.

Learn how to determine if 12.6 N of biceps force is sufficient to hold a baseball weighing 1.421 N. This physics problem involves calculating torques and applying the principle of equilibrium. Suitable for high school students in Grades 11-12.

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