https://file.aiquickdraw.com/mathbot/file/1729622148542c2j1ajlo.jpg

To solve the problem presented in the image, we need to approach the two parts (a and b) based on the given information. Here's how we can proceed:

### Part a) **Determine the configuration of the spring before the grip is assembled.**
The spring configuration refers to the effective number of active coils, denoted by \( N_a \). This value was already provided as \( N_a = 2.413 \).

To understand the configuration:
- **Material**: The wire is A227 hard-drawn steel.
- **Turns**: The wire is wound 2.5 times around a mandrel.
- The figure describes a torsional spring with a helical form. The calculation of active coils involves considering the geometry and how many coils actively contribute to the spring’s stiffness.

From the problem, we can state that the spring's initial configuration can be described as having approximately 2.413 active turns, which is typical for determining the stiffness and spring rate.

### Part b) **Find the force necessary to close the grip.**
The force needed to close the grip is already provided as \( F = 87.3 \, \text{N} \).

This force calculation likely involves the use of torsional spring formulas, specifically:
\[
F = \frac{k \cdot \theta}{r}
\]
Where:
- \( k \) is the spring constant,
- \( \theta \) is the angular displacement,
- \( r \) is the radial distance or the lever arm (likely related to the 75 mm shown in the diagram).

Since the force is given, the calculation or reference can be checked for consistency, assuming the necessary spring constant and deflection angle were determined based on material properties and geometry.

Would you like to explore more details about how these formulas are derived, or do you have any specific questions about the process?

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Here are five related questions to consider:
1. How is the number of active coils \( N_a \) typically calculated in spring design?
2. What role does the material (A227 hard-drawn steel) play in the stiffness of the spring?
3. How do we compute the spring constant \( k \) for a torsional spring?
4. How does the radial distance (lever arm) influence the closing force of the grip?
5. What safety factors are considered in spring design to prevent exceeding permissible stress?

**Tip**: For spring-based systems, always consider both the material properties and the geometric constraints to ensure accurate force and displacement calculations.

Determine the configuration of the spring before the grip is assembled and find the force necessary to close the grip.

Explore how to calculate the configuration of a torsion spring and the force required to close a finger exerciser grip. Using principles of spring mechanics, this problem involves determining the number of active coils and applying the force equation for a spring system.

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