# A spring that cannot compress to the target height

Mechanics study · 2024-11-15

English translation of the Portuguese source. Original solid-height calculation. The later redesign advice is omitted because it did not resolve the stated solid-height constraint.

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Let's assess whether the spring can compress to **10 mm**, now using **1.6 mm** wire instead of 1.8 mm.

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### Adjustment for the new wire diameter:
1. **Total height occupied by the wire (\(L_{\text{wire}}\)):**
   \[
   L_{\text{wire}} = 14 \times 1.6 = 22.4 \, \text{mm}
   \]

2. **Initial free space:**
   The initial height is **40 mm**, so the space available for compression (\(Space\)) is:
   \[
   Space = L_0 - L_{\text{wire}} = 40 - 22.4 = 17.6 \, \text{mm}
   \]

3. **Required compressed height:**
   - For the spring to reach a compressed height of 10 mm, the **remaining free space** would be:
     \[
     Remaining\ space = L_c - L_{\text{wire}} = 10 - 22.4 = -12.4 \, \text{mm}
     \]

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### Conclusion:
Even with **1.6 mm** wire, the **remaining space would still be negative** when trying to compress the spring to 10 mm. With 14 coils, the coils would touch before the spring reached 10 mm.

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