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Difficulty: HardScrews and Threads

Rank the following jackscrew configurations in order from the highest Ideal Mechanical Advantage (IMA) to the lowest IMA.

  1. 1Jackscrew with an 8-inch handle and 8 threads per inch (TPI)
  2. 2Jackscrew with a 10-inch handle and 6 threads per inch (TPI)
  3. 3Jackscrew with a 12-inch handle and 4 threads per inch (TPI)
  4. 4Jackscrew with a 15-inch handle and 3 threads per inch (TPI)

Answer

The correct order from highest to lowest Ideal Mechanical Advantage is: the 8-inch handle with 8 TPI, followed by the 10-inch handle with 6 TPI, then the 12-inch handle with 4 TPI, and finally the 15-inch handle with 3 TPI.
The Ideal Mechanical Advantage of a jackscrew is determined by multiplying the circumference of the effort circle (2×π×L2 \times \pi \times L) by the Threads Per Inch (TPI). Because 2π2\pi is constant for all options, we can simply compare the product of the handle length (LL) and the TPI. The 8-inch/8 TPI setup yields the highest proportional factor (8×8=648 \times 8 = 64), followed by the 10-inch/6 TPI setup (6060), the 12-inch/4 TPI setup (4848), and finally the 15-inch/3 TPI setup (4545).

Step-by-Step Solution

1
Identify the formula for the Ideal Mechanical Advantage (IMA) of a jackscrew.
IMA = (2 × π × Handle Length) / Pitch. Since Pitch = 1 / TPI, this simplifies to IMA = 2 × π × Handle Length × TPI.
To find the relative IMA, we need to compare the product of the handle length and TPI for each configuration.
2
Calculate the proportional IMA factor (Handle Length × TPI) for each jackscrew configuration.
8-inch handle, 8 TPI: 8 × 8 = 64. 10-inch handle, 6 TPI: 10 × 6 = 60. 12-inch handle, 4 TPI: 12 × 4 = 48. 15-inch handle, 3 TPI: 15 × 3 = 45.
This provides a comparative numerical value to rank the mechanical advantages without needing to calculate the exact factor of 2π.
3
Order the configurations based on the calculated factors.
64 > 60 > 48 > 45.
The prompt requests ranking from the highest IMA to the lowest IMA.

Key Concept

Ideal Mechanical Advantage of a Screw
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Topics

Screws and Threads

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