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Difficulty: MediumScrews and Threads

A mechanic needs to lift a heavy engine using a screw jack. They can equip the jack with one of two interchangeable threaded rods: Rod X has a coarse thread with 44 threads per inch (TPI), and Rod Y has a fine thread with 88 TPI.

Assuming the jack's handle length is identical for both setups and friction is negligible, which of the following statements accurately describes the required effort force and total work done if the mechanic uses Rod Y instead of Rod X to lift the engine by exactly 1010 inches?

  1. Rod Y requires half the effort force on the handle, but the total work done to lift the engine remains the same.Answer
  2. B
    Rod Y requires half the effort force on the handle, and it reduces the total work done to lift the engine by half.
  3. C
    Rod Y requires twice the effort force on the handle, but the total work done to lift the engine remains the same.
  4. D
    Rod Y requires twice the effort force on the handle, and it doubles the total work done to lift the engine.

Answer

Rod Y requires half the effort force on the handle, but the total work done to lift the engine remains the same.
A screw is essentially an inclined plane wrapped around a central cylinder. Increasing the Threads Per Inch from 44 to 88 halves the pitch of the thread, making the 'incline' less steep. This doubles the mechanical advantage of the jack, cutting the required effort force on the handle in half. However, the fundamental principle of all simple machines is that they do not reduce the total amount of work required to move a load; they merely trade increased input distance (more rotations of the handle) for decreased input force. Because the engine is still being lifted exactly 1010 inches, the total output work remains identical.

Step-by-Step Solution

1
Analyze the relationship between Threads Per Inch (TPI) and pitch.
Rod Y (88 TPI) has half the pitch of Rod X (44 TPI), meaning it advances half the linear distance per full rotation.
Pitch is the mathematical inverse of TPI (1/TPI1/\text{TPI}). It determines the steepness of the screw's thread.
2
Determine the effect of a smaller pitch on Mechanical Advantage and effort force.
Because Rod Y advances half as far per rotation, its Ideal Mechanical Advantage is doubled. Thus, it requires half the effort force to lift the same load.
A screw is an inclined plane wrapped around a cylinder. A finer thread equates to a shallower incline, which trades distance for force.
3
Evaluate the total work done by the system in both scenarios.
The total work done remains identical regardless of the rod used.
Total output work is calculated as Load Force ×\times Lift Distance. Since the engine's weight and the 1010-inch lift distance do not change, the total work is conserved.

Key Concept

Mechanical Advantage of Screws and Conservation of Work
Estimated Time:1m 0s
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Topics

Screws and Threads

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