Velocity ratio of a simple screw jack (one full turn) A simple screw jack has screw pitch p = 9 mm. The operating handle length is L = 45 cm. For one complete turn of the handle, what is the velocity ratio (distance moved by effort / distance moved by load)?

Introduction / Context:
The velocity ratio (VR) of a lifting machine relates the motion of the effort point to the motion of the load. For a screw jack, the effort moves around a circle while the load rises by one pitch per revolution. This problem reinforces the geometric meaning of VR for screw mechanisms.

Given Data / Assumptions:

• Pitch p = 9 mm = 0.9 cm per turn.
• Handle length L = 45 cm; effort travels a circumference per turn.
• One full rotation of the handle.

Concept / Approach:

VR = distance moved by effort in one turn / distance moved by load in one turn. Effort path is circumference 2πL; load rise is one pitch p. Use consistent units (cm).

Step-by-Step Solution:

Verification / Alternative check:

Dimensional reasonableness: a fine pitch and long handle imply large mechanical advantage and thus large VR, consistent with ≈314.

Why Other Options Are Wrong:

1.5, 5, and 25 are far too small; 100 omits the π factor.

Common Pitfalls:

Forgetting to convert mm to cm; using handle diameter instead of radius; using π incorrectly when computing circumference.

Final Answer:

314