Systems of Pulleys – First System with 4 Pulleys For the first system of pulleys having 4 pulleys, what is the velocity ratio (VR)?

Introduction / Context:
Velocity ratio (VR) in pulley systems measures how far the effort moves compared with the load. In the first system of pulleys, each additional pulley doubles the number of supporting rope segments of the load, doubling the VR.

Given Data / Assumptions:

• First system of pulleys.
• Number of pulleys n = 4.
• Light, inextensible rope; ideal kinematics for VR.

Concept / Approach:
The well-known expression for the first system is VR = 2^n. The reason is that each pulley effectively doubles the number of load-supporting rope segments, thereby doubling how many units the effort must move to raise the load by 1 unit.

Step-by-Step Solution:
Write formula: VR = 2^n. Substitute n = 4. Compute: VR = 2^4 = 16.

Verification / Alternative check:
Count rope segments supporting the moving block in a standard diagram with 4 pulleys; you will find 16 units of effort travel per unit of load travel under ideal conditions.

Why Other Options Are Wrong:
4 and 8 underestimate the doubling effect; 20 and 32 do not match 2^n.

Common Pitfalls:
Confusing first, second, and third pulley systems, which have distinct VR formulas.

Final Answer:
16