Engineering mechanics: How do pulley systems achieve mechanical advantage to lift large loads with smaller applied forces?
Define and calculate mechanical advantage and velocity ratio in single fixed, single movable, block-and-tackle and compound pulley systems, and apply efficiency to find actual mechanical advantage
A focused answer to the HSC Engineering Studies Lifting Devices dot point on pulleys. Mechanical advantage, velocity ratio, the number-of-rope-segments rule, efficiency, block and tackle, and worked HSC-style past exam questions.
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What this dot point is asking
NESA wants you to define and calculate mechanical advantage and velocity ratio for pulley systems (single fixed, single movable, block and tackle, compound), apply efficiency to convert between ideal and actual mechanical advantage, and use the distance trade-off to find input travel.
The answer
Definitions
Mechanical advantage (MA) is the ratio of load force to effort force.
Velocity ratio (VR) is the ratio of effort distance (or speed) to load distance (or speed).
Efficiency is the ratio of actual mechanical advantage to velocity ratio (or equivalently, output work over input work):
Pulley systems
- Single fixed pulley
- Changes direction only. IMA = 1, VR = 1. Effort equals load.
- Single movable pulley
- Two rope segments support the load. IMA = 2, VR = 2. Effort is half the load; rope travels twice the load distance.
- Block and tackle
- A fixed block and a movable block, each with one or more pulleys. The IMA equals the number of rope segments supporting the load block, not the total number of pulleys.
| Configuration | IMA | VR |
|---|---|---|
| Single fixed | 1 | 1 |
| Single movable | 2 | 2 |
| 2-and-1 (one in each block, 3 segments) | 3 | 3 |
| 2-and-2 (4 segments) | 4 | 4 |
| 3-and-2 (5 segments) | 5 | 5 |
Compound pulley. Two or more separate block-and-tackle systems in series. The overall IMA is the product of the individual IMAs.
Friction and efficiency
Real pulleys have friction in the bearings and rope bending stiffness. Efficiency drops as the number of pulleys increases (more bearings, more bends). Typical efficiency:
| Number of supporting segments | Efficiency |
|---|---|
| 1 | 0.95 |
| 2 | 0.90 |
| 4 | 0.80 |
| 6 | 0.70 |
| 8 | 0.62 |
This is the engineering reason most cranes do not use more than six rope falls; beyond that the friction losses outweigh the further force reduction.
Australian application
Tower cranes on Sydney CBD construction sites use jib hoists with 2-fall or 4-fall configurations depending on the lift weight. Mining draglines use single-fall and double-fall configurations on bucket-hauling ropes. Manual block-and-tackle systems are still used in arborist work, sailing and theatrical rigging.
Past exam questions, worked
Real questions from past NESA papers on this dot point, with our answer explainer.
2021 HSC style5 marksA block-and-tackle system has four rope segments supporting the load block. The system is used to lift a 2400 N load. The efficiency is 80 percent. Calculate (a) the ideal mechanical advantage, (b) the velocity ratio, (c) the actual effort force required, and (d) the input distance the operator must pull to raise the load by 1.5 m.Show worked answer β
(a) Ideal mechanical advantage (IMA). In a frictionless pulley system, the number of rope segments supporting the load equals the IMA.
(b) Velocity ratio (VR). For an ideal pulley system, the velocity ratio equals the number of supporting segments.
The input distance is the load distance multiplied by the velocity ratio.
(c) Actual effort force. Efficiency is the ratio of actual mechanical advantage (AMA) to velocity ratio.
Effort force:
(d) Input distance. The operator must pull a length equal to the load distance times the velocity ratio.
The trade-off is the central lesson of pulleys: less force, more distance. Friction dissipates some of the input work as heat, which is why actual effort is higher than the ideal N.
Markers reward (1) the rope-segment rule for IMA, (2) the efficiency-AMA-VR relationship, (3) numerical answer with units, and (4) the distance trade-off in part (d).
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