What are pulley systems?

Single fixed pulley. Changes direction only. IMA = 1, VR = 1. Effort equals load.

What is single fixed pulley?

Changes direction only. IMA = 1, VR = 1. Effort equals load.

What is single movable pulley?

Two rope segments support the load. IMA = 2, VR = 2. Effort is half the load; rope travels twice the load distance.

What is 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.

§-Syllabus dot point

NSWEngineering StudiesSyllabus dot point

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.

Generated by Claude Opus 4.86 min answerUpdated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

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In plain English

A pulley is a wheel with a groove that a rope runs over, and the trick of a "block and tackle" is threading one rope back and forth through several pulleys so that several strands of rope are all helping hold up the load at once. If four strands of rope are sharing the weight of a load, you only need to pull with roughly a quarter of the force, exactly like four people sharing one heavy suitcase instead of one person carrying it alone. The catch is that to lift the load by 1 metre, you have to pull in 4 metres of rope, because all four strands have to shorten by 1 metre each and that rope all comes from your end. Real pulleys also have friction in their bearings and stiffness in the rope as it bends around each wheel, so you never get the full "free lunch" the segment count promises; some of your pulling effort is always lost as heat, which is why cranes and riggers rarely use more than about six rope strands before the friction losses start to outweigh the benefit.

Note: Lifting Devices is a Preliminary (Year 11) module of NSW Engineering Studies, not an HSC module. The four HSC modules are Civil Structures, Personal and Public Transport, Aeronautical Engineering, and Telecommunications Engineering. This page is kept as Preliminary reference; it is not assessed in the HSC Engineering Studies exam.

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.

MA = \frac{F_{\text{load}}}{F_{\text{effort}}}

Velocity ratio (VR) is the ratio of effort distance (or speed) to load distance (or speed).

VR = \frac{d_{\text{effort}}}{d_{\text{load}}} = \frac{v_{\text{effort}}}{v_{\text{load}}}

Efficiency is the ratio of actual mechanical advantage to velocity ratio (or equivalently, output work over input work):

\eta = \frac{AMA}{VR} = \frac{W_{\text{out}}}{W_{\text{in}}}

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.

The conservation-of-energy basis

Mechanical advantage never creates energy; it trades force for distance. In an ideal system the work in equals the work out, $F_E \, d_E = F_L \, d_L$ , which rearranges directly to $VR = IMA$ . Once friction is present, some input work becomes heat in the bearings and from rope flexing, so the input work always exceeds the output work, and the shortfall is the efficiency. This is why a clear energy statement is the safest way to check any pulley answer: compute input work and output work separately, and their ratio must equal the stated efficiency.

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.

Marker's note: worked example

A 2-and-2 block-and-tackle lifts a 1000 N load at 80 percent efficiency.

Step 1: find IMA, VR and AMA. Four rope segments support the load block, so $IMA = VR = 4$ , and

AMA = \eta \times VR = 0.80 \times 4 = 3.2

Step 2: find the effort force.

F_{effort} = \frac{1000}{3.2} = 312.5\ \text{N}

Step 3: check by conservation of energy. To lift the load 2 m, pull 8 m of rope ( $d_{effort} = VR \times d_{load} = 4 \times 2 = 8$ m).

W_{in} = 312.5 \times 8 = 2500\ \text{J}, \qquad W_{out} = 1000 \times 2 = 2000\ \text{J}

\eta = \frac{2000}{2500} = 0.80 \quad \checkmark

Marker's note: always finish a pulley calculation with this energy check, if the ratio of output work to input work does not match the given efficiency, a segment-count or arithmetic error has been made somewhere earlier.

Exam-style practice questions

Practice questions written in the style of NESA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

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 →

(a) Ideal mechanical advantage (IMA). In a frictionless pulley system, the number of rope segments supporting the load equals the IMA.

IMA = n = 4

(b) Velocity ratio (VR). For an ideal pulley system, the velocity ratio equals the number of supporting segments.

VR = 4

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.

\eta = \frac{AMA}{VR} \quad \Rightarrow \quad AMA = \eta \times VR = 0.80 \times 4 = 3.2

Effort force:

F_E = \frac{F_L}{AMA} = \frac{2400}{3.2} = 750 \text{ N}

(d) Input distance. The operator must pull a length equal to the load distance times the velocity ratio.

d_E = d_L \times VR = 1.5 \times 4 = 6.0 \text{ m}

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 $2400 / 4 = 600$ 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).

HSC 20192 marksDistinguish between ideal mechanical advantage and actual mechanical advantage for a pulley system.

Show worked answer →

Ideal mechanical advantage (IMA) assumes a frictionless system and equals the number of rope segments supporting the load block (it also equals the velocity ratio). Actual mechanical advantage (AMA) is the real ratio of load to effort once friction in the bearings and rope stiffness are included, so AMA is always less than IMA. The two are linked by efficiency: $AMA = \eta \times VR$ . Markers award one mark for each definition and credit the link through efficiency.

HSC 20226 marksA compound pulley arrangement is formed by two block-and-tackle systems in series, the first with 3 supporting segments and the second with 2 supporting segments. The overall efficiency is 70 percent. The system lifts a 5400 N load. Determine the overall velocity ratio, the actual effort force required, and the input work needed to raise the load 0.8 m.

Show worked answer →

Overall velocity ratio (series multiplies).

VR = VR_1 \times VR_2 = 3 \times 2 = 6

Actual mechanical advantage.

AMA = \eta \times VR = 0.70 \times 6 = 4.2

Actual effort force.

F_E = \frac{F_L}{AMA} = \frac{5400}{4.2} = 1286 \text{ N}

Input work. The effort moves $d_E = d_L \times VR = 0.8 \times 6 = 4.8$ m, so

W_{\text{in}} = F_E \times d_E = 1286 \times 4.8 = 6171 \text{ J}

Check: output work $= 5400 \times 0.8 = 4320$ J, and $4320 / 6171 = 0.70$ , matching the stated efficiency. Markers reward the product of velocity ratios for series systems, the AMA from efficiency, the effort force, and a consistent input-work figure verified against efficiency.

Practice questions

Original practice questions graded from foundation to exam level, each with a full worked solution. Try them before revealing the solution.

foundation3 marksA single movable pulley is used to lift a 600 N load. Assuming an ideal (frictionless) system, calculate the effort force required and the distance the rope must be pulled to raise the load by 0.5 m.

Show worked solution →

Step 1: IMA of a single movable pulley. Two rope segments support the load, so $IMA = VR = 2$ .

Step 2: effort force.

F_{effort} = \frac{F_{load}}{IMA} = \frac{600}{2} = 300\ \text{N}

Step 3: rope distance.

d_{effort} = VR \times d_{load} = 2 \times 0.5 = 1.0\ \text{m}

Marking criteria: 1 mark for correctly identifying IMA = 2 from the two supporting segments, 1 mark for the correct effort force (300 N), 1 mark for the correct effort distance (1.0 m) with units.

foundation3 marksA 2-and-1 block-and-tackle (3 supporting rope segments) operates at 90 percent efficiency and lifts an 1800 N load. Calculate the actual mechanical advantage and the actual effort force required.

Show worked solution →

Step 1: IMA and VR.

IMA = VR = 3

Step 2: AMA from efficiency.

AMA = \eta \times VR = 0.90 \times 3 = 2.7

Step 3: actual effort force.

F_{effort} = \frac{F_{load}}{AMA} = \frac{1800}{2.7} = 666.7\ \text{N}

Marking criteria: 1 mark for correct IMA/VR from the segment count, 1 mark for correct AMA using efficiency, 1 mark for the correct actual effort force (about 667 N) with units.

core4 marksThe table below gives measured actual mechanical advantage (AMA) for block-and-tackle systems with different numbers of supporting rope segments, all lifting the same 2000 N load. Segments: 2, AMA 1.8; segments: 4, AMA 3.2; segments: 6, AMA 4.2; segments: 8, AMA 5.0. (a) Calculate the efficiency at each configuration. (b) Describe the trend and explain the engineering cause.

Show worked solution →

(a) Efficiency at each configuration. Using $\eta = AMA / VR$ , with $VR$ equal to the segment count:

2 segments: $\eta = 1.8 / 2 = 0.90$ (90 percent)

4 segments: $\eta = 3.2 / 4 = 0.80$ (80 percent)

6 segments: $\eta = 4.2 / 6 = 0.70$ (70 percent)

8 segments: $\eta = 5.0 / 8 = 0.625$ (62.5 percent)

(b) Trend and cause. Efficiency falls steadily as the number of supporting segments increases, from 90 percent at 2 segments to 62.5 percent at 8 segments. This occurs because each additional rope segment requires an additional pulley, adding another bearing (a source of friction) and another point where the rope bends around a sheave (adding rope-stiffness losses); these losses accumulate with every extra pulley in the system.

Marking criteria: 1 mark for correct method, 2 marks for all four correct efficiency values, 1 mark for correctly explaining the falling trend in terms of accumulating bearing friction and rope-bending losses (not just "more friction" without a mechanism).

core5 marksA compound pulley system is built from two block-and-tackle stages in series: the first stage has IMA 2, the second has IMA 3. Overall efficiency is 75 percent. The system lifts a 3000 N load a height of 1.2 m. Calculate the overall velocity ratio, the actual effort force, and the input work required.

Show worked solution →

Step 1: overall velocity ratio (series stages multiply).

VR = VR_1 \times VR_2 = 2 \times 3 = 6

Step 2: actual mechanical advantage.

AMA = \eta \times VR = 0.75 \times 6 = 4.5

Step 3: actual effort force.

F_{effort} = \frac{F_{load}}{AMA} = \frac{3000}{4.5} = 666.7\ \text{N}

Step 4: input work. Effort distance $= VR \times d_{load} = 6 \times 1.2 = 7.2$ m.

W_{in} = F_{effort} \times d_{effort} = 666.7 \times 7.2 = 4800\ \text{J}

Check: $W_{out} = 3000 \times 1.2 = 3600$ J, and $3600 / 4800 = 0.75$ , matching the stated efficiency.

Marking criteria: 1 mark for the product rule for series velocity ratios, 1 mark for correct AMA, 1 mark for correct effort force, 1 mark for correct input work, 1 mark for the efficiency-check calculation confirming consistency.

exam6 marksAssess the effectiveness of a manual block-and-tackle system, compared with a hydraulic lifting cylinder, for raising a 4000 N load by 3 m in a workshop with no electrical power supply, considering force, distance/effort, and reliability.

Show worked solution →

This is a 6-mark ASSESS: markers reward a supported judgement, not just a description of each system.

Plan.

Thesis: without electrical power, a manual block-and-tackle is more effective than a hydraulic cylinder because it needs no external power source or hydraulic fluid supply, even though it demands far greater physical effort and rope travel from the operator.
Force: a hydraulic cylinder amplifies force through fluid pressure and needs a pump (manual or motor-driven) to build pressure; a manual pump can still work without electricity, but a purely mechanical block-and-tackle with, say, 6 supporting segments and around 70 percent efficiency can reduce a 4000 N load to about $4000/(0.70\times6) \approx 952$ N of hand effort with no fluid system required at all.
Distance/effort: the block-and-tackle requires the operator to pull about $6 \times 3 = 18$ m of rope for a 3 m lift, which is physically demanding and slow, whereas a well-designed hydraulic jack needs many short pump strokes but each stroke moves comparatively little fluid, so overall operator effort is spread out.
Reliability: a rope-and-pulley system has few failure modes (worn rope, seized bearing) and is easy to inspect visually on site; a hydraulic system risks seal leaks, air in the fluid, or valve failure, and is harder to diagnose without test equipment, though it is far less physically tiring to operate.
Judgement: for a genuinely power-free workshop task, a manual block-and-tackle is the more effective and reliable choice, since it needs no fluid system to maintain and cannot suffer a hydraulic leak, even though it is slower and more physically demanding to operate than an equivalent hydraulic lift.

Marker's note: top-band answers (1) explicitly compare BOTH systems on all three named criteria rather than describing only one, (2) use correct numerical support (segment count, efficiency, effort force or rope distance), (3) acknowledge a genuine trade-off rather than declaring one system unconditionally better, and (4) close with an explicit judgement tied to the "no electrical power" constraint in the stem.

exam5 marksA crane operator must choose between a 4-fall (4 supporting segments) and a 6-fall (6 supporting segments) reeving configuration for lifting a 12 000 N load. Using the efficiency data (4 segments: 80 percent; 6 segments: 70 percent), calculate the actual effort force for each configuration and the input work needed to raise the load 2 m in each case, then recommend which configuration is more efficient overall.

Show worked solution →

4-fall configuration.

AMA = 0.80 \times 4 = 3.2, \qquad F_{effort} = \frac{12\,000}{3.2} = 3750\ \text{N}

d_{effort} = 4 \times 2 = 8\ \text{m}, \qquad W_{in} = 3750 \times 8 = 30\,000\ \text{J}

6-fall configuration.

AMA = 0.70 \times 6 = 4.2, \qquad F_{effort} = \frac{12\,000}{4.2} = 2857\ \text{N}

d_{effort} = 6 \times 2 = 12\ \text{m}, \qquad W_{in} = 2857 \times 12 = 34\,286\ \text{J}

Recommendation. The 6-fall configuration needs a smaller effort force (2857 N versus 3750 N), which may be necessary if the winch motor's rated pull force cannot reach 3750 N. However, it requires more input work overall (34 286 J versus 30 000 J) because of the lower efficiency at 6 falls, and more rope must be paid out (12 m versus 8 m) for the same lift height. If the winch can supply 3750 N of pull, the 4-fall configuration is the more efficient overall choice; the 6-fall configuration should only be selected if the extra force reduction is genuinely needed.

Marking criteria: 1 mark for correct 4-fall effort force, 1 mark for correct 6-fall effort force, 1 mark for both correct input-work values, 2 marks for a justified recommendation that weighs force capability against total input work/efficiency rather than assuming "more falls is always better".