A hydraulic press can lift a large load using a much smaller force. That sentence sounds like a free gain until we ask what happens to distance moved. The useful G3 Physics idea is a trade-off: pressure can be transmitted through a confined liquid, so a larger piston area produces a larger force, while that piston moves a shorter distance in the ideal model.
Quick route: find the two piston areas; convert square centimetres to square metres if calculating pressure in pascals; apply the ideal pressure relationship; check the direction of force and motion; balance liquid displacement; compare input and output work; explain why real devices may fall below ideal estimates.
What the 2027 G3 SEC actually assesses
SEAB’s 2027 SEC G3 school-candidate directory is the starting point for current subject codes. The SEC overview explains that the SEC replaces the former N- and O-Level certificates from 2027 while retaining the respective assessment standards. A subject at G3 is not an invented new level of difficulty. Read the relevant syllabus rather than relying on unverified social-media lists of question types. This is an independent learning guide, not an official examination paper.
For all three strands of EMS, the purpose of a worked setting is transfer: learn the idea, practise it with fully labelled hypothetical information, and apply it to the question actually set. None of our sample scenes, apparatus readings or trials is a record of a real experiment or an indication that SEAB will use that precise scenario.
Where this lesson fits
First revise Sengkang’s post-PSLE G3 entry route if foundational terminology is unclear; the PSLE learning-routine guide is available to families making the earlier transition. Subject owners remain separate: G3 English, G3 Mathematics and G3 Science. The Physics manometer guide, Volume 1055 explains the science of the reading; Mathematics manometer guide, Volume 1056 owns the height-difference calculations. This article concentrates on hydraulic-press mechanism, displacement and energy conservation, rather than repeating those lessons.
This volume is a focused application of the Pressure section in the official 2027 SEC G3 Physics syllabus K323. It explicitly includes the transmission of pressure in hydraulic systems, especially a hydraulic press, as well as p = F/A. The earlier general pressure and hydraulics owner, Volume 0679 supplies the overview; this chapter owns force–stroke–work trade-offs and careful problem interpretation. The syllabus lists Paper 1 multiple-choice (40 marks, 30%, one hour), Paper 2 structured/free response (80 marks, 50%, one hour 45 minutes), and Paper 3 practical (40 marks, 20%, one hour 50 minutes).
The essential picture in words
Picture two pistons closing the ends of the same confined liquid. One piston has a smaller cross-sectional area. When a force acts on it, it generates an additional pressure. In the ideal stationary model at corresponding levels, that pressure is transmitted through the liquid. The larger piston then experiences the same pressure over a larger area, so its force is greater.
The equal quantity is pressure change, not force. Saying ‘the force is transmitted unchanged’ is a classic error. Write F1/A1 = F2/A2, with subscripts that match the diagram. If the output area is twenty times the input area, the ideal output force is twenty times the input force. This is a force multiplication, not energy creation.
Work out a complete example
Let the input piston area be 4 cm², the output area 80 cm² and the applied input force 120 N. The ratio of areas is 80/4 = 20, so the ideal output force is 2,400 N. Pressure at the small piston is 120 N divided by 0.0004 m² = 300,000 Pa. The same result follows from 2,400 N divided by 0.008 m².
Now push the small piston 50 cm into the cylinder. It displaces 4 × 50 = 200 cm³ of ideal incompressible liquid. The large piston therefore moves 200/80 = 2.5 cm. Input work is 120 × 0.50 = 60 J. Output work is 2,400 × 0.025 = 60 J. The numbers agree because the ideal model has ignored friction, leakage and other losses.
Area ratios are not length ratios
If both pistons are circular, cross-sectional area depends on the square of the radius. Doubling diameter makes the area four times as large, not twice as large. This matters for diagrams labelled only by diameter. Calculate the area ratio as (D2/D1)² before converting it into a force ratio. If the diameters are measured in the same unit, that unit cancels in the ratio.
Volume conservation explains the motion
The ideal incompressible-volume relationship is A1s1 = A2s2. It says the same displaced liquid volume passes through the connected system. Hence s2/s1 = A1/A2. The larger-force piston has the smaller stroke. For a real device, compressibility, trapped air, elastic expansion and leaks can alter the movement. Treat the formula as a model rather than a guaranteed engineering specification.
Pressure is not the same as weight capacity
A hydraulic press’s nominal output force is not a complete declaration of its safe working load. Physical equipment has structural ratings, seal limits, stability requirements and operating procedures. Neither a calculated ideal piston force nor an online classroom example authorises operation or testing. For education, use manufacturer-approved resources and supervised school practical arrangements.
G3 command words matter
If a question asks to state a relationship, give the relationship clearly. If it asks to explain, identify pressure transmission and why greater area means greater force. If it asks to calculate, show the equation and substituted quantities. If asked to evaluate, discuss the ideal assumption and a realistic source of discrepancy rather than merely repeating the answer.
Distinguish useful and wasted energy
In a real device the mechanical work delivered to the load may be less than the work supplied. Some input energy is dissipated through friction and fluid resistance or stored transiently in parts. An efficiency such as 80% must be interpreted as useful work output divided by work input for the stated boundaries. It is not a reason to multiply a pressure by 80% unless that relationship is specifically justified.
Recognise a diagram before using an equation
Read which piston is pressed, which moves the load, which areas are provided and whether distances refer to piston travel or load elevation. Then choose either the pressure equality or the displaced-volume equality. Several errors arise from memorising the two formulas without checking which quantity is being compared.
Why a larger piston moves less
The liquid displaced by a small piston can cover only a thin layer over a much broader piston. This physical picture is often clearer than the equation alone. Use an imagined teaspoon of water spread across a saucer versus a tall narrow tube. The same volume occupies different heights according to area.
Boundary conditions and orientation
Hydrostatic pressure differences can matter if pistons are at different elevations. Most introductory problems assume corresponding levels and neglect height differences unless given. Do not insert an atmospheric-pressure term when both relevant pressure changes are gauge pressures. If the problem explicitly mentions unequal heights or densities, define the pressures at the correct positions before writing an equality.
Practical reasoning without hazardous experimentation
A safe classroom investigation may use a teacher-approved syringe demonstration or a simulation to show relative forces and movements. Students should not improvise high-pressure rigs or place hands beneath loads. The exam-worthy skills include identifying variables, observing systematic differences and explaining why a model does not perfectly describe an apparatus.
How to check whether an answer is plausible
For a small input area and large output area, output force should exceed input force in the ideal model; output travel should be shorter. If your arithmetic gives both force multiplication and distance multiplication, it violates ideal work conservation. Check the two ratios. If a force is implausibly enormous, inspect square-unit conversion before trusting the result.
A structured explanation template
First state that applying force F1 on area A1 creates pressure change Δp = F1/A1. Next state that this pressure change is transmitted through the confined liquid in the ideal model. Then write F2 = Δp A2. Finally explain that a larger A2 produces a larger output force, but conservation of displaced volume gives a proportionally smaller output movement. Add a limitation if the context asks for evaluation.
Progressive worked questions: learn the whole chain
All cases in this section are invented, idealised classroom calculations. Use the stated inputs, check units and write conclusions. In examination work, your actual question’s assumptions and requested accuracy override the illustrative conventions here.
Worked problem 1: pressure transmission
Question. Small and large piston areas are 2 cm² and 8 cm². The small piston receives 30 N. Find the ideal output force.
Solution and explanation. The area ratio is 4:1, so the ideal output force is 120 N. We did not assume the two forces are equal; we assumed matching pressure changes, F/A. A diagram showing the load on the large piston is essential to the interpretation. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 2: unit conversion
Question. The input piston area is 3 cm² and the input force 40 N. Find the additional pressure in pascals.
Solution and explanation. Convert the area to 0.0003 m² before dividing. The pressure increase is 133333.3333 Pa. Dividing by 3 without unit conversion would yield N/cm², not pascals. Name the pressure change rather than confusing it with atmospheric absolute pressure. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 3: reverse calculation
Question. An ideal press has areas 4 cm² and 32 cm² and must exert 400 N at the larger piston. Find the input force.
Solution and explanation. Reverse the area ratio: F1 = 400 × 4/32 = 50 N. This is a useful check on understanding. The direction of the algebra matters more than memorising a fixed multiplication instruction. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 4: displacement conservation
Question. A 5 cm² piston travels 25 cm while the other has 50 cm² area. How far does the output piston move?
Solution and explanation. Displaced liquid volume is 125 cm³. Dividing by 50 cm² gives 2.5 cm of output movement. The larger piston moves less because the same displaced volume spreads over more cross-sectional area. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 5: work conservation
Question. A press uses 70 N and an input stroke of 30 cm. Find the ideal input work, then the expected ideal output work.
Solution and explanation. The input moves 0.3 m, so input work is 21 J. In an ideal lossless system, useful output work is also 21 J. Larger force is balanced by shorter travel; there is no free energy. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 6: inverse motion
Question. The piston-area ratio is 4:1. If the large piston rises 1.5 cm, determine the small piston’s ideal travel.
Solution and explanation. The input displacement is 6 cm, from A1s1 = A2s2. Reversing this ratio is common because students transfer the force multiplier directly to distance. Explain why force and distance move in opposite directions. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 7: model versus observation
Question. An ideal press would deliver 540 N. A hypothetical trial delivers only 85% of that force under otherwise stated conditions. Find the observed figure and identify a limitation.
Solution and explanation. 85% of 540 N is 459 N. The percentage here is an explicitly supplied force ratio, not necessarily overall energy efficiency. Real differences might reflect resistance or losses. Never assume every mechanical quantity falls by precisely 15%. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 8: condition and feasibility
Question. A large piston has 24 cm² area and an output requirement of 720 N; the small piston has 3 cm² area. Find the ideal minimum input force.
Solution and explanation. F1 = 720 × 3/24 = 90 N. If a real machine must meet a rated load, this ideal mathematical minimum is not a safety guarantee. A competent design requires independent engineering margins and approved operating limits. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 9: pressure transmission
Question. Small and large piston areas are 4 cm² and 40 cm². The small piston receives 110 N. Find the ideal output force.
Solution and explanation. The area ratio is 10:1, so the ideal output force is 1100 N. We did not assume the two forces are equal; we assumed matching pressure changes, F/A. A diagram showing the load on the large piston is essential to the interpretation. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 10: unit conversion
Question. The input piston area is 5 cm² and the input force 30 N. Find the additional pressure in pascals.
Solution and explanation. Convert the area to 0.0005 m² before dividing. The pressure increase is 60000 Pa. Dividing by 5 without unit conversion would yield N/cm², not pascals. Name the pressure change rather than confusing it with atmospheric absolute pressure. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 11: reverse calculation
Question. An ideal press has areas 6 cm² and 24 cm² and must exert 160 N at the larger piston. Find the input force.
Solution and explanation. Reverse the area ratio: F1 = 160 × 6/24 = 40 N. This is a useful check on understanding. The direction of the algebra matters more than memorising a fixed multiplication instruction. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 12: displacement conservation
Question. A 7 cm² piston travels 25 cm while the other has 42 cm² area. How far does the output piston move?
Solution and explanation. Displaced liquid volume is 175 cm³. Dividing by 42 cm² gives 4.1667 cm of output movement. The larger piston moves less because the same displaced volume spreads over more cross-sectional area. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 13: work conservation
Question. A press uses 60 N and an input stroke of 30 cm. Find the ideal input work, then the expected ideal output work.
Solution and explanation. The input moves 0.3 m, so input work is 18 J. In an ideal lossless system, useful output work is also 18 J. Larger force is balanced by shorter travel; there is no free energy. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 14: inverse motion
Question. The piston-area ratio is 10:1. If the large piston rises 1.5 cm, determine the small piston’s ideal travel.
Solution and explanation. The input displacement is 15 cm, from A1s1 = A2s2. Reversing this ratio is common because students transfer the force multiplier directly to distance. Explain why force and distance move in opposite directions. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 15: model versus observation
Question. An ideal press would deliver 960 N. A hypothetical trial delivers only 85% of that force under otherwise stated conditions. Find the observed figure and identify a limitation.
Solution and explanation. 85% of 960 N is 816 N. The percentage here is an explicitly supplied force ratio, not necessarily overall energy efficiency. Real differences might reflect resistance or losses. Never assume every mechanical quantity falls by precisely 15%. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 16: condition and feasibility
Question. A large piston has 20 cm² area and an output requirement of 324 N; the small piston has 5 cm² area. Find the ideal minimum input force.
Solution and explanation. F1 = 324 × 5/20 = 81 N. If a real machine must meet a rated load, this ideal mathematical minimum is not a safety guarantee. A competent design requires independent engineering margins and approved operating limits. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 17: pressure transmission
Question. Small and large piston areas are 6 cm² and 36 cm². The small piston receives 100 N. Find the ideal output force.
Solution and explanation. The area ratio is 6:1, so the ideal output force is 600 N. We did not assume the two forces are equal; we assumed matching pressure changes, F/A. A diagram showing the load on the large piston is essential to the interpretation. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 18: unit conversion
Question. The input piston area is 7 cm² and the input force 110 N. Find the additional pressure in pascals.
Solution and explanation. Convert the area to 0.0007 m² before dividing. The pressure increase is 157142.8571 Pa. Dividing by 7 without unit conversion would yield N/cm², not pascals. Name the pressure change rather than confusing it with atmospheric absolute pressure. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 19: reverse calculation
Question. An ideal press has areas 2 cm² and 20 cm² and must exert 300 N at the larger piston. Find the input force.
Solution and explanation. Reverse the area ratio: F1 = 300 × 2/20 = 30 N. This is a useful check on understanding. The direction of the algebra matters more than memorising a fixed multiplication instruction. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 20: displacement conservation
Question. A 3 cm² piston travels 25 cm while the other has 36 cm² area. How far does the output piston move?
Solution and explanation. Displaced liquid volume is 75 cm³. Dividing by 36 cm² gives 2.0833 cm of output movement. The larger piston moves less because the same displaced volume spreads over more cross-sectional area. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 21: work conservation
Question. A press uses 50 N and an input stroke of 30 cm. Find the ideal input work, then the expected ideal output work.
Solution and explanation. The input moves 0.3 m, so input work is 15 J. In an ideal lossless system, useful output work is also 15 J. Larger force is balanced by shorter travel; there is no free energy. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 22: inverse motion
Question. The piston-area ratio is 6:1. If the large piston rises 1.5 cm, determine the small piston’s ideal travel.
Solution and explanation. The input displacement is 9 cm, from A1s1 = A2s2. Reversing this ratio is common because students transfer the force multiplier directly to distance. Explain why force and distance move in opposite directions. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 23: model versus observation
Question. An ideal press would deliver 560 N. A hypothetical trial delivers only 85% of that force under otherwise stated conditions. Find the observed figure and identify a limitation.
Solution and explanation. 85% of 560 N is 476 N. The percentage here is an explicitly supplied force ratio, not necessarily overall energy efficiency. Real differences might reflect resistance or losses. Never assume every mechanical quantity falls by precisely 15%. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 24: condition and feasibility
Question. A large piston has 70 cm² area and an output requirement of 720 N; the small piston has 7 cm² area. Find the ideal minimum input force.
Solution and explanation. F1 = 720 × 7/70 = 72 N. If a real machine must meet a rated load, this ideal mathematical minimum is not a safety guarantee. A competent design requires independent engineering margins and approved operating limits. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 25: pressure transmission
Question. Small and large piston areas are 2 cm² and 24 cm². The small piston receives 90 N. Find the ideal output force.
Solution and explanation. The area ratio is 12:1, so the ideal output force is 1080 N. We did not assume the two forces are equal; we assumed matching pressure changes, F/A. A diagram showing the load on the large piston is essential to the interpretation. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 26: unit conversion
Question. The input piston area is 3 cm² and the input force 100 N. Find the additional pressure in pascals.
Solution and explanation. Convert the area to 0.0003 m² before dividing. The pressure increase is 333333.3333 Pa. Dividing by 3 without unit conversion would yield N/cm², not pascals. Name the pressure change rather than confusing it with atmospheric absolute pressure. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 27: reverse calculation
Question. An ideal press has areas 4 cm² and 24 cm² and must exert 660 N at the larger piston. Find the input force.
Solution and explanation. Reverse the area ratio: F1 = 660 × 4/24 = 110 N. This is a useful check on understanding. The direction of the algebra matters more than memorising a fixed multiplication instruction. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 28: displacement conservation
Question. A 5 cm² piston travels 25 cm while the other has 40 cm² area. How far does the output piston move?
Solution and explanation. Displaced liquid volume is 125 cm³. Dividing by 40 cm² gives 3.125 cm of output movement. The larger piston moves less because the same displaced volume spreads over more cross-sectional area. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 29: work conservation
Question. A press uses 40 N and an input stroke of 30 cm. Find the ideal input work, then the expected ideal output work.
Solution and explanation. The input moves 0.3 m, so input work is 12 J. In an ideal lossless system, useful output work is also 12 J. Larger force is balanced by shorter travel; there is no free energy. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 30: inverse motion
Question. The piston-area ratio is 12:1. If the large piston rises 1.5 cm, determine the small piston’s ideal travel.
Solution and explanation. The input displacement is 18 cm, from A1s1 = A2s2. Reversing this ratio is common because students transfer the force multiplier directly to distance. Explain why force and distance move in opposite directions. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 31: model versus observation
Question. An ideal press would deliver 240 N. A hypothetical trial delivers only 85% of that force under otherwise stated conditions. Find the observed figure and identify a limitation.
Solution and explanation. 85% of 240 N is 204 N. The percentage here is an explicitly supplied force ratio, not necessarily overall energy efficiency. Real differences might reflect resistance or losses. Never assume every mechanical quantity falls by precisely 15%. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 32: condition and feasibility
Question. A large piston has 18 cm² area and an output requirement of 378 N; the small piston has 3 cm² area. Find the ideal minimum input force.
Solution and explanation. F1 = 378 × 3/18 = 63 N. If a real machine must meet a rated load, this ideal mathematical minimum is not a safety guarantee. A competent design requires independent engineering margins and approved operating limits. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 33: pressure transmission
Question. Small and large piston areas are 4 cm² and 32 cm². The small piston receives 80 N. Find the ideal output force.
Solution and explanation. The area ratio is 8:1, so the ideal output force is 640 N. We did not assume the two forces are equal; we assumed matching pressure changes, F/A. A diagram showing the load on the large piston is essential to the interpretation. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 34: unit conversion
Question. The input piston area is 5 cm² and the input force 90 N. Find the additional pressure in pascals.
Solution and explanation. Convert the area to 0.0005 m² before dividing. The pressure increase is 180000 Pa. Dividing by 5 without unit conversion would yield N/cm², not pascals. Name the pressure change rather than confusing it with atmospheric absolute pressure. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 35: reverse calculation
Question. An ideal press has areas 6 cm² and 72 cm² and must exert 1200 N at the larger piston. Find the input force.
Solution and explanation. Reverse the area ratio: F1 = 1200 × 6/72 = 100 N. This is a useful check on understanding. The direction of the algebra matters more than memorising a fixed multiplication instruction. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 36: displacement conservation
Question. A 7 cm² piston travels 25 cm while the other has 28 cm² area. How far does the output piston move?
Solution and explanation. Displaced liquid volume is 175 cm³. Dividing by 28 cm² gives 6.25 cm of output movement. The larger piston moves less because the same displaced volume spreads over more cross-sectional area. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 37: work conservation
Question. A press uses 30 N and an input stroke of 30 cm. Find the ideal input work, then the expected ideal output work.
Solution and explanation. The input moves 0.3 m, so input work is 9 J. In an ideal lossless system, useful output work is also 9 J. Larger force is balanced by shorter travel; there is no free energy. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 38: inverse motion
Question. The piston-area ratio is 8:1. If the large piston rises 1.5 cm, determine the small piston’s ideal travel.
Solution and explanation. The input displacement is 12 cm, from A1s1 = A2s2. Reversing this ratio is common because students transfer the force multiplier directly to distance. Explain why force and distance move in opposite directions. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 39: model versus observation
Question. An ideal press would deliver 500 N. A hypothetical trial delivers only 85% of that force under otherwise stated conditions. Find the observed figure and identify a limitation.
Solution and explanation. 85% of 500 N is 425 N. The percentage here is an explicitly supplied force ratio, not necessarily overall energy efficiency. Real differences might reflect resistance or losses. Never assume every mechanical quantity falls by precisely 15%. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 40: condition and feasibility
Question. A large piston has 60 cm² area and an output requirement of 648 N; the small piston has 5 cm² area. Find the ideal minimum input force.
Solution and explanation. F1 = 648 × 5/60 = 54 N. If a real machine must meet a rated load, this ideal mathematical minimum is not a safety guarantee. A competent design requires independent engineering margins and approved operating limits. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 41: pressure transmission
Question. Small and large piston areas are 6 cm² and 24 cm². The small piston receives 70 N. Find the ideal output force.
Solution and explanation. The area ratio is 4:1, so the ideal output force is 280 N. We did not assume the two forces are equal; we assumed matching pressure changes, F/A. A diagram showing the load on the large piston is essential to the interpretation. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 42: unit conversion
Question. The input piston area is 7 cm² and the input force 80 N. Find the additional pressure in pascals.
Solution and explanation. Convert the area to 0.0007 m² before dividing. The pressure increase is 114285.7143 Pa. Dividing by 7 without unit conversion would yield N/cm², not pascals. Name the pressure change rather than confusing it with atmospheric absolute pressure. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 43: reverse calculation
Question. An ideal press has areas 2 cm² and 16 cm² and must exert 720 N at the larger piston. Find the input force.
Solution and explanation. Reverse the area ratio: F1 = 720 × 2/16 = 90 N. This is a useful check on understanding. The direction of the algebra matters more than memorising a fixed multiplication instruction. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 44: displacement conservation
Question. A 3 cm² piston travels 25 cm while the other has 30 cm² area. How far does the output piston move?
Solution and explanation. Displaced liquid volume is 75 cm³. Dividing by 30 cm² gives 2.5 cm of output movement. The larger piston moves less because the same displaced volume spreads over more cross-sectional area. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 45: work conservation
Question. A press uses 110 N and an input stroke of 30 cm. Find the ideal input work, then the expected ideal output work.
Solution and explanation. The input moves 0.3 m, so input work is 33 J. In an ideal lossless system, useful output work is also 33 J. Larger force is balanced by shorter travel; there is no free energy. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 46: inverse motion
Question. The piston-area ratio is 4:1. If the large piston rises 1.5 cm, determine the small piston’s ideal travel.
Solution and explanation. The input displacement is 6 cm, from A1s1 = A2s2. Reversing this ratio is common because students transfer the force multiplier directly to distance. Explain why force and distance move in opposite directions. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 47: model versus observation
Question. An ideal press would deliver 240 N. A hypothetical trial delivers only 85% of that force under otherwise stated conditions. Find the observed figure and identify a limitation.
Solution and explanation. 85% of 240 N is 204 N. The percentage here is an explicitly supplied force ratio, not necessarily overall energy efficiency. Real differences might reflect resistance or losses. Never assume every mechanical quantity falls by precisely 15%. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 48: condition and feasibility
Question. A large piston has 56 cm² area and an output requirement of 360 N; the small piston has 7 cm² area. Find the ideal minimum input force.
Solution and explanation. F1 = 360 × 7/56 = 45 N. If a real machine must meet a rated load, this ideal mathematical minimum is not a safety guarantee. A competent design requires independent engineering margins and approved operating limits. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 49: pressure transmission
Question. Small and large piston areas are 2 cm² and 20 cm². The small piston receives 60 N. Find the ideal output force.
Solution and explanation. The area ratio is 10:1, so the ideal output force is 600 N. We did not assume the two forces are equal; we assumed matching pressure changes, F/A. A diagram showing the load on the large piston is essential to the interpretation. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 50: unit conversion
Question. The input piston area is 3 cm² and the input force 70 N. Find the additional pressure in pascals.
Solution and explanation. Convert the area to 0.0003 m² before dividing. The pressure increase is 233333.3333 Pa. Dividing by 3 without unit conversion would yield N/cm², not pascals. Name the pressure change rather than confusing it with atmospheric absolute pressure. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 51: reverse calculation
Question. An ideal press has areas 4 cm² and 16 cm² and must exert 320 N at the larger piston. Find the input force.
Solution and explanation. Reverse the area ratio: F1 = 320 × 4/16 = 80 N. This is a useful check on understanding. The direction of the algebra matters more than memorising a fixed multiplication instruction. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 52: displacement conservation
Question. A 5 cm² piston travels 25 cm while the other has 30 cm² area. How far does the output piston move?
Solution and explanation. Displaced liquid volume is 125 cm³. Dividing by 30 cm² gives 4.1667 cm of output movement. The larger piston moves less because the same displaced volume spreads over more cross-sectional area. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 53: work conservation
Question. A press uses 100 N and an input stroke of 30 cm. Find the ideal input work, then the expected ideal output work.
Solution and explanation. The input moves 0.3 m, so input work is 30 J. In an ideal lossless system, useful output work is also 30 J. Larger force is balanced by shorter travel; there is no free energy. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 54: inverse motion
Question. The piston-area ratio is 10:1. If the large piston rises 1.5 cm, determine the small piston’s ideal travel.
Solution and explanation. The input displacement is 15 cm, from A1s1 = A2s2. Reversing this ratio is common because students transfer the force multiplier directly to distance. Explain why force and distance move in opposite directions. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 55: model versus observation
Question. An ideal press would deliver 360 N. A hypothetical trial delivers only 85% of that force under otherwise stated conditions. Find the observed figure and identify a limitation.
Solution and explanation. 85% of 360 N is 306 N. The percentage here is an explicitly supplied force ratio, not necessarily overall energy efficiency. Real differences might reflect resistance or losses. Never assume every mechanical quantity falls by precisely 15%. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Worked problem 56: condition and feasibility
Question. A large piston has 12 cm² area and an output requirement of 144 N; the small piston has 3 cm² area. Find the ideal minimum input force.
Solution and explanation. F1 = 144 × 3/12 = 36 N. If a real machine must meet a rated load, this ideal mathematical minimum is not a safety guarantee. A competent design requires independent engineering margins and approved operating limits. Self-test. Redraw the two pistons with arrows. Name the quantity that remains equal or is conserved, and the physical assumption that makes your calculation possible.
Common questions
Is pressure multiplied by the piston ratio? No. Under the ideal comparison at corresponding levels, the pressure change is the same; it is force that scales with area.
Does the bigger piston always move upward? Direction depends on configuration and applied forces. A diagram must establish the motion.
Does ideal force tell me a safe lifting capacity? No. Real ratings and controls are separate.
What does energy conservation add? It shows why multiplying force does not multiply delivered work. More force comes with less travel.
What should I study next? The following Mathematics volume uses this physical model as a starting point for algebraic constraints, rounding intervals and choosing feasible solutions. Those are separate mathematical skills.
