No Machine Ever Gives You More Energy Than You Put Into It
Define load, effort, mechanical advantage, velocity ratio and efficiency, derive the relation between the three, see why every real machine has an efficiency below one, classify levers including the ones in your own body, and compare the three pulley systems.
How can a small effort lift a heavy load without breaking any law of physics?
One person can lift a car with a jack, and a child can raise an adult on a see-saw. It looks as though the machine has created force out of nothing. It has not.
Watch what the machine takes in exchange. The jack handle has to be pumped through a long distance to raise the car a few centimetres. The child on the see-saw sits far from the pivot and swings through a long arc to lift the adult a little way. In every machine, the force you save is paid for in distance.
So a machine is not a source of energy. It is a device that redistributes force and distance, and the work you put in is always at least as much as the work you get out.
That trade is described by three quantities, and this part of the chapter is mostly about keeping them apart:
- Mechanical advantage — how many times the load exceeds the effort. This is the force gain
- Velocity ratio — how many times further the effort moves than the load. This is the distance cost, and it is fixed by the machine's design alone
- Efficiency — how much of the work you put in comes out as useful work
For a perfect machine the force gain would exactly equal the distance cost, and the two ratios would be identical. For every real machine the force gain is less, because part of your effort is spent on friction and on lifting the machine's own moving parts.
Which gives the single most examined result in this part: for all practical machines the mechanical advantage is less than the velocity ratio, and the efficiency is less than one.
The chapter then applies all of this to two families of machine: levers, of which there are three classes and several inside your own body, and pulleys, from a single fixed wheel to a block-and-tackle system.
This page covers the fourth part of the ICSE Class 10 Physics chapter on force, work, power and energy: mechanical advantage, velocity ratio, efficiency, levers and pulleys.
Watch what the machine takes in exchange. The jack handle has to be pumped through a long distance to raise the car a few centimetres. The child on the see-saw sits far from the pivot and swings through a long arc to lift the adult a little way. In every machine, the force you save is paid for in distance.
So a machine is not a source of energy. It is a device that redistributes force and distance, and the work you put in is always at least as much as the work you get out.
That trade is described by three quantities, and this part of the chapter is mostly about keeping them apart:
- Mechanical advantage — how many times the load exceeds the effort. This is the force gain
- Velocity ratio — how many times further the effort moves than the load. This is the distance cost, and it is fixed by the machine's design alone
- Efficiency — how much of the work you put in comes out as useful work
For a perfect machine the force gain would exactly equal the distance cost, and the two ratios would be identical. For every real machine the force gain is less, because part of your effort is spent on friction and on lifting the machine's own moving parts.
Which gives the single most examined result in this part: for all practical machines the mechanical advantage is less than the velocity ratio, and the efficiency is less than one.
The chapter then applies all of this to two families of machine: levers, of which there are three classes and several inside your own body, and pulleys, from a single fixed wheel to a block-and-tackle system.
This page covers the fourth part of the ICSE Class 10 Physics chapter on force, work, power and energy: mechanical advantage, velocity ratio, efficiency, levers and pulleys.
Formula
What do mechanical advantage, velocity ratio and efficiency mean?
Mechanical advantage compares the forces, velocity ratio compares the distances, and efficiency compares the work.
Load and effort first. The load () is the resistance the machine overcomes; the effort () is the force you apply to the machine.
Mechanical advantage has no unit, being a ratio of two forces. A value greater than one means the machine is a force multiplier.
where is the distance moved by the effort and the distance moved by the load in the same time. The velocity ratio is also unitless, and it depends only on the design of the machine — never on friction, and never on how big the load is.
Efficiency is a fraction, usually written as a percentage.
The derivation of the relation between the three, which is a standard examination request. The work output is the load times the distance the load moves, and the work input is the effort times the distance the effort moves:
So the mechanical advantage is the velocity ratio multiplied by the efficiency, and since the efficiency of a real machine is below one, the mechanical advantage must be below the velocity ratio.
Worked example 1 — all three from one situation. A machine lifts a load of N through m when an effort of N moves through m. Find its mechanical advantage, velocity ratio and efficiency.
Check by computing the work directly:
The same answer by two routes, and the missing J went into friction and into moving the machine's own parts.
Worked example 2 — finding the effort from the efficiency. A machine has a velocity ratio of and an efficiency of . Find its mechanical advantage and the effort needed to raise a load of kgf.
Check the distances. The effort must move five times as far as the load, since the velocity ratio is . **So to raise the load m the effort end travels m**, and the work input kgf m exceeds the work output kgf m by exactly the that is wasted.
Worked example 3 — an ideal machine. If the machine above were frictionless and weightless, what effort would be needed?
For an ideal machine , so and
Less effort, as expected — and the difference between kgf and kgf is the price of friction. **An ideal machine has and , but no such machine exists.
Three quantities, three different dependencies, and this list is worth memorising because questions test it directly:
- VR depends only on the design of the machine
- MA depends on the design and on the friction and the weight of the moving parts
- Efficiency depends on the friction** and the weight of the moving parts
Load and effort first. The load () is the resistance the machine overcomes; the effort () is the force you apply to the machine.
Mechanical advantage has no unit, being a ratio of two forces. A value greater than one means the machine is a force multiplier.
where is the distance moved by the effort and the distance moved by the load in the same time. The velocity ratio is also unitless, and it depends only on the design of the machine — never on friction, and never on how big the load is.
Efficiency is a fraction, usually written as a percentage.
The derivation of the relation between the three, which is a standard examination request. The work output is the load times the distance the load moves, and the work input is the effort times the distance the effort moves:
So the mechanical advantage is the velocity ratio multiplied by the efficiency, and since the efficiency of a real machine is below one, the mechanical advantage must be below the velocity ratio.
Worked example 1 — all three from one situation. A machine lifts a load of N through m when an effort of N moves through m. Find its mechanical advantage, velocity ratio and efficiency.
Check by computing the work directly:
The same answer by two routes, and the missing J went into friction and into moving the machine's own parts.
Worked example 2 — finding the effort from the efficiency. A machine has a velocity ratio of and an efficiency of . Find its mechanical advantage and the effort needed to raise a load of kgf.
Check the distances. The effort must move five times as far as the load, since the velocity ratio is . **So to raise the load m the effort end travels m**, and the work input kgf m exceeds the work output kgf m by exactly the that is wasted.
Worked example 3 — an ideal machine. If the machine above were frictionless and weightless, what effort would be needed?
For an ideal machine , so and
Less effort, as expected — and the difference between kgf and kgf is the price of friction. **An ideal machine has and , but no such machine exists.
Three quantities, three different dependencies, and this list is worth memorising because questions test it directly:
- VR depends only on the design of the machine
- MA depends on the design and on the friction and the weight of the moving parts
- Efficiency depends on the friction** and the weight of the moving parts
Why is the efficiency of every real machine less than one?
Because part of the work you put in is spent on things other than moving the load — overcoming friction at the moving joints, and lifting the weight of the machine's own parts.
Write the work input as a sum and the reason becomes obvious:
The first term is the useful output; the other two are unavoidable losses. So
**and since , it follows immediately that .
Notice that this is not a defect of engineering but a consequence of the conservation of energy.** A machine with would give out more energy than it took in, which is impossible. **A machine with would waste nothing at all, which would need frictionless joints and weightless parts. So every real efficiency lies strictly between zero and one.
The same statement in terms of power**, which is how a question may phrase it. Dividing the work input and output by the time,
and the same argument applies: the input power is shared between useful output power and wasted power, so the output power is smaller.
Worked example — locating the losses. In worked example 1 of the previous section, the work input was J and the output J. Where did the J go?
Into friction at the moving surfaces, and into raising the machine's own moving parts. Both end up as heat and as a small amount of sound, which is why machinery warms up and why it is oiled. And that is the answer to "how can the efficiency be improved?" — reduce the friction by lubricating the moving parts, and reduce the weight of the moving parts themselves.
Two boundary cases to state precisely.
- **A machine can have and still be useful. It then needs a larger effort than the load, but it gains something else — a greater speed of the load, or a more convenient direction of the effort
- A machine can have , as a single fixed pulley does. It then multiplies no force at all, and its whole value lies in changing the direction in which you pull
One relation that is often misread.** Because , a high velocity ratio does not by itself mean a high mechanical advantage. A badly made machine with a velocity ratio of and an efficiency of has a mechanical advantage of only , while a well-made one with a velocity ratio of and an efficiency of has . The design sets the ceiling; the workmanship decides how close you get to it.
Write the work input as a sum and the reason becomes obvious:
The first term is the useful output; the other two are unavoidable losses. So
**and since , it follows immediately that .
Notice that this is not a defect of engineering but a consequence of the conservation of energy.** A machine with would give out more energy than it took in, which is impossible. **A machine with would waste nothing at all, which would need frictionless joints and weightless parts. So every real efficiency lies strictly between zero and one.
The same statement in terms of power**, which is how a question may phrase it. Dividing the work input and output by the time,
and the same argument applies: the input power is shared between useful output power and wasted power, so the output power is smaller.
Worked example — locating the losses. In worked example 1 of the previous section, the work input was J and the output J. Where did the J go?
Into friction at the moving surfaces, and into raising the machine's own moving parts. Both end up as heat and as a small amount of sound, which is why machinery warms up and why it is oiled. And that is the answer to "how can the efficiency be improved?" — reduce the friction by lubricating the moving parts, and reduce the weight of the moving parts themselves.
Two boundary cases to state precisely.
- **A machine can have and still be useful. It then needs a larger effort than the load, but it gains something else — a greater speed of the load, or a more convenient direction of the effort
- A machine can have , as a single fixed pulley does. It then multiplies no force at all, and its whole value lies in changing the direction in which you pull
One relation that is often misread.** Because , a high velocity ratio does not by itself mean a high mechanical advantage. A badly made machine with a velocity ratio of and an efficiency of has a mechanical advantage of only , while a well-made one with a velocity ratio of and an efficiency of has . The design sets the ceiling; the workmanship decides how close you get to it.
How are levers classified, and which ones are inside your body?
By the relative positions of the fulcrum, the load and the effort. There are exactly three arrangements, and each gives a characteristic mechanical advantage.
A lever is a rigid bar capable of turning about a fixed point called the fulcrum. For an ideal lever the principle of moments gives
so
and for a lever the velocity ratio equals the same ratio of arms, since the two ends move through arcs proportional to their distances from the fulcrum. **So for an ideal lever .
First-class lever — the fulcrum lies between the load and the effort.
- Examples: a see-saw, a pair of scissors, a crowbar, a beam balance, a claw hammer pulling out a nail, a pair of pliers
- In the human body: the nodding of the head, where the skull turns on the topmost vertebra
- Mechanical advantage can be greater than, equal to, or less than one, depending on where the fulcrum sits
Second-class lever — the load lies between the fulcrum and the effort.
- Examples: a wheelbarrow, a nutcracker, a bottle opener, a lemon squeezer, a paper cutter
- In the human body: raising the heel to stand on tiptoe, where the toes are the fulcrum and the body's weight is the load
- Mechanical advantage is always greater than one, because the effort arm is necessarily longer than the load arm. These are always force multipliers
Third-class lever — the effort lies between the fulcrum and the load.
- Examples: a pair of sugar tongs, forceps, fire tongs, a pair of tweezers, a fishing rod
- In the human body: the forearm lifting a weight, where the elbow is the fulcrum, the biceps applies the effort a short way along, and the load is in the hand
- Mechanical advantage is always less than one, because the effort arm is necessarily shorter. These need a larger effort than the load, and their purpose is control and speed rather than force
The forearm example is worth dwelling on, because students assume the body must be efficient. It is not built for force multiplication here — it is built for range and speed. A small contraction of the biceps sweeps the hand through a large arc, which is exactly what a third-class lever does: it trades force for distance in the direction opposite to a jack.
Worked example 1 — a crowbar.** A crowbar cm long has its fulcrum cm from the load end. Find its mechanical advantage.
**So an effort of N would raise a load of N, and this is a first-class lever used as a force multiplier.
Worked example 2 — a wheelbarrow.** A wheelbarrow carries a load of kgf whose centre is cm from the wheel, and the handles are held cm from the wheel. Find the effort needed, assuming an ideal lever.
The wheel is the fulcrum, and taking moments about it:
Check that it is a second-class lever: the load sits between the wheel and the handles, so the mechanical advantage must exceed one — and . Correct.
Worked example 3 — a third-class lever. In a forearm, the biceps applies its effort cm from the elbow and a load is held cm from the elbow. Find the mechanical advantage and the effort needed to hold a kgf load.
Eight times the load, which is why holding even a modest weight at arm's length is so tiring. The mechanical advantage being less than one is not an error — it is the defining feature of a third-class lever, and an answer greater than one here would mean the arms had been swapped.
A lever is a rigid bar capable of turning about a fixed point called the fulcrum. For an ideal lever the principle of moments gives
so
and for a lever the velocity ratio equals the same ratio of arms, since the two ends move through arcs proportional to their distances from the fulcrum. **So for an ideal lever .
First-class lever — the fulcrum lies between the load and the effort.
- Examples: a see-saw, a pair of scissors, a crowbar, a beam balance, a claw hammer pulling out a nail, a pair of pliers
- In the human body: the nodding of the head, where the skull turns on the topmost vertebra
- Mechanical advantage can be greater than, equal to, or less than one, depending on where the fulcrum sits
Second-class lever — the load lies between the fulcrum and the effort.
- Examples: a wheelbarrow, a nutcracker, a bottle opener, a lemon squeezer, a paper cutter
- In the human body: raising the heel to stand on tiptoe, where the toes are the fulcrum and the body's weight is the load
- Mechanical advantage is always greater than one, because the effort arm is necessarily longer than the load arm. These are always force multipliers
Third-class lever — the effort lies between the fulcrum and the load.
- Examples: a pair of sugar tongs, forceps, fire tongs, a pair of tweezers, a fishing rod
- In the human body: the forearm lifting a weight, where the elbow is the fulcrum, the biceps applies the effort a short way along, and the load is in the hand
- Mechanical advantage is always less than one, because the effort arm is necessarily shorter. These need a larger effort than the load, and their purpose is control and speed rather than force
The forearm example is worth dwelling on, because students assume the body must be efficient. It is not built for force multiplication here — it is built for range and speed. A small contraction of the biceps sweeps the hand through a large arc, which is exactly what a third-class lever does: it trades force for distance in the direction opposite to a jack.
Worked example 1 — a crowbar.** A crowbar cm long has its fulcrum cm from the load end. Find its mechanical advantage.
**So an effort of N would raise a load of N, and this is a first-class lever used as a force multiplier.
Worked example 2 — a wheelbarrow.** A wheelbarrow carries a load of kgf whose centre is cm from the wheel, and the handles are held cm from the wheel. Find the effort needed, assuming an ideal lever.
The wheel is the fulcrum, and taking moments about it:
Check that it is a second-class lever: the load sits between the wheel and the handles, so the mechanical advantage must exceed one — and . Correct.
Worked example 3 — a third-class lever. In a forearm, the biceps applies its effort cm from the elbow and a load is held cm from the elbow. Find the mechanical advantage and the effort needed to hold a kgf load.
Eight times the load, which is why holding even a modest weight at arm's length is so tiring. The mechanical advantage being less than one is not an error — it is the defining feature of a third-class lever, and an answer greater than one here would mean the arms had been swapped.
How do the three pulley systems compare?
A single fixed pulley changes only the direction of the effort; a single movable pulley halves the effort; a block and tackle multiplies it by the number of pulleys.
Single fixed pulley. The pulley is fixed to a rigid support and the load hangs from one end of the rope while the effort is applied at the other.
- Velocity ratio , since the two ends of the rope move through equal distances
- Ideal mechanical advantage , so it multiplies no force
- Actual mechanical advantage is a little less than one, because of friction at the axle
- Its use is to change the direction of the effort — you pull down to raise a load up, which lets you use your own weight and is far more convenient
A common example is drawing water from a well, and the pulley there gains no force at all. Its whole value is the change of direction.
Single movable pulley. The pulley itself moves with the load, and the rope passes round it with one end fixed and the effort applied to the other.
- Velocity ratio , because to raise the load m both segments of rope must shorten by m, so the effort end moves m
- Ideal mechanical advantage , so it acts as a force multiplier, halving the effort
- Its drawback is that the effort must be applied upward, which is awkward — so in practice it is combined with a fixed pulley to change the direction as well
Block and tackle. Two blocks, one fixed and one movable, carrying pulleys in all with a single rope passing round them.
- Velocity ratio , the total number of pulleys
- Ideal mechanical advantage
- Actual mechanical advantage , which is less
- Efficiency improves with light pulleys, well-oiled axles and a light rope
Worked example 1 — a block and tackle. A block-and-tackle system has pulleys and an efficiency of . Find its velocity ratio and mechanical advantage, and the effort needed to raise a load of kgf.
Worked example 2 — the distances involved. In the same system, through what distance must the effort move to raise the load through m, and how much work is done?
The efficiency comes back out, which confirms every step.
Worked example 3 — a single movable pulley. Through what distance must the effort move to raise a load m with a single movable pulley, and what effort is needed for a kgf load at efficiency?
Worked example 4 — comparing the three at a glance. For a load of kgf and an ideal machine in each case:
- Single fixed pulley: , so kgf, with the rope pulled down instead of the load being lifted directly
- Single movable pulley: , so kgf, pulled up
- **Block and tackle with pulleys**: , so kgf
The pattern is clear: more pulleys, less effort, more rope to pull. And in every case the work is the same — kgf m to raise the load m — which is the whole point of the chapter.
The boundary case that questions ask about. Why is a single fixed pulley used at all, if its mechanical advantage is one and friction makes it slightly worse than one? Because the direction of the effort matters practically. A person can pull down using their own weight far more effectively than they can lift the same load straight up, so the pulley makes the task easier without making it require less energy.
Single fixed pulley. The pulley is fixed to a rigid support and the load hangs from one end of the rope while the effort is applied at the other.
- Velocity ratio , since the two ends of the rope move through equal distances
- Ideal mechanical advantage , so it multiplies no force
- Actual mechanical advantage is a little less than one, because of friction at the axle
- Its use is to change the direction of the effort — you pull down to raise a load up, which lets you use your own weight and is far more convenient
A common example is drawing water from a well, and the pulley there gains no force at all. Its whole value is the change of direction.
Single movable pulley. The pulley itself moves with the load, and the rope passes round it with one end fixed and the effort applied to the other.
- Velocity ratio , because to raise the load m both segments of rope must shorten by m, so the effort end moves m
- Ideal mechanical advantage , so it acts as a force multiplier, halving the effort
- Its drawback is that the effort must be applied upward, which is awkward — so in practice it is combined with a fixed pulley to change the direction as well
Block and tackle. Two blocks, one fixed and one movable, carrying pulleys in all with a single rope passing round them.
- Velocity ratio , the total number of pulleys
- Ideal mechanical advantage
- Actual mechanical advantage , which is less
- Efficiency improves with light pulleys, well-oiled axles and a light rope
Worked example 1 — a block and tackle. A block-and-tackle system has pulleys and an efficiency of . Find its velocity ratio and mechanical advantage, and the effort needed to raise a load of kgf.
Worked example 2 — the distances involved. In the same system, through what distance must the effort move to raise the load through m, and how much work is done?
The efficiency comes back out, which confirms every step.
Worked example 3 — a single movable pulley. Through what distance must the effort move to raise a load m with a single movable pulley, and what effort is needed for a kgf load at efficiency?
Worked example 4 — comparing the three at a glance. For a load of kgf and an ideal machine in each case:
- Single fixed pulley: , so kgf, with the rope pulled down instead of the load being lifted directly
- Single movable pulley: , so kgf, pulled up
- **Block and tackle with pulleys**: , so kgf
The pattern is clear: more pulleys, less effort, more rope to pull. And in every case the work is the same — kgf m to raise the load m — which is the whole point of the chapter.
The boundary case that questions ask about. Why is a single fixed pulley used at all, if its mechanical advantage is one and friction makes it slightly worse than one? Because the direction of the effort matters practically. A person can pull down using their own weight far more effectively than they can lift the same load straight up, so the pulley makes the task easier without making it require less energy.
Exam tip
Which habits keep a machines answer correct?
**Write down MA, VR and efficiency as three separate labelled lines, and use rather than recomputing work whenever you can.
- Read which two of the three the question gives you, and use the relation to get the third
- VR comes from the design alone — the number of pulleys, or the ratio of the arms — so it never depends on friction
- Express the efficiency as a fraction** before multiplying: becomes
- **Check that in every answer unless the machine is stated to be ideal
- Check that lies between and — a value above one means MA and VR have been swapped
- For a lever use , measuring both arms from the fulcrum
- Classify a lever by what lies in the middle: fulcrum in the middle is first class, load in the middle second, effort in the middle third
- A second-class lever always has and a third-class lever always — use this to check your answer
- For pulleys, equals the number of pulleys** in a block and tackle, for a single movable one and for a single fixed one
- Keep the units consistent — kgf with kgf, newton with newton — and note that MA, VR and efficiency have no units at all
The misconception to name. A machine does not reduce the work you have to do. It reduces the force while increasing the distance, and for an ideal machine the product is unchanged. A block and tackle that lets you lift a load with a quarter of the effort makes you pull four times as much rope, so the energy you supply is the same — and in a real machine it is more, because of friction. A machine that reduced the work would be creating energy.
A second trap. Assuming that a mechanical advantage less than one means something has gone wrong. **A third-class lever always has ** — a forearm holding a kgf load may need kgf of muscle force — and a single fixed pulley has just under one. Those machines are used for direction, speed or range, not for force, and saying so is the answer to "what is the use of such a machine?"
- Read which two of the three the question gives you, and use the relation to get the third
- VR comes from the design alone — the number of pulleys, or the ratio of the arms — so it never depends on friction
- Express the efficiency as a fraction** before multiplying: becomes
- **Check that in every answer unless the machine is stated to be ideal
- Check that lies between and — a value above one means MA and VR have been swapped
- For a lever use , measuring both arms from the fulcrum
- Classify a lever by what lies in the middle: fulcrum in the middle is first class, load in the middle second, effort in the middle third
- A second-class lever always has and a third-class lever always — use this to check your answer
- For pulleys, equals the number of pulleys** in a block and tackle, for a single movable one and for a single fixed one
- Keep the units consistent — kgf with kgf, newton with newton — and note that MA, VR and efficiency have no units at all
The misconception to name. A machine does not reduce the work you have to do. It reduces the force while increasing the distance, and for an ideal machine the product is unchanged. A block and tackle that lets you lift a load with a quarter of the effort makes you pull four times as much rope, so the energy you supply is the same — and in a real machine it is more, because of friction. A machine that reduced the work would be creating energy.
A second trap. Assuming that a mechanical advantage less than one means something has gone wrong. **A third-class lever always has ** — a forearm holding a kgf load may need kgf of muscle force — and a single fixed pulley has just under one. Those machines are used for direction, speed or range, not for force, and saying so is the answer to "what is the use of such a machine?"
Did you know
Why is your own arm built as the least advantageous kind of lever?
The biceps attaches to the forearm only a few centimetres from the elbow, while the hand is roughly eight times further out. That makes the arm a third-class lever with a mechanical advantage of about one-eighth — so holding a five-kilogram load needs a muscle force of the order of forty kilograms-force.
That seems like a poor piece of engineering. It is nothing of the kind, once you look at what the arrangement buys.
Run the trade the other way. A lever that loses force gains distance and speed. When the biceps shortens by a couple of centimetres, the hand sweeps through something like sixteen — and it does so in the same time, so the hand moves about eight times faster than the muscle contracts.
And that is what an arm is for. Throwing, catching, writing and reaching all need the hand to move fast and far over a wide range. A muscle can only contract by a fraction of its own length, so the only way to get a large, fast hand movement out of a small, slow muscle contraction is a lever that multiplies distance rather than force.
The body uses the other classes where force matters.
- Standing on tiptoe is a second-class lever with the toes as the fulcrum, and it lifts the whole body weight — so here the mechanical advantage is greater than one
- Nodding the head is a first-class lever, with the skull balanced on the topmost vertebra, and it needs only a small force because the load is nearly balanced
Which explains why the jaw and the calf feel strong while the outstretched arm feels weak. The difference is not muscle quality but lever geometry.
The same reasoning explains a familiar frustration with tools. A pair of scissors cuts paper easily near the pivot and struggles near the tips, because the load arm grows as the material moves outward and the mechanical advantage falls with it. Cutting thick card near the hinge is not a trick — it is a first-class lever being used where its advantage is greatest.
And it explains why a long spanner loosens a stubborn nut. The effort arm is longer, so the mechanical advantage is greater, so the same hand force produces a larger moment. Nothing about the nut has changed; only the geometry of the lever has.
One last observation that ties the whole part together. Every machine in this chapter — lever, pulley, inclined plane, jack — does the same thing: it lets you choose the force and the distance separately, while the product of the two stays fixed. A machine cannot lower the energy bill of a job. What it can do is put the job within reach of the force you happen to be able to apply, and that is the entire reason machines exist.
That seems like a poor piece of engineering. It is nothing of the kind, once you look at what the arrangement buys.
Run the trade the other way. A lever that loses force gains distance and speed. When the biceps shortens by a couple of centimetres, the hand sweeps through something like sixteen — and it does so in the same time, so the hand moves about eight times faster than the muscle contracts.
And that is what an arm is for. Throwing, catching, writing and reaching all need the hand to move fast and far over a wide range. A muscle can only contract by a fraction of its own length, so the only way to get a large, fast hand movement out of a small, slow muscle contraction is a lever that multiplies distance rather than force.
The body uses the other classes where force matters.
- Standing on tiptoe is a second-class lever with the toes as the fulcrum, and it lifts the whole body weight — so here the mechanical advantage is greater than one
- Nodding the head is a first-class lever, with the skull balanced on the topmost vertebra, and it needs only a small force because the load is nearly balanced
Which explains why the jaw and the calf feel strong while the outstretched arm feels weak. The difference is not muscle quality but lever geometry.
The same reasoning explains a familiar frustration with tools. A pair of scissors cuts paper easily near the pivot and struggles near the tips, because the load arm grows as the material moves outward and the mechanical advantage falls with it. Cutting thick card near the hinge is not a trick — it is a first-class lever being used where its advantage is greatest.
And it explains why a long spanner loosens a stubborn nut. The effort arm is longer, so the mechanical advantage is greater, so the same hand force produces a larger moment. Nothing about the nut has changed; only the geometry of the lever has.
One last observation that ties the whole part together. Every machine in this chapter — lever, pulley, inclined plane, jack — does the same thing: it lets you choose the force and the distance separately, while the product of the two stays fixed. A machine cannot lower the energy bill of a job. What it can do is put the job within reach of the force you happen to be able to apply, and that is the entire reason machines exist.
Exam relevance
How do machines and efficiency prepare you for JEE and NEET?
This is foundation work for Class 11 Work, Energy and Power and Systems of Particles and Rotational Motion, and the efficiency reasoning here reappears across JEE and NEET Physics.
Where the MA, VR and efficiency relation leads. Class 11 does not name these three, but it uses the underlying statement constantly: the useful work out can never exceed the work in, and the ratio of the two is the efficiency. That becomes the efficiency of a heat engine in thermodynamics, where and the Carnot limit places a ceiling on it. JEE Main sets efficiency numericals on engines and refrigerators, and the structure — output over input, always below one — is identical.
Where the lever reasoning leads. It is the principle of moments applied to a rigid body, which becomes torque balance in Class 11. **The relation is rearranged, and JEE problems on hinged rods, ladders and balanced planks are solved by exactly the same step. NEET Biology also uses the lever classification directly when discussing the human skeleton and muscle action.
Where the pulley reasoning leads. Class 11 treats pulley systems with Newton's laws instead of velocity ratios, writing the equations of motion for each block and using the constraint that the string is inextensible. The velocity ratio of for a single movable pulley is that string constraint in disguise** — if the load rises m, the free end must move m. JEE Advanced sets multi-pulley constraint problems, and candidates who understand where the comes from write the constraint correctly.
Where the force-for-distance trade leads. It is the idea behind the inclined plane, the screw, the hydraulic press and gears, and in Class 11 it becomes the general statement that a conservative system can redistribute force and displacement but not create energy. The hydraulic press in fluid mechanics is the same bargain with pressure in place of moments.
Where the "efficiency below one" statement leads. Class 11 thermodynamics gives it teeth: the second law forbids an efficiency of one for a heat engine even in principle, not merely in practice. This chapter's reason — friction and the weight of moving parts — is the practical version of that limit, and NEET asks for both kinds of reasoning.
Question types to expect. At this level: MA, VR and efficiency from given data, the derivation of their relation, lever classification with body examples, and pulley numericals. In competitive papers: torque balance on rigid bodies, pulley constraint equations, engine efficiency, and hydraulic systems.
The single trap that costs marks. Treating the velocity ratio as something friction can change. VR is fixed by the design alone — five pulleys means whatever the friction — and only MA and efficiency fall. At JEE level the same error appears as altering a string constraint because of friction, which never happens.
A second trap. Rejecting a mechanical advantage below one as impossible. Third-class levers and single fixed pulleys both have it, and they are useful for reasons other than force. In competitive problems the equivalent is dismissing a valid solution because it does not match an expectation about which way the inequality should go.
Board versus competitive emphasis. The ICSE paper marks the definitions, the derivation, the lever class with an example and the substituted numerical; a competitive paper marks a tension, a torque or an efficiency. The transferable habit is writing the work input and the work output as two separate expressions before dividing — because that single step is how efficiency is computed for a pulley, a lever, an engine and a transformer alike.
Where the MA, VR and efficiency relation leads. Class 11 does not name these three, but it uses the underlying statement constantly: the useful work out can never exceed the work in, and the ratio of the two is the efficiency. That becomes the efficiency of a heat engine in thermodynamics, where and the Carnot limit places a ceiling on it. JEE Main sets efficiency numericals on engines and refrigerators, and the structure — output over input, always below one — is identical.
Where the lever reasoning leads. It is the principle of moments applied to a rigid body, which becomes torque balance in Class 11. **The relation is rearranged, and JEE problems on hinged rods, ladders and balanced planks are solved by exactly the same step. NEET Biology also uses the lever classification directly when discussing the human skeleton and muscle action.
Where the pulley reasoning leads. Class 11 treats pulley systems with Newton's laws instead of velocity ratios, writing the equations of motion for each block and using the constraint that the string is inextensible. The velocity ratio of for a single movable pulley is that string constraint in disguise** — if the load rises m, the free end must move m. JEE Advanced sets multi-pulley constraint problems, and candidates who understand where the comes from write the constraint correctly.
Where the force-for-distance trade leads. It is the idea behind the inclined plane, the screw, the hydraulic press and gears, and in Class 11 it becomes the general statement that a conservative system can redistribute force and displacement but not create energy. The hydraulic press in fluid mechanics is the same bargain with pressure in place of moments.
Where the "efficiency below one" statement leads. Class 11 thermodynamics gives it teeth: the second law forbids an efficiency of one for a heat engine even in principle, not merely in practice. This chapter's reason — friction and the weight of moving parts — is the practical version of that limit, and NEET asks for both kinds of reasoning.
Question types to expect. At this level: MA, VR and efficiency from given data, the derivation of their relation, lever classification with body examples, and pulley numericals. In competitive papers: torque balance on rigid bodies, pulley constraint equations, engine efficiency, and hydraulic systems.
The single trap that costs marks. Treating the velocity ratio as something friction can change. VR is fixed by the design alone — five pulleys means whatever the friction — and only MA and efficiency fall. At JEE level the same error appears as altering a string constraint because of friction, which never happens.
A second trap. Rejecting a mechanical advantage below one as impossible. Third-class levers and single fixed pulleys both have it, and they are useful for reasons other than force. In competitive problems the equivalent is dismissing a valid solution because it does not match an expectation about which way the inequality should go.
Board versus competitive emphasis. The ICSE paper marks the definitions, the derivation, the lever class with an example and the substituted numerical; a competitive paper marks a tension, a torque or an efficiency. The transferable habit is writing the work input and the work output as two separate expressions before dividing — because that single step is how efficiency is computed for a pulley, a lever, an engine and a transformer alike.
Key takeaways
What must you be able to do from this part?
Three ratios, one relation and two families of machine.
- A machine redistributes force and distance; it does not create energy
- **, the force gain, with no unit
- , the distance cost, fixed by the design alone
- **, derived by substituting and
- ** N through m by N through m** gives , , — confirmed by
- ** with ** gives , so a kgf load needs kgf of effort; an ideal machine would need kgf
- Efficiency is below one because work is spent on friction and on moving the machine's own parts, so ** for every real machine
- Improve efficiency by lubricating the moving parts and making them lighter
- For a lever, **, and for an ideal lever
- First class has the fulcrum in the middle — see-saw, scissors, crowbar, beam balance; in the body, nodding the head. MA can be any value
- Second class has the load in the middle — wheelbarrow, nutcracker, bottle opener; in the body, standing on tiptoe. MA is always above one
- Third class has the effort in the middle — sugar tongs, forceps, fishing rod; in the body, the forearm. MA is always below one
- **A cm crowbar with its fulcrum cm from the load** has
- **A wheelbarrow with a kgf load at cm and handles at cm** needs kgf, giving
- **A forearm with arms of cm and cm** has , so a kgf load needs kgf of muscle force
- Single fixed pulley: , gains no force, and is used to change the direction of the effort
- Single movable pulley: , halves the effort, but the effort must be applied upward
- **Block and tackle with pulleys**: and
- **Five pulleys at ** give , so a kgf load needs kgf and the effort travels m to raise the load m
- MA below one is not an error — such machines are used for direction, speed or range
The most convincing self-test is a pair of scissors. Cut a thick piece of card once near the hinge and once near the tips, notice how much harder the second is, and then say in one sentence which arm changed and by how much.
- A machine redistributes force and distance; it does not create energy
- **, the force gain, with no unit
- , the distance cost, fixed by the design alone
- **, derived by substituting and
- ** N through m by N through m** gives , , — confirmed by
- ** with ** gives , so a kgf load needs kgf of effort; an ideal machine would need kgf
- Efficiency is below one because work is spent on friction and on moving the machine's own parts, so ** for every real machine
- Improve efficiency by lubricating the moving parts and making them lighter
- For a lever, **, and for an ideal lever
- First class has the fulcrum in the middle — see-saw, scissors, crowbar, beam balance; in the body, nodding the head. MA can be any value
- Second class has the load in the middle — wheelbarrow, nutcracker, bottle opener; in the body, standing on tiptoe. MA is always above one
- Third class has the effort in the middle — sugar tongs, forceps, fishing rod; in the body, the forearm. MA is always below one
- **A cm crowbar with its fulcrum cm from the load** has
- **A wheelbarrow with a kgf load at cm and handles at cm** needs kgf, giving
- **A forearm with arms of cm and cm** has , so a kgf load needs kgf of muscle force
- Single fixed pulley: , gains no force, and is used to change the direction of the effort
- Single movable pulley: , halves the effort, but the effort must be applied upward
- **Block and tackle with pulleys**: and
- **Five pulleys at ** give , so a kgf load needs kgf and the effort travels m to raise the load m
- MA below one is not an error — such machines are used for direction, speed or range
The most convincing self-test is a pair of scissors. Cut a thick piece of card once near the hinge and once near the tips, notice how much harder the second is, and then say in one sentence which arm changed and by how much.