No Machine Reduces the Work, It Only Spreads It Further
Learn to calculate power and convert between watt, kilowatt and horsepower, see how a pulley changes effort, find the mechanical advantage of an inclined plane, and classify the three orders of lever.
Does a ramp actually make the work of lifting smaller?
No. It makes the force smaller and the distance longer, and the work comes out exactly the same.
Rolling a N drum straight up onto a truck bed m high needs
Push it instead along a plank m long resting against the same truck bed. The force needed drops to N, but it must be applied over m:
Identical. The ramp reduced the effort to a fifth and multiplied the distance by five, and the product never changed.
That is the honest description of every simple machine on this page. A pulley, a ramp and a lever each let you trade force against distance, and none of them reduces the energy you must supply. This page covers the third part of the CBSE Class 9 Science chapter on work, energy and simple machines.
Rolling a N drum straight up onto a truck bed m high needs
Push it instead along a plank m long resting against the same truck bed. The force needed drops to N, but it must be applied over m:
Identical. The ramp reduced the effort to a fifth and multiplied the distance by five, and the product never changed.
That is the honest description of every simple machine on this page. A pulley, a ramp and a lever each let you trade force against distance, and none of them reduces the energy you must supply. This page covers the third part of the CBSE Class 9 Science chapter on work, energy and simple machines.
Formula
How do you calculate power, and what are its units?
Power is the rate of doing work:
The unit is the watt (W), and — one joule of work done each second.
The conversions to know:
-
-
-
- The commercial unit of energy is the kilowatt-hour (kWh), also called one unit, and
That last figure is worth checking rather than memorising: .
Worked example 1. J of work is done in s.
Worked example 2 — a person climbing. A kg boy climbs m in s.
Worked example 3 — a pump. A pump raises kg of water through m in s.
Worked example 4 — horsepower. A hp motor has a power of
Worked example 5 — the electricity bill. A kW heater runs for hours.
In joules that is J — which is why bills are quoted in units rather than joules.
Worked example 6. A W bulb left on for hours uses
Power is the rate, so the same work done faster means more power and not more work. Two people carry identical loads up the same staircase; one takes s and the other s. Both do J of work. The faster one develops W and the slower one W. The work is a property of the job; the power is a property of how it was done.
A kilowatt-hour is a unit of energy, not of power. It looks like a rate because watt appears in it, and it is a power multiplied by a time — which is an energy. A meter reading of units records energy consumed, not the rate at which it was used.
The unit is the watt (W), and — one joule of work done each second.
The conversions to know:
-
-
-
- The commercial unit of energy is the kilowatt-hour (kWh), also called one unit, and
That last figure is worth checking rather than memorising: .
Worked example 1. J of work is done in s.
Worked example 2 — a person climbing. A kg boy climbs m in s.
Worked example 3 — a pump. A pump raises kg of water through m in s.
Worked example 4 — horsepower. A hp motor has a power of
Worked example 5 — the electricity bill. A kW heater runs for hours.
In joules that is J — which is why bills are quoted in units rather than joules.
Worked example 6. A W bulb left on for hours uses
Power is the rate, so the same work done faster means more power and not more work. Two people carry identical loads up the same staircase; one takes s and the other s. Both do J of work. The faster one develops W and the slower one W. The work is a property of the job; the power is a property of how it was done.
A kilowatt-hour is a unit of energy, not of power. It looks like a rate because watt appears in it, and it is a power multiplied by a time — which is an energy. A meter reading of units records energy consumed, not the rate at which it was used.
How does a pulley change the effort needed to lift a load?
A fixed pulley changes only the direction of the effort; a movable pulley halves it.
The useful measure is the mechanical advantage:
A single fixed pulley. The wheel is attached to a support and does not move. It gives , so the effort equals the load — you gain no force at all.
What you gain is direction: you pull down instead of lifting up, which lets you use your weight and is far more convenient. A flagpole pulley and the pulley over a well both work this way.
Worked example 1. A fixed pulley lifting a N load needs an effort of N. .
A single movable pulley. The wheel moves up with the load, and the load hangs from two segments of rope, so each segment carries half the weight:
Worked example 2. A movable pulley lifting a N load needs only N of effort. But to raise the load m, both supporting segments must shorten by m, so ** m of rope must be pulled.
Check the work.** Lifting directly: J. With the pulley: J. Identical, exactly as the ramp was.
A block and tackle. With rope segments supporting the load, .
Worked example 3. A block and tackle with four supporting segments lifts a N load with an effort of
and the rope must be pulled m to raise the load m.
The velocity ratio measures that distance trade:
For this system . For an ideal machine , and the efficiency is
Worked example 4 — a real machine. A pulley system with lifts a N load with an effort of N.
**No machine ever has an efficiency above .** The missing went into overcoming friction in the pulleys and lifting the weight of the movable pulley itself. So is always less than for a real machine, and an answer with greater than is impossible before it is checked.
The useful measure is the mechanical advantage:
A single fixed pulley. The wheel is attached to a support and does not move. It gives , so the effort equals the load — you gain no force at all.
What you gain is direction: you pull down instead of lifting up, which lets you use your weight and is far more convenient. A flagpole pulley and the pulley over a well both work this way.
Worked example 1. A fixed pulley lifting a N load needs an effort of N. .
A single movable pulley. The wheel moves up with the load, and the load hangs from two segments of rope, so each segment carries half the weight:
Worked example 2. A movable pulley lifting a N load needs only N of effort. But to raise the load m, both supporting segments must shorten by m, so ** m of rope must be pulled.
Check the work.** Lifting directly: J. With the pulley: J. Identical, exactly as the ramp was.
A block and tackle. With rope segments supporting the load, .
Worked example 3. A block and tackle with four supporting segments lifts a N load with an effort of
and the rope must be pulled m to raise the load m.
The velocity ratio measures that distance trade:
For this system . For an ideal machine , and the efficiency is
Worked example 4 — a real machine. A pulley system with lifts a N load with an effort of N.
**No machine ever has an efficiency above .** The missing went into overcoming friction in the pulleys and lifting the weight of the movable pulley itself. So is always less than for a real machine, and an answer with greater than is impossible before it is checked.
What is the mechanical advantage of an inclined plane?
The length of the slope divided by the height it rises:
Instead of lifting the load vertically through , you push it along the slope through the longer distance — and the force needed falls in the same ratio.
Worked example 1 — the drum from the opening. A plank m long rests against a truck bed m high.
So a N drum needs an ideal effort of
Check the work both ways. Lifting: J. Along the ramp: J. Equal.
Worked example 2. A ramp m long rising m.
A N barrel needs an effort of N.
Worked example 3 — a gentler slope. Make the plank m long to the same height of m.
Half the effort of worked example 1, over twice the distance — and the work is J again. A gentler slope means a larger mechanical advantage and a longer push.
Everyday evidence. A plank is laid against a truck to roll heavy drums up. A wheelchair ramp replaces a step with a long gentle slope. And a hill road climbs in hairpin bends rather than straight up: the winding road is a very long inclined plane, so a vehicle can climb it with a force its engine can actually supply.
The incline reduces force, never work. That is the same statement as for the pulley, and for the same reason — the energy needed to raise the load by is whatever path it takes, which is exactly the only the vertical height counts rule from the previous part of this chapter.
A real ramp has friction, so the actual effort exceeds the ideal figure and the efficiency is below . The calculated is the ideal value, and a question giving the actual effort is asking for the real , which will be smaller.
Instead of lifting the load vertically through , you push it along the slope through the longer distance — and the force needed falls in the same ratio.
Worked example 1 — the drum from the opening. A plank m long rests against a truck bed m high.
So a N drum needs an ideal effort of
Check the work both ways. Lifting: J. Along the ramp: J. Equal.
Worked example 2. A ramp m long rising m.
A N barrel needs an effort of N.
Worked example 3 — a gentler slope. Make the plank m long to the same height of m.
Half the effort of worked example 1, over twice the distance — and the work is J again. A gentler slope means a larger mechanical advantage and a longer push.
Everyday evidence. A plank is laid against a truck to roll heavy drums up. A wheelchair ramp replaces a step with a long gentle slope. And a hill road climbs in hairpin bends rather than straight up: the winding road is a very long inclined plane, so a vehicle can climb it with a force its engine can actually supply.
The incline reduces force, never work. That is the same statement as for the pulley, and for the same reason — the energy needed to raise the load by is whatever path it takes, which is exactly the only the vertical height counts rule from the previous part of this chapter.
A real ramp has friction, so the actual effort exceeds the ideal figure and the efficiency is below . The calculated is the ideal value, and a question giving the actual effort is asking for the real , which will be smaller.
How do you classify a lever and find its mechanical advantage?
By the order of the three points — fulcrum, load and effort — along the bar.
A lever is a rigid bar turning about a fulcrum, with a load to be moved and an effort applied. Its mechanical advantage is
where each arm is the distance from the fulcrum to that force.
First class lever — the fulcrum lies between the effort and the load.
- may be greater than, equal to, or less than , depending on the arm lengths
- Examples: a seesaw, a crowbar, scissors, pliers, a beam balance
Second class lever — the load lies between the fulcrum and the effort.
- The effort arm is always the longer, so ** is always greater than — force is always gained
- Examples: a wheelbarrow, a nutcracker, a bottle opener, a lemon squeezer
Third class lever — the effort lies between the fulcrum and the load.
- The effort arm is always the shorter, so is always less than — force is always lost
- Examples: a pair of tongs, forceps, a fishing rod, a broom, and the human forearm
Worked example 1 — a crowbar.** The effort is applied cm from the fulcrum and the load sits cm from it.
A N load therefore needs an effort of N.
Worked example 2 — a seesaw. A child of kg sits m from the pivot. Where must a kg child sit to balance?
For balance, load load arm effort effort arm:
The lighter child sits further out, which is why children on a seesaw shuffle along the plank rather than swapping seats.
Worked example 3 — a wheelbarrow. The load is m from the wheel and the handles are gripped m from it.
A N load needs N of effort.
Worked example 4 — the human forearm. The biceps attaches about cm from the elbow and the load in the hand is about cm from it.
So the muscle must pull eight times the load — which is exactly the N needed for a N weight, calculated in the tissues chapter of this course. The forearm is a third class lever, and its mechanical advantage is deliberately less than one.
**A mechanical advantage below is not a design failure. The forearm gives up force to gain range and speed of movement**: the hand sweeps through a wide arc while the muscle shortens only a few centimetres. For an arm that must reach, throw and catch, that is the better bargain — and it is the same force-against-distance trade that the ramp and the pulley make, chosen in the opposite direction.
A lever is a rigid bar turning about a fulcrum, with a load to be moved and an effort applied. Its mechanical advantage is
where each arm is the distance from the fulcrum to that force.
First class lever — the fulcrum lies between the effort and the load.
- may be greater than, equal to, or less than , depending on the arm lengths
- Examples: a seesaw, a crowbar, scissors, pliers, a beam balance
Second class lever — the load lies between the fulcrum and the effort.
- The effort arm is always the longer, so ** is always greater than — force is always gained
- Examples: a wheelbarrow, a nutcracker, a bottle opener, a lemon squeezer
Third class lever — the effort lies between the fulcrum and the load.
- The effort arm is always the shorter, so is always less than — force is always lost
- Examples: a pair of tongs, forceps, a fishing rod, a broom, and the human forearm
Worked example 1 — a crowbar.** The effort is applied cm from the fulcrum and the load sits cm from it.
A N load therefore needs an effort of N.
Worked example 2 — a seesaw. A child of kg sits m from the pivot. Where must a kg child sit to balance?
For balance, load load arm effort effort arm:
The lighter child sits further out, which is why children on a seesaw shuffle along the plank rather than swapping seats.
Worked example 3 — a wheelbarrow. The load is m from the wheel and the handles are gripped m from it.
A N load needs N of effort.
Worked example 4 — the human forearm. The biceps attaches about cm from the elbow and the load in the hand is about cm from it.
So the muscle must pull eight times the load — which is exactly the N needed for a N weight, calculated in the tissues chapter of this course. The forearm is a third class lever, and its mechanical advantage is deliberately less than one.
**A mechanical advantage below is not a design failure. The forearm gives up force to gain range and speed of movement**: the hand sweeps through a wide arc while the muscle shortens only a few centimetres. For an arm that must reach, throw and catch, that is the better bargain — and it is the same force-against-distance trade that the ramp and the pulley make, chosen in the opposite direction.
Exam tip
Exam tip: check that the work comes out the same both ways
** in watts**, with , W and W.
A kilowatt-hour is an energy, not a power: J, and it is one unit on a bill.
Work is fixed by the job; power depends on the time. Two people lifting the same load up the same stairs do equal work and develop different powers.
** and **, with efficiency .
**Fixed pulley: , and it changes only the direction. Movable pulley: , but twice the rope must be pulled. Block and tackle: ** for supporting segments.
**Inclined plane: .** A m plank to a m height gives , so a N drum needs N.
Always check the work is unchanged: J. If it is not, the answer is wrong.
For levers, name the order: fulcrum in the middle is first class; load in the middle is second class with ; effort in the middle is third class with .
Use **load load arm effort effort arm** for balance problems: .
And remember **no efficiency exceeds **, so is always below for a real machine.
A kilowatt-hour is an energy, not a power: J, and it is one unit on a bill.
Work is fixed by the job; power depends on the time. Two people lifting the same load up the same stairs do equal work and develop different powers.
** and **, with efficiency .
**Fixed pulley: , and it changes only the direction. Movable pulley: , but twice the rope must be pulled. Block and tackle: ** for supporting segments.
**Inclined plane: .** A m plank to a m height gives , so a N drum needs N.
Always check the work is unchanged: J. If it is not, the answer is wrong.
For levers, name the order: fulcrum in the middle is first class; load in the middle is second class with ; effort in the middle is third class with .
Use **load load arm effort effort arm** for balance problems: .
And remember **no efficiency exceeds **, so is always below for a real machine.
Did you know
Why a hill road winds instead of going straight up
Look at a road climbing a hill and it almost never takes the direct line. It zig-zags across the slope in long traverses joined by hairpin bends, covering several kilometres of road to gain a few hundred metres of height.
That is an inclined plane, built at the largest scale a civil engineer works at. The winding road makes very large for the same , so the mechanical advantage is large and the force needed to climb it is small.
The alternative is worth imagining. A road straight up the slope would have a small , a small mechanical advantage, and would demand a force most engines cannot deliver and most tyres cannot grip. Loaded lorries would stall, and coming down, brakes would have to remove the same energy over a much shorter distance — which, as the previous part of this chapter showed, means a far larger force and brakes that overheat.
The energy accounting is unchanged by any of it. A lorry of a given mass climbing to a given height must gain exactly of potential energy whichever road it takes. The winding road does not make the climb cheaper in fuel; it makes the climb possible at each instant, by never demanding more force than the vehicle has.
The same reasoning shapes a spiral staircase, which is an inclined plane wrapped around a column, and the thread of a screw, which is an inclined plane wrapped around a cylinder. Turning a screw many times through a small distance drives it a short way into wood with enormous force — force traded for distance, again.
So a machine cannot reduce the work sounds at first like a disappointing limitation. What the hill road shows is that reducing the force is usually the whole point, and the extra distance is a price well worth paying.
That is an inclined plane, built at the largest scale a civil engineer works at. The winding road makes very large for the same , so the mechanical advantage is large and the force needed to climb it is small.
The alternative is worth imagining. A road straight up the slope would have a small , a small mechanical advantage, and would demand a force most engines cannot deliver and most tyres cannot grip. Loaded lorries would stall, and coming down, brakes would have to remove the same energy over a much shorter distance — which, as the previous part of this chapter showed, means a far larger force and brakes that overheat.
The energy accounting is unchanged by any of it. A lorry of a given mass climbing to a given height must gain exactly of potential energy whichever road it takes. The winding road does not make the climb cheaper in fuel; it makes the climb possible at each instant, by never demanding more force than the vehicle has.
The same reasoning shapes a spiral staircase, which is an inclined plane wrapped around a column, and the thread of a screw, which is an inclined plane wrapped around a cylinder. Turning a screw many times through a small distance drives it a short way into wood with enormous force — force traded for distance, again.
So a machine cannot reduce the work sounds at first like a disappointing limitation. What the hill road shows is that reducing the force is usually the whole point, and the extra distance is a price well worth paying.
Exam relevance
How do power and simple machines feed into JEE Main and NEET?
This page is the foundation for the Class 11 Physics chapter Work, Energy and Power, examined in JEE Main and in NEET Physics, and it also underlies a whole chapter of Class 11 mechanics that students rarely connect to it.
Power is treated in that chapter both as the average used here and as the instantaneous power , which is the form competitive papers prefer — a question giving a vehicle's engine power and asking for its maximum speed against a known resistance is a standard JEE Main item, and it is this page's formula rearranged. The kilowatt-hour returns in Class 12 Current Electricity for electrical energy consumption.
The lever and the mechanical advantage lead into Class 11 System of Particles and Rotational Motion, where the *load load arm effort effort arm* rule used above becomes the principle of moments and then torque, written . Every balance problem on this page is a torque problem in disguise, and recognising that makes the Class 11 chapter far less abstract.
The inclined plane becomes a standing situation in Class 11 Laws of Motion, where the weight is resolved along and perpendicular to the slope, friction is added, and the acceleration is found. The Class 9 statement that the ramp reduces force and not work is what the energy method in that chapter confirms.
Efficiency reappears in Class 11 Thermodynamics, where the efficiency of a heat engine is defined the same way — useful output over total input — and the impossibility of exceeding becomes a law rather than an observation.
What the questions look like. Numericals on power are the most common form, usually giving a mass, a height and a time, or an engine power and asking for a force or a speed. Match-the-column items pair a tool with its lever class, and the pairs most often missed are the wheelbarrow (second class) and tongs (third class). Assertion-reason questions favour the statement that a machine cannot reduce the work done, and the statement that a third class lever has .
How board and competitive emphasis differ. A board paper asks you to define power, convert horsepower to watts, and classify three levers with examples. A competitive paper is far more likely to use , or to set a moments problem with three forces on a beam — so the principle of moments matters more than the lever classification. Board papers reward the examples; competitive papers reward the balance equation.
The single trap that costs the most marks. Treating the kilowatt-hour as a unit of power. It is a unit of energy, equal to J, and a question asking how much energy a heater consumes wants kWh or joules, while one asking its rating wants watts.
A second trap worth naming. Assuming a pulley or ramp reduces the work. It reduces the force and multiplies the distance, and a question asking for the work done is asking for the same number either way — J in every version of the drum calculation above. Checking that the work matches is both the fastest verification and the concept being examined.
Power is treated in that chapter both as the average used here and as the instantaneous power , which is the form competitive papers prefer — a question giving a vehicle's engine power and asking for its maximum speed against a known resistance is a standard JEE Main item, and it is this page's formula rearranged. The kilowatt-hour returns in Class 12 Current Electricity for electrical energy consumption.
The lever and the mechanical advantage lead into Class 11 System of Particles and Rotational Motion, where the *load load arm effort effort arm* rule used above becomes the principle of moments and then torque, written . Every balance problem on this page is a torque problem in disguise, and recognising that makes the Class 11 chapter far less abstract.
The inclined plane becomes a standing situation in Class 11 Laws of Motion, where the weight is resolved along and perpendicular to the slope, friction is added, and the acceleration is found. The Class 9 statement that the ramp reduces force and not work is what the energy method in that chapter confirms.
Efficiency reappears in Class 11 Thermodynamics, where the efficiency of a heat engine is defined the same way — useful output over total input — and the impossibility of exceeding becomes a law rather than an observation.
What the questions look like. Numericals on power are the most common form, usually giving a mass, a height and a time, or an engine power and asking for a force or a speed. Match-the-column items pair a tool with its lever class, and the pairs most often missed are the wheelbarrow (second class) and tongs (third class). Assertion-reason questions favour the statement that a machine cannot reduce the work done, and the statement that a third class lever has .
How board and competitive emphasis differ. A board paper asks you to define power, convert horsepower to watts, and classify three levers with examples. A competitive paper is far more likely to use , or to set a moments problem with three forces on a beam — so the principle of moments matters more than the lever classification. Board papers reward the examples; competitive papers reward the balance equation.
The single trap that costs the most marks. Treating the kilowatt-hour as a unit of power. It is a unit of energy, equal to J, and a question asking how much energy a heater consumes wants kWh or joules, while one asking its rating wants watts.
A second trap worth naming. Assuming a pulley or ramp reduces the work. It reduces the force and multiplies the distance, and a question asking for the work done is asking for the same number either way — J in every version of the drum calculation above. Checking that the work matches is both the fastest verification and the concept being examined.
Key takeaways
Power, pulleys, ramps and levers: quick revision
- **, in watts**, with .
- W, W, W, and J — one unit of energy.
- J in s is W. A kg boy climbing m in s does J at W. A pump raising kg through m in s develops W.
- A hp motor is W. A kW heater for hours uses units; a W bulb for hours uses unit.
- Work is fixed by the job; power depends on the time taken.
- A kilowatt-hour is an energy, not a power.
- **, **, and efficiency , never above .
- Fixed pulley: , changes only direction — flagpole and well pulleys.
- Movable pulley: , but m of rope per m of lift. A N load needs N.
- Block and tackle: for supporting segments. Four segments lift N with N.
- A real system with lifting N for N has and ** efficiency.
- Inclined plane**: . A m plank to m gives , so a N drum needs N; a m ramp to m gives ; a m plank to m gives and only N.
- The work is unchanged every time: J.
- Levers: first class has the fulcrum in the middle (seesaw, crowbar, scissors), second class has the load in the middle with (wheelbarrow, nutcracker), third class has the effort in the middle with (tongs, fishing rod, forearm).
- . A crowbar with arms cm and cm gives ; a wheelbarrow with m and m gives .
- Balance: , so the lighter child sits further from the pivot.
- The forearm has , so the biceps pulls eight times the load — force given up for range and speed.
- No machine reduces the work; a hill road winds to reduce the force, and a screw thread is an inclined plane wrapped round a cylinder.
Work out the effort needed to push a load up a ramp, then check that effort times slope length equals weight times height — if the two agree, you have understood what a machine actually does.
- W, W, W, and J — one unit of energy.
- J in s is W. A kg boy climbing m in s does J at W. A pump raising kg through m in s develops W.
- A hp motor is W. A kW heater for hours uses units; a W bulb for hours uses unit.
- Work is fixed by the job; power depends on the time taken.
- A kilowatt-hour is an energy, not a power.
- **, **, and efficiency , never above .
- Fixed pulley: , changes only direction — flagpole and well pulleys.
- Movable pulley: , but m of rope per m of lift. A N load needs N.
- Block and tackle: for supporting segments. Four segments lift N with N.
- A real system with lifting N for N has and ** efficiency.
- Inclined plane**: . A m plank to m gives , so a N drum needs N; a m ramp to m gives ; a m plank to m gives and only N.
- The work is unchanged every time: J.
- Levers: first class has the fulcrum in the middle (seesaw, crowbar, scissors), second class has the load in the middle with (wheelbarrow, nutcracker), third class has the effort in the middle with (tongs, fishing rod, forearm).
- . A crowbar with arms cm and cm gives ; a wheelbarrow with m and m gives .
- Balance: , so the lighter child sits further from the pivot.
- The forearm has , so the biceps pulls eight times the load — force given up for range and speed.
- No machine reduces the work; a hill road winds to reduce the force, and a screw thread is an inclined plane wrapped round a cylinder.
Work out the effort needed to push a load up a ramp, then check that effort times slope length equals weight times height — if the two agree, you have understood what a machine actually does.