Simple Machines: Levers, Pulleys, Formulas and PYQs
Notes on simple machines for exams: mechanical advantage, velocity ratio and efficiency, classes of levers, pulley systems, inclined planes, wedges and screws.
By GK24 Editorial Team· Published · 5 min read
A simple machine is a device that changes the size or the direction of a force so that a job becomes easier to do. It does not create energy and it does not reduce the work to be done: whatever force it saves, it takes back in the distance over which that force must be applied. Six of them are counted as the classical simple machines, the lever, the pulley, the wheel and axle, the inclined plane, the wedge and the screw, and every complicated machine is built out of these. Examiners ask the three ratios that describe any machine, the three classes of lever with their everyday examples, and the simple arithmetic of pulleys and slopes.
The three ratios of a machine
Mechanical advantage is the load divided by the effort, and it tells how many times the machine multiplies the force applied to it. Velocity ratio is the distance moved by the effort divided by the distance moved by the load in the same time, and it is fixed by the shape of the machine alone. Efficiency is the work got out divided by the work put in, expressed as a percentage, and it is also equal to the mechanical advantage divided by the velocity ratio. All three are pure numbers with no unit. In an ideal machine there is no friction, efficiency is one hundred per cent and the mechanical advantage equals the velocity ratio. In every real machine some work is spent against friction and in lifting the parts of the machine itself, so the mechanical advantage is less than the velocity ratio and the efficiency is below one hundred per cent. A machine with a mechanical advantage greater than one multiplies force, and one with a mechanical advantage less than one multiplies speed or range instead.
| Quantity | Formula | Meaning |
|---|---|---|
| Mechanical advantage | Load divided by effort | How many times the force is multiplied |
| Velocity ratio | Distance moved by effort divided by distance moved by load | Fixed by the design of the machine |
| Efficiency | Work output divided by work input, or mechanical advantage divided by velocity ratio | Always less than one in a real machine |
Levers and the principle of moments
A lever is a rigid bar that turns about a fixed point called the fulcrum. When it is balanced, the principle of moments holds: the load multiplied by the load arm equals the effort multiplied by the effort arm, so the mechanical advantage of a lever is the effort arm divided by the load arm. A long effort arm therefore means a large mechanical advantage. Levers are grouped into three classes by the order of the three points along the bar.
| Class | Arrangement | Mechanical advantage | Examples |
|---|---|---|---|
| First class | Fulcrum between the effort and the load | May be more than, equal to or less than one | See-saw, crowbar, scissors, beam balance, pliers |
| Second class | Load between the fulcrum and the effort | Always more than one | Wheelbarrow, nutcracker, bottle opener, lemon squeezer |
| Third class | Effort between the fulcrum and the load | Always less than one | Fishing rod, forceps, sugar tongs, broom, the human forearm |
Pulleys
A pulley is a wheel with a grooved rim over which a rope passes. A single fixed pulley, such as the one over a well, has a velocity ratio of one; it does not multiply the force at all, and its use is that it lets a man pull downwards, with the help of his own weight, to raise a load. A single movable pulley, in which the pulley itself rises with the load, has a velocity ratio of two, so in the ideal case an effort of half the load will lift it. In a block and tackle, several pulleys are mounted in two blocks and the velocity ratio equals the number of rope segments supporting the movable block, which is usually the number of pulleys in the system. Because the mechanical advantage of a real pulley system is reduced by friction and by the weight of the movable block, its efficiency is always below one hundred per cent, and it improves as the load becomes larger.
The inclined plane, the wedge and the screw
An inclined plane is a sloping surface up which a load is pushed instead of being lifted straight up. Its velocity ratio is the length of the slope divided by the vertical height, so a longer and gentler ramp needs a smaller effort; on a smooth plane the effort needed is the weight of the body multiplied by the sine of the angle of the slope. This is why a hill road climbs in zigzags instead of running straight up. A wedge is a pair of inclined planes joined back to back, and an axe, a knife, a chisel and a nail are all wedges; a thin wedge with a long slope and a narrow edge gives the greater mechanical advantage. A screw is an inclined plane wrapped round a cylinder, and the distance between two of its consecutive threads is called the pitch; the velocity ratio of a screw is the circumference of the circle traced by the handle divided by the pitch, which is why a jackscrew can lift a car with the force of one hand. The wheel and axle, the sixth machine, has a velocity ratio equal to the radius of the wheel divided by the radius of the axle, and a steering wheel, a screwdriver and the windlass of a well all work on it.
Points students forget
A machine never multiplies work or energy; the work done by the effort is always at least as much as the work done on the load, and the difference is lost in friction and heat. A machine with a mechanical advantage below one is not useless: a fishing rod and a pair of tongs are built to move the load through a greater distance or at a greater speed than the hand that drives them. Friction can be reduced by oiling and by using ball bearings, but never removed, so no real machine reaches a hundred per cent efficiency, and a machine that claims to do more work than is put into it is a perpetual motion machine, which the law of conservation of energy forbids.
Exam Point of View
Numerical questions are the commonest: find the load from the effort and the mechanical advantage, find the efficiency from the mechanical advantage and the velocity ratio, or find the effort on a ramp of a given length and height. Learn that efficiency equals mechanical advantage divided by velocity ratio and the rest follows. The second favourite is classification: given a tool, name the class of lever, where the traps are scissors, which is first class, the nutcracker, which is second, and the forceps, the broom and the forearm, which are third. The third is the pulley: a fixed pulley gives no gain in force, a movable pulley gives a velocity ratio of two, and a block and tackle gives a velocity ratio equal to the number of supporting rope segments. Also asked are the definitions of pitch, the wedge as a double inclined plane, and the rule that no machine can have an efficiency of one hundred per cent, because mechanical advantage, velocity ratio and efficiency have no units.
Important Facts
| Simple machines | Lever, pulley, wheel and axle, inclined plane, wedge, screw |
|---|---|
| Mechanical advantage | Load divided by effort; no unit |
| Velocity ratio | Distance moved by effort divided by distance moved by load |
| Efficiency | Mechanical advantage divided by velocity ratio, in per cent |
| Principle of moments | Load times load arm equals effort times effort arm |
| First class lever | Fulcrum in the middle: see-saw, crowbar, scissors, beam balance |
| Second class lever | Load in the middle: wheelbarrow, nutcracker, bottle opener |
| Third class lever | Effort in the middle: forceps, fishing rod, human forearm |
| Fixed pulley | Velocity ratio one; changes only the direction of the force |
| Movable pulley | Velocity ratio two |
| Block and tackle | Velocity ratio equals the number of rope segments supporting the load |
| Inclined plane | Velocity ratio equals slope length divided by height |
| Wedge | Two inclined planes placed back to back: axe, knife, chisel, nail |
| Screw | Inclined plane round a cylinder; pitch is the distance between consecutive threads |
Practice MCQs on this topic
The effort applied to move a load is 15 units and the mechanical advantage is observed to be 3. Find the load.
- A.5 units
- B.3 units
- C.15 units
- D.45 units
Show answer
Mechanical advantage is defined as the load divided by the effort, so the load is the mechanical advantage multiplied by the effort, that is three multiplied by fifteen, which gives forty-five units.
Read the full explanation →Find the efficiency of a pulley system which has a mechanical advantage of 2.5 and where the load lifts by 2.5 metres on pulling the rope by 10 m.
- A.62.50%
- B.25.00%
- C.40.00%
- D.100.00%
Show answer
The velocity ratio is the distance moved by the effort divided by the distance moved by the load, that is ten divided by two point five, which is four.
Read the full explanation →The velocity ratio of a simple machine is the ratio of distance travelled by the ________ to the distance travelled by the ________ in the machine.
- A.load; load
- B.effort; load
- C.load; effort
- D.effort; effort
Show answer
Velocity ratio is defined as the distance moved by the effort divided by the distance moved by the load in the same interval of time, and because it depends only on the design of the machine it does not change with friction, unlike the mechanical advantage.
Read the full explanation →Which of the following mechanical devices efficiently distributes or multiplies loads with little effort?
- A.Gears
- B.Lever
- C.Shafts
- D.Bearings
Show answer
A lever is a rigid bar turning about a fulcrum, and by the principle of moments the load multiplied by the load arm equals the effort multiplied by the effort arm, so a long effort arm lets a small effort balance a large load; this is the simplest way of…
Read the full explanation →A wheelbarrow is an example of which class of lever?
- A.First class
- B.Second class
- C.Third class
- D.It is not a lever
Show answer
In a wheelbarrow the wheel acts as the fulcrum, the load sits in the tray between the wheel and the hands, and the effort is applied at the handles, which is the arrangement of a second class lever; because the effort arm is always longer than the load arm, its…
Read the full explanation →A pair of forceps or sugar tongs is an example of which class of lever?
- A.First class
- B.Second class
- C.Third class
- D.Fourth class
Show answer
In a pair of tongs the joint is the fulcrum, the hand presses somewhere in the middle of the arms and the object held lies at the far end, so the effort is between the fulcrum and the load; the effort arm is shorter than the load arm, the mechanical…
Read the full explanation →What is the velocity ratio of a single fixed pulley?
- A.One
- B.Two
- C.Four
- D.Zero
Show answer
In a single fixed pulley the rope that is pulled down moves exactly as far as the load rises, so the distance moved by the effort equals the distance moved by the load and the velocity ratio is one; the pulley gives no gain in force and is used only…
Read the full explanation →An inclined plane is 10 metres long and 2 metres high. What is its velocity ratio?
- A.2
- B.5
- C.10
- D.20
Show answer
The velocity ratio of an inclined plane is the length of the slope divided by its vertical height, because the load is pushed along the whole slope while it is raised only through the height; here ten divided by two gives five, so in the ideal case an effort of…
Read the full explanation →The distance between two consecutive threads of a screw is called its:
- A.Pitch
- B.Lead angle
- C.Torque
- D.Velocity ratio
Show answer
The pitch of a screw is the distance between two consecutive threads measured along its axis, and it is also the distance through which the screw advances in one complete turn; the velocity ratio of a screw is the circumference of the circle described by the handle divided by the…
Read the full explanation →Which of the following is an example of a wedge?
- A.A crowbar
- B.An axe
- C.A pulley block
- D.A steering wheel
Show answer
A wedge is two inclined planes joined back to back, and an axe, a knife, a chisel and a nail all work on that principle: a force applied at the blunt end is turned into a much larger sideways force at the sharp edge, and the thinner and longer the…
Read the full explanation →Why is the efficiency of every real machine less than one hundred per cent?
- A.Because the load is always greater than the effort
- B.Because part of the work done is spent against friction
- C.Because the velocity ratio is always less than one
- D.Because machines create energy of their own
Show answer
In every real machine some of the work put in is used in overcoming friction between the moving parts and in lifting the parts of the machine itself, and that work leaves the system as heat and sound, so the work delivered to the load is always less than the…
Read the full explanation →Frequently Asked Questions
What is the difference between mechanical advantage and velocity ratio?
Mechanical advantage is the load divided by the effort and depends on friction, so it changes with the load. Velocity ratio is the distance moved by the effort divided by the distance moved by the load and depends only on the design of the machine. Their ratio, mechanical advantage divided by velocity ratio, is the efficiency.
Why can no machine be hundred per cent efficient?
Because some of the work put in is always spent against friction between the moving parts and in lifting parts of the machine itself, and that work is converted into heat and sound instead of being delivered to the load. Oiling and ball bearings reduce friction but cannot remove it, so the work output always stays below the work input.
Which class of lever is a pair of scissors?
A pair of scissors is a first class lever: the rivet is the fulcrum, the hand applies the effort on one side of it and the load, the paper or cloth, is on the other side. A nutcracker, by contrast, is a second class lever and a pair of forceps is a third class lever.
What is the use of a single fixed pulley if it does not multiply force?
Its velocity ratio is one, so an ideal fixed pulley gives no gain in force; it changes the direction of the effort. That is a real convenience, because a person can pull downwards and use his own weight to raise a load, which is easier and safer than lifting the load upwards by hand.
How does an inclined plane make work easier?
It lets a load be raised through a given height with a smaller force applied over a longer distance. The velocity ratio is the length of the slope divided by the height, so a longer and gentler ramp needs less effort, which is why hill roads climb in zigzags and heavy drums are rolled up a plank instead of being lifted.
What is the pitch of a screw?
The pitch is the distance between two consecutive threads of a screw, measured along its axis; it is also the distance the screw advances in one complete turn. The velocity ratio of a screw is the circumference of the circle described by the handle divided by the pitch, so a fine thread gives a large mechanical advantage.
Sources
- Science (Class IX), Chapter on Work and Energy — NCERT
- Physics Part I (Class XI), Chapter on Systems of Particles and Rotational Motion — NCERT
- Science (Class VII), Chapter on Motion and Measurement and Simple Machines — NCERT
