Last Updated on May 14, 2026 by sanjjeett
Chapter 3: Machines
Core Concepts
Functions of a Machine
A machine is a device that overcomes a large resistive force (load) by applying a small force (effort) at a convenient point and in a desired direction. It serves four main functions:
- Force Multiplier: Overcoming a large load with less effort (M.A. > 1). E.g., a jack lifting a car.
- Speed Multiplier: Obtaining a gain in speed, where the load moves faster than the effort (M.A. < 1). E.g., a pair of scissors cutting cloth.
- Changing Point of Application: Shifting the point where effort is applied. E.g., the rear wheel of a bicycle.
- Changing Direction of Effort: Making it convenient to apply force. E.g., a single fixed pulley used to lift a bucket from a well.
Note: A machine can NEVER act as a force multiplier and a speed multiplier simultaneously.
The Principle of a Machine
The principle of a machine is based on the law of conservation of energy. It establishes the relationship between Work Input, Work Output, and Efficiency.
- Ideal Machine: A hypothetical machine with no friction or weight of moving parts. Here, Work Output = Work Input, making efficiency 100%.
- Practical Machine: In reality, energy is always lost to friction. Therefore, Work Output < Work Input, and efficiency is always less than 100%.
- The Golden Relation: Mechanical Advantage (M.A.) = Velocity Ratio (V.R.) × Efficiency (η).
Levers and Their Classes
A lever is a rigid, straight, or bent bar capable of turning about a fixed axis called the fulcrum. They operate on the principle of moments.
- Class I (Fulcrum in middle): Can be force multipliers (pliers), speed multipliers (scissors), or neither (see-saw). M.A. can be >1, <1, or =1.
- Class II (Load in middle): The effort arm is always longer than the load arm. M.A. is always > 1. They are always force multipliers (e.g., wheelbarrow, nutcracker).
- Class III (Effort in middle): The effort arm is always shorter than the load arm. M.A. is always < 1. They are always speed multipliers (e.g., sugar tongs, forearm).
Pulleys and Block & Tackle
Pulleys are wheels with a grooved rim used to lift loads. They can be combined to alter mechanical advantage.
- Single Fixed Pulley: Fixed to a rigid support. V.R. = 1. Used purely to change the direction of effort.
- Single Movable Pulley: Not fixed; moves with the load. V.R. = 2. Acts as a force multiplier but requires effort in an upward direction.
- Block and Tackle System: A combination of fixed and movable blocks. The Velocity Ratio is exactly equal to the total number of pulleys (n) or the number of rope segments supporting the movable block.
Important Definitions
Formulas to Remember
Differentiate Between
| Basis | Single Fixed Pulley | Single Movable Pulley |
|---|---|---|
| Position of axis | Its axis of rotation is fixed to a rigid support. | Its axis of rotation is movable. |
| Ideal M.A. & V.R. | Ideal M.A. = 1, V.R. = 1 | Ideal M.A. = 2, V.R. = 2 |
| Function | Used only to change the direction of effort. | Used as a force multiplier. |
| Weight of pulley | Its weight does not affect its M.A. | Its weight reduces its M.A. |
| Basis | Class II Lever | Class III Lever |
|---|---|---|
| Position | Load is between fulcrum and effort. | Effort is between fulcrum and load. |
| Arms Relation | Effort arm is always longer than load arm. | Effort arm is always shorter than load arm. |
| Mechanical Advantage | M.A. > 1 | M.A. < 1 |
| Function | Acts as a force multiplier. | Acts as a speed multiplier. |
Give Reasons
Why is the mechanical advantage of a practical machine always less than its velocity ratio?
In a practical machine, some input energy is wasted in overcoming friction between moving parts and in lifting the weight of the moving parts. Thus, useful work output is less than work input, causing efficiency to be < 100%, making M.A. < V.R.
If a single fixed pulley has a mechanical advantage of 1, why is it used?
It is used purely to change the direction of the effort to be applied. It is much more convenient to pull downwards (utilizing one’s body weight) rather than lifting a heavy load vertically upwards.
Why does a Class III lever always have a mechanical advantage of less than 1?
In a Class III lever, the effort lies between the fulcrum and the load. Consequently, the effort arm is always shorter than the load arm. Since M.A. = Effort Arm / Load Arm, its M.A. is always < 1, making it a speed multiplier.
Why is the lower block of a block and tackle system made as light as possible?
The weight of the lower movable block adds to the total load being lifted. To maximize the efficiency and mechanical advantage of the system, this extra useless weight must be kept to an absolute minimum.
Can a machine be used as both a force multiplier and a speed multiplier simultaneously?
No. A machine acting as a force multiplier requires M.A. > 1 (effort moves a greater distance). A speed multiplier requires M.A. < 1 (load moves a greater distance). It is impossible for both conditions to be true at the same time.
Diagrams to Know
Draw a neat labelled diagram of a block and tackle system having a velocity ratio of 4. Indicate the direction of load, effort, and tension.
1. Draw 2 pulleys in the upper fixed block and 2 in the lower movable block.
2. Tie the rope to the hook of the upper fixed block.
3. Thread it down to the first movable pulley, up to the first fixed, down to the second movable, and finally over the second fixed pulley.
4. Mark ‘E’ (effort) pointing downwards at the free end.
5. Mark ‘L’ (load) pointing downwards from the movable block.
6. Mark 4 ‘T’ (tension) arrows pointing upwards along the 4 rope segments supporting the movable block.
Name a machine which is used to multiply speed. Which class of lever is it? Give its mechanical advantage.
A pair of scissors used for cutting cloth or a pair of sugar tongs. Sugar tongs belong to the Class III lever system. The mechanical advantage of such a machine is always less than 1.
Establish the relationship between mechanical advantage, velocity ratio, and efficiency of a machine.
We know, Efficiency (η) = Work Output / Work Input
Work Output = Load × displacement of load (L × dL)
Work Input = Effort × displacement of effort (E × dE)
η = (L × dL) / (E × dE) = (L / E) × (dL / dE)
Since L / E = Mechanical Advantage (M.A.) and dE / dL = Velocity Ratio (V.R.)
Therefore, η = M.A. / V.R. or M.A. = V.R. × η
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