Simple Machines

Evolution has taught humans to make work easier. Various tools and devices have been designed to make work effective and less time-consuming. Without these tools, life would be very difficult. For example, if we were to load and unload some concrete (cement) from a truck, then without a shovel, it would be very difficult. Similarly, without an ax or saw, the chopping of a tree would be very time-consuming. That is why we use several types of instruments in our daily life to make our work faster and easier. These instruments are called simple machines

Simple machines are devices that are simple in construction and help to do our work easier and faster. Complex machines are made by the combination of more than one simple machine. Brooms, shovels, jackscrews, spanners, nail-cutters, etc. are examples of simple machines whereas cars, buses, cycles, etc are complex machines.

Advantages of Simple Machines

Simple machines make our work easier and efficient in the following ways.

Terms & Definitions

1. Load (L): The force which we should overcome to do certain work is called load. Its SI unit is Newton (N). 
2. Effort (E): The force which we apply on the simple machine is called an effort. Its SI unit is Newton (N)
3. Fulcrum (F): It is a fixed point about which a simple machine rotates.
4. Load distance (LD): The distance traveled by an effort or the distance between an effort and a fulcrum is called the effort distance. Its SI unit is meter (m).
5. Load distance (LD): The distance traveled by a load or the distance between a load and a fulcrum is called the load distance. Its SI unit is also meter (m).
6. Work Input (W_in): The work done by an effort on a simple machine is called work input.
   
   i.e., work input (W_in) = Effort (E) × Effort distance (ED)
   
   ∴ W_in = E  × ED
   Its SI unit is Joule
   
   
7. Work Output (Wout): The work done by a load or by a simple machine is called work output. 
   
   i.e., work output (Wout) = Load (L) × Load distance (LD)
   
   ∴ Wout = L × LD
   Its SI unit is Joule.
   
   
8. Mechanical Advantage (MA): It is the ratio of a load to an effort applied in a simple machine. 
   
   i.e., machanical advantage, \(MA=\frac{Load(L)}{Effort(E)}\)
   ∴ \(MA=\frac LE\)
   
   A mechanical advantage has no unit. It is the ratio of the same physical quantities i.e. forces. It shows the number of times the force applied on a machine is multiplied by it. Thus, if the MA of a simple machine is 3, it means that the machine can multiply our applied force by 3 times.
   
   

   NOTE: Because Mechanical advantage is the ratio of two forces, it can be affected by frictional force.

   
   
   
9. Velocity ration(VR): It is the ratio of an effort distance to the load distance or it is the ratio of the velocity of an effort to the velocity of the load at the same time.
   
   i.e., velocity ratio, \(VR=\frac{ED}{LD}\)
   
   ∴ \(VR=\frac{ED}{LD}\)
   
   The velocity ratio has no unit. As it is the ratio of two distances. If the VR of a machine is 2, it means that the effort has to travel two times more distance than the load to overcome the load.

NOTE: The velocity ratio (VR) is not affected by friction. In an ideal condition, (Mechanical advantage) MA = VR. So the VR is also known as an ideal MA. But in real practice, no simple machine is frictionless. So, MA is always less than VR in real practice.

Efficiency (η)

Efficiency is the ratio of the output work to the input work and is expressed in percent.

i.e., \(Efficiency(\eta)=\frac{Work\;output(W_{out)}}{Work\;output(W_{in})}\times100\%\)

∴ \(\eta=\frac{W_{out}}{W_{in}}\times100\%\)

If the efficiency of a simple machine is 70%, it means that only 70% of our effort is converted into useful work and 30% of our applied force is wasted to overcome the friction and gravitational force. No Simple machine is frictionless. SO, no simple machine is 100% efficient in practice.

NOTE: Any simple machine of 100% efficiency is called an ideal simple machine. In real life no such machines are possible.

Relation Among MA, VR, and η

We have from efficiency,

\(\eta=\frac{W_{out}}{W_{in}}\times100\%\)
Or, \(\eta=\frac{L\times LD}{E\times ED}\times100\%\)   [ from the definition of Input and output work ]
Or, \(\eta=\frac LE\times\frac{LD}{ED}\times100\%\)
Or, \(\eta=MA\times\frac1{VR}\times100\%\)  [ From the definition of MA and VR ]
∴ \(\eta=\frac{MA}{VR}\times100\%\)

Principle of a Simple Machine

The principle of a simple machine is based on the principle of conservation of energy. It states that "In a balanced condition, work done on the machine (input work) is equal to the work done by the machine".

Work Input = Work Output
\(\therefore E\times ED=L\times LD\)

The total amount of energy inserted into the system must be the same as the energy emitted by the system in the form of work. During the process, no energy is lost or gained. But depending on the load and its distance we achieve different mechanical advantages and velocity ratios, and hence different efficiency.

Types of Simple Machines

There are six types of simple that are used in our daily life in many forms. They are:

1. Lever
2. Pulley
3. Inclined plane
4. Wheel and axle
5. Screw
6. Wedge

1. Lever

A lever is a solid (rigid) bar that may be straight or bent. It rotates freely about a fixed point called the fulcrum or pivot. It is the simplest and the only simple machine that possesses all the properties of simple machines. There are three subtypes of the lever on the basis of the position of the fulcrum (, load, and effort)

This type of lever can multiply our effort when its fulcrum is closer to load or when it has more effort distance (ED). For example, a crowbar is used to lift a heavy stone. Similarly, when the fulcrum lies closer to the effort or when effort distance is less, it can accelerate our work, e.g, Dhiki. So, in the first-class lever,

V.R = 1 when E.D = L.D
V.R > 1 when E.D > L.D
V.R < 1 when E.D < L.D

The second class lever can magnify our work but cannot increase the speed of doing work because, in this kind of lever, the load distance (LD) is never greater than the effort distance (ED).

The third class lever can increase the rate of doing work but it cannot magnify our force. This is because the effort distance is never greater than the load distance.

Check this question for the difference between second class lever and third class lever

2. Pulley

A pully is a circular disc having a groove as its circumference, through which a rope is passed. The load is tied at one end and the effort is applied to the other end of the rope. There are three main types of pulleys.

3. Inclined Plane

4. Wheel and Axle

5. Screw

6. Wedge

Wedge is a combination of two inclined planes. One of its end is sharp and the other is blunt. For example, all the cutting and piercing tools like, a knife, a neddle, a nail, etc. All of these help us to magnify the input force.

The machines which are simple in construction and help to make our work easier and faster are called simple machines.

• The ratio of the load to the effort is called the MA of a simple machine.
• A machine having 100 % efficiency is called an ideal machine. No such simple is ideal in real life.
• A lever is a rigid bar. It may be straight or bent, and it rotates about fixed points called a fulcrum.
• There are three classes of a lever based on the location of fulcrum, effort, and load.
• Pulleys are of three types, i) Fixed pulley, ii) Movable pulley, iii) Block and tackle
• The slanted surface is called an inclined plane.
• The wheel and axle are a combination of two cylinders of different diameters.
• A screw is a cylinder having spirally wounded threads around it.
• All cutting and piercing instruments are called wedges.