Published by: Nuru
Published date: 12 Jan 2022
The simple tools which are used to do daily life activities are simple machines. Those tools or devices which make our work easier and convenient in the direction of the force is called simple machine.
Purpose of using simple machine are:
1. Mechanical advantage (MA):
The simple machine requires force to do work. The resistive force to be overcome is called load and the force applied to overcome the load is called effort.
MA = load / effort applied
The ratio of the load to the effort in a simple machine is called mechanical advantages or actual advantage of the machine.
2. Velocity ratio:
If a machine overcomes a load ‘L’ and the distance travelled by the load is ‘Ld’. Similarly, the effort applied in the machine is ‘E’ and the distance travelled by effort is ‘Ed’, then
Velocity ratio = Velocity of effort / Velocity of load = (Ed / T) / (Ld / T) = Ed / Ld
Velocity ratio is the ratio of distance travelled by an effort to the distance travelled by the load in the machine. As velocity ratio or ideal mechanical advantage is a simple ratio of two distances, it also does not have the unit. The friction is not involved in it.
3. Efficiency
If a machine overcomes a load ‘L’ and the distance travelled by the load is ‘Ld’, the work done by the load is L × Ld. It is also called output work or useful work. Therefore,
Output work = L × Ld
Likewise, the effort applied to overcome the load is E and the distance covered by effort is Ed, the work done by effort is E × Ed. It is also called input work. Therefore,
Input work = E × Ed
The efficiency of a simple machine is defined as the ratio of useful work done by machine (output work) to the total work put into the machine (input work).
For ideal or perfect machine, work output will be equal to the work input. Ideal machinesare those imaginary machines which are frictionless. In practice, the work output of a machine is always less than work input due to the effect of friction. If the frictional force in the machine increases the efficiency decreases. Because machines are frictionless in practice, the efficiency of a machine can never be 100%.
Relation between MA, VR, and η
We know that,
η= output / input ×100%
or,η=( work done by load / work done by effort) ×100%
or,η= (L×Ld) / {E×Ed)×100%
But the mechanical advantages =L / Eand velocity ratio = Ed / Ld
η= MA / VR ×100%
Thus, the relation shows that efficiency is the ratio of mechanical advantage to velocity ratio in percentage.
Principle of simple machine are:
The principle of simple machine states that “if there is no friction in a simple machine, work output and work input are found equal in that machine”. In an ideal machine, efficiency will be 100%.
Mathematically,
Output work = Input work
Or, L × Ld = E × Ed
Simple machines are of the following types:
1. Lever
A lever is a rigid bar may be straight or bent which is capable of rotating fixed point called fulcrum. In a lever, effort distance and load distance are measured from fulcrum. The distance between fulcrum and load is load distance and fulcrum and effort is effort distance.
2. Pulley
A pulley is a metallic or wooden disc with a grooved rim. The rim rotates about a horizontal axis passing through its centre.
A pulley can be used in single fixed pulley, single movable pulley or combined form (block and tackle). A single fixed pulley makes our work easier by changing the direction only; mechanical advantage is not gained because value of effort and load distance is equal. But in single movable pulley, mechanical advantage is gained. In a block and tackle, MA and VR are directly proportional with the number of pulleys used. If the number of pulley increases in block and tackle the VR also increases. In the same way MA increases.
VR in pulleys = No. of pulleys used (except in single movable pulley) or number of rope segments that support the load.
We have,
MA = Load / Effort
3. Inclined plane
Slanted surface which is used to lift the heavy load by applying less effort is called inclined plane. In this device, the length of slope (l) acts as effort distance and height of slope (h) acts as load distance. The value of length of slope is always greater than value of height of slope; therefore value of VR is always greater than 1.
Input work = E × Ed = E × l (∴ l= length of slope)
Output work = L × L d = L × h (∴ h = height of slope)
VR =l / h
We have,
MA = Load / Effort
4. Wheel and axle
Wheel and axle consists of two coaxial cylinders of different diameters. Some examples of wheel and axle are string roller, screw driver etc. in wheel and axle effort is applied on big cylinder called wheel and load is overcome by small cylinder called axle. The circumference of big cylinder 9wheel) is considered as effort distance and circumference of small cylinder (axle) is known as load distance. Therefore, the calculation of VR in wheel and axle can be done by following formula
We have,
MA = Load / Effort
When a force is acted on a body, it results in either displacement of the body or its rotation about a point or axis. This rotation or turning effect of force may be clockwise or anticlockwise. The turning effect of the force acting on a body about an axis is called the moment of the force.
Law of moment
The law of moment states that “In the equilibrium condition of the lever, the sum of the anticlockwise moment is equal to the sum of the clockwise moment”
