Definition of Machine and Simple Machine
An arrangement by which work can be done conveniently on a load or against a resistance is known as machine
A simple machine is a machine in its simplest form. They are devices that use energy to do work. The work is being done by the machine when a small effort is used to overcome a large resistance.
A machine can be defined as a tool or devices that allows a force (or effort) applied to one point to overcome a resisting force (or load) at another point.
Simple machine can be classified into different categories namely the lever, the pulley, the inclined plane, the wedge, the wheel and axle, the screw, the hydraulic press.
Some common examples of simple machines are, scissors, drill brace, the shovel (a form of lever), the pulley at the top of a flagpole, the steering wheel of an automobile (a form of wheel and axle), and the wheelchair ramp (a form of inclined plane). An everyday example of a complex machine is the can opener, which combines a lever (the hinged handle), a wheel and axle (the turning knob), and a wedge (the sharpened cutting disk).
Mechanical Advantage/Force Ratio
Mechanical advantage/Force ratio of a machine is defined as the ratio of the load to the effort.
Mechanical Advantage =LoadEffort=Le
If the laod is bigger than the effort, the mechanical Advantage is greater than one.
In pratice,all machines have some friction in them and this reduces the efficiency. Part of the work put into a machine is thus always wasted in overcoming friction and in moving some parts of the machine. Thus, no machine is hundred percent (100%) efficient.
Velocity Ratio
The velocity ratio of a machine is defined as the distance moved by the effort to the distance moved by the load.
Velocity Ratio =Distance moved by EffortDistance moved by Load=dedL
Efficiency of a Machine
The efficiency of a machine is defined as the ratio of work obtained from the machine to work put into the machine expressed in percentage.
It also defined as the ratio of work output of the machine to the total work input expressed in percentage.
Efficiency =Work outputWork input×100
Derivation of the Formula
Efficiency E=MAVR×100
The efficiency of a machine can be determined by taking ratio of the work output to work input of the machine or its velocity ratio and mechanical advantage.
Therefore:
Efficiency (E)=Work outputWork input×100
Efficiency (E)=Work done in loadWork done in effort×100
Since Work=force×distance
Efficiency
| (E)=Load(L)×distance moved by load(dL)Effort(E)×distance moved by effort(de)×100 |
Therefore, E=L×dLe×(de)×100
But MA=Leand1VR=dLde
Therefore, E=M.AV.R×100
Mechanical Advantage (M.A)=Le
Efficiency (E)=MechanicalAdvantageVelocityRatio×100
Example 1:
A system of lever with velocity ratio 30 overcomes resistance of 2500 Newton when an effort of 125 Newton is applied to it, calculate
- The mechanical advantage of the system.
- It’s efficiency.
Solution:
Mechanical Advantage =LoadEffort=2500125=20N
Efficiency =M.AV.R×100
Efficiency =2030×100=2003=66.75
GENERAL EVALUATION
- Explain what is meant by a machine.
- Define the terms: mechanical advantage, velocity ratio and efficiency as applied to a machine.
- Show that the efficiency E, the force ratio M.A and the velocity ratio V.R of a machine are related by the equation E=M.AV.A×100
- Explain why the efficiency of a machine is usually less than 100%.
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