MACHINE This is a device which makes work easier and faster. Machine can also be defined as a device that uses the application of small effort to overcome a great amount of load.
- Mechanical Advantage: this is the ratio of the load to the effort. It is also called Force Ratio. It can be expressed mathematically as
- Velocity ratio: this is the ratio of the distance moved by the effort to the distance moved by the load. i.e
NB: Velocity Ratio is not affected by friction - Workoutput: this is the work done on load. i.e
Workoutput = Load × Load distance
= L × dl
- Workinput: this is the work done by effort. i.e
Workoutput = Effort × Effort distance
= E × dE
- Efficiency: This is the ratio of the workoutput to workinput. It is expressed in percentage. i.e
The reason why the Efficiency of a machine is always less than 100% is because;
- Friction.
- Workinput is greater than workoutput.
- Velocity ratio is greater than mechanical advantage.
NB: ANY MACHINE WHOSE EFFICIENCY IS 100% IS REFER TO AS AN IDEAL MACHINE.
Examples of machine and their formula for calculating their velocity ratio.
- Inclined plane
- Pulley system
V.R = n , where n is known as the number of pulley.
- Gear system
- Hydraulic press
- Wheel and axle
where ‘R’ and ‘D’ represent radius and diameter of the wheel while ‘r’ and ‘d’ represent radius and diameter of the axle.
- Screw jack
where ‘a’ represents arms length and ‘p’ represent the pitch
Examples
- A wheel and axle is used to raise a load of 500N by the application of an effort of 250N. if the radii of the wheel and the axle are 0.4cm and 0.1cm respectively, the efficiency of the machine is
- Calculate the velocity ratio of a screw jack of pitch 0.5cm if the length of the tommy-bar is 12cm.
- A machine of efficiency 80% is used to raise a load of mass 75kg through a vertical height of 3m. Calculate the workinput. ( g = 10m/s)
- A simple machine with an efficiency of 75% lifts a load of 5000N with a force of 500N applied to it. Calculate the velocity ratio of the machine.
Lever can be classified into three. They are
- First class lever: in this lever system, the fulcrum is between the load and the effort.eg plier, scissors, a crow bar,a claw hammer etc
- Second class system: in this lever system, the load is between the fulcrum and the effort eg wheelbarrow, nutcracker, bottle opener etc
- Third class system: In this lever system, the effort is between the load and the fulcrum eg tongs, forearm, tweezers etc
Exercises
- The efficiency of a machine is 80%. Determine the workdone by a person using this machine to raise a load of 200N through a vertical distance of 3m(take g =10m/s²)
- A machine whose efficiency is 60% has a velocity ratio of 5. If a force of 500N is applied to lift a load P, what is the magnitude of P?
- A machine whose efficiency is 75% is used to lift a load of 1000N. Calculate the effort put in to the machine if it has a velocity ratio of 4.
- If a barrel is rolled up a plane inclined at 30° to the horizontal, its velocity ratio will be
- A machine of velocity ratio 6 requires an effort of 400N to raise a load of 800N through 1m. find the efficiency of the machine
- Calculate the velocity ratio of a screw jack of pitch 0.2cm if the length of the tommy-bar is 23cm
Solve the Exercises and write down your answers in the comment section below