WEEK 10
Posted: Thu Jul 02, 2015 9:57 pm
Content - MACHINES
Definition
Types of machines
Mechanical advantage of machines
Velocity ratio of machines
Efficiency of machines
MACHINES
Machines make our work simpler .It is a force producing device by which a large force called load can be overcome by a small applied force called effort
Terminologies used in machines
1. Force ratio ( mechanical advantage )
2. Velocity ratio
3. Efficiency
MECHANICAL ADVANTAGE
We define effort as the force applied to a machine and load as the resistance overcome by the machine. The ability of a machine to overcome a large load through a small effort is known as its mechanical advantage .It is given by
M.A = [sup]Load[/sup]/[sub] Effort [/sub] = L/E …………………………. 1
The mechanical advantage of a machine is influenced by friction in parts
VELOCITY RATIO (V.R)
The velocity ratio is the ratio of distance moved by the effort and load in the same interval
V.R = [sup]Distance moved by effort [/sup] / [sub] Distance moved by the load [/sub] ……………………….. 2
The velocity ratio depends on the geometry of the machine
EFFICIENCY ( E)
The efficiency of a machine is defined as
Ef =[sup]Useful work done by the machine[/sup]/ [sub]Work put into the machine[/sub] x 100 …………………………………… 3
Work = force x distance
Ef = [sup]load x distance moved by load[/sup] /[sub]Effort x distance moved by effort[/sub] x 100 ………………………………………….. 4
Then V.R =M.A
TYPES OF MACHINES.
1. LEVER
This is the simplest form of machine . It consist of a rigid rod pivoted about a point called the fulcrum F with a small effort applied at one end of the lever to overcome a large load L at the other end . There are various types of lever depending on the relative positions of the load, effort and fulcrum.
Examples of first class lever are the crowbar, pair of scissors or pincers, claw hammer , see-saw ,pliers etc
In second order lever , the load is between the fulcrum and effort
Examples are wheel barrow, nut cracker tarp door , an oar etc .
In the third order lever, the effort is between the fulcrum and the load . Human fore arm , laboratory tong etc.
https://youtu.be/A0y_2b8SSbs
https://youtu.be/MWHRVnQ9O4I
https://youtu.be/DXtr9-S3lxw
2.WHEEL AND AXLE
It consists of a large wheel to which a rope or string is attached and an axle or small wheel with the rope or string wound round it in opposite direction . The load to be lifted is hung at the free end of the rope on the axle while the effort is applied at the end of the rope on the wheel . For each complete rotation the load and the effort move through distance equal to the circumference of the wheel and axle respectively.
V.R = R/r …………………………………………. 5
The principle of wheel and axle is used in brace screw driver but spanner windless and gear-boxes
In gear boxes , there are toothed wheels of different diameter interlocked to give turning force at low speed depending on which gear is the driver and which is the driven
THE HYDRAULIC PRESS
The machine is widely used for compressing waste paper and cotton into compact bales forging different alloys into desirable shape etc .It s work is based on Pascal’s principle which states that pressure is transmitted equally in fluid Oil is the liquid normally used in hydraulic press
THE WEDGE
The wedge is a combination of two inclined planes >It is used to separate bodies which are held together by large force .Examples of wedge type of machines are axes chisels knives etc
PULLEY
A simple pulley is a fixed wheel hung on a suitable support with a rope passing round its groove. For a set of pulley, the velocity ratio is the number of pulley in the system.
BLOCK AND TACKLE (PULLEY )
This is the more practical system of pulleys in which one or more pulley are mounted on the same axle with one continuous rope passing all round the pulleys
INCLINED PLANE : This is in form of a sloping plank commonly used to raise heavy load such as barrels of oil with little applied effort than by lifting it vertically.
THE SCREW
Geometrically speaking the screw is an inclined plane wrapped round a cylinder to form a thread . The distance between successive threads on a screw is called its pitch. For one complete revolution of screw through an effort , the load moves a distance equal to its pitch e.g screw jack nut and bolt
In a screw jack where length of the operating handle is a , the effort moved a distance equal to the pitch P. If frictional forces are negligible
Thus V.R= [sup]2πa[/sup]/[sub]P[/sub] = [sup] 2πr[/sup]/[sub]P[/sub] …………………….. 10
EFFECTS OF FRICTION ON MACHINE
Work is always wasted in machines to overcome the frictional forces present between the moving parts and also to lift to part of the machine. The greater the friction , the greater the effort required and the smaller the M.A . M.A depends on friction but depends on the geometry of moving parts .
In practical machines the efficiency is usually less than 100% because of friction in the moving parts of the machine.
https://youtu.be/ybpFEB6Mt88
https://youtu.be/Qjf9esG76WM
ASSIGNMENT
1. A machine with a velocity ratio of 30 moves a load of 3000N when an effort of 200N is applied. The efficiency of the machine is (a) 30% (b) 50% (c) 60% (d) 75%.
2. The efficiency of a wheel and axle system is 80% and the ratio of radius of wheel to radius of the axle is 4 : 1, In order to lift a mass of 20kg,the effort required is (a) 60N (b) 62.5N (c) 32.5N (d) 250 (e) 50N.
3. The velocity ratio of an inclined plane whose angle of inclination is Ɵ is
(a) sin Ɵ (b) cos Ɵ (c) tan Ɵ (d) 1/sin Ɵ (e) 1/cos Ɵ.
4. Which of the following is not an example of levers of the first order (a) crow bar (b) Nutcracker (c) scissors (d) pliers (e) claw hammer.
5. Draw a block and tackle system of pulleys with a velocity ratio of 5.
THEORY
1. Show that efficiency E, the force ration (MA) and the velocity ratio (VR) of a machine are related by the equation E = MA/VR X 100.
2. (a) What is meant by a machine?
(b) Explain why a machine can never be 100% efficient.
GENERAL EVALUATION QUESTION
1. A body travels from rest over a distance x in time t. if it has a uniform acceleration a, the value of t expressed in terms of a and x is?
2. A uniform meter rule of mass 0.42Kg is balanced at the 60cm mark when a mass of m is placed at the 90cm mark. Calculate the value of m.
Definition
Types of machines
Mechanical advantage of machines
Velocity ratio of machines
Efficiency of machines
MACHINES
Machines make our work simpler .It is a force producing device by which a large force called load can be overcome by a small applied force called effort
Terminologies used in machines
1. Force ratio ( mechanical advantage )
2. Velocity ratio
3. Efficiency
MECHANICAL ADVANTAGE
We define effort as the force applied to a machine and load as the resistance overcome by the machine. The ability of a machine to overcome a large load through a small effort is known as its mechanical advantage .It is given by
M.A = [sup]Load[/sup]/[sub] Effort [/sub] = L/E …………………………. 1
The mechanical advantage of a machine is influenced by friction in parts
VELOCITY RATIO (V.R)
The velocity ratio is the ratio of distance moved by the effort and load in the same interval
V.R = [sup]Distance moved by effort [/sup] / [sub] Distance moved by the load [/sub] ……………………….. 2
The velocity ratio depends on the geometry of the machine
EFFICIENCY ( E)
The efficiency of a machine is defined as
Ef =[sup]Useful work done by the machine[/sup]/ [sub]Work put into the machine[/sub] x 100 …………………………………… 3
Work = force x distance
Ef = [sup]load x distance moved by load[/sup] /[sub]Effort x distance moved by effort[/sub] x 100 ………………………………………….. 4
Then V.R =M.A
TYPES OF MACHINES.
1. LEVER
This is the simplest form of machine . It consist of a rigid rod pivoted about a point called the fulcrum F with a small effort applied at one end of the lever to overcome a large load L at the other end . There are various types of lever depending on the relative positions of the load, effort and fulcrum.
Examples of first class lever are the crowbar, pair of scissors or pincers, claw hammer , see-saw ,pliers etc
In second order lever , the load is between the fulcrum and effort
Examples are wheel barrow, nut cracker tarp door , an oar etc .
In the third order lever, the effort is between the fulcrum and the load . Human fore arm , laboratory tong etc.
https://youtu.be/A0y_2b8SSbs
https://youtu.be/MWHRVnQ9O4I
https://youtu.be/DXtr9-S3lxw
2.WHEEL AND AXLE
It consists of a large wheel to which a rope or string is attached and an axle or small wheel with the rope or string wound round it in opposite direction . The load to be lifted is hung at the free end of the rope on the axle while the effort is applied at the end of the rope on the wheel . For each complete rotation the load and the effort move through distance equal to the circumference of the wheel and axle respectively.
V.R = R/r …………………………………………. 5
The principle of wheel and axle is used in brace screw driver but spanner windless and gear-boxes
In gear boxes , there are toothed wheels of different diameter interlocked to give turning force at low speed depending on which gear is the driver and which is the driven
THE HYDRAULIC PRESS
The machine is widely used for compressing waste paper and cotton into compact bales forging different alloys into desirable shape etc .It s work is based on Pascal’s principle which states that pressure is transmitted equally in fluid Oil is the liquid normally used in hydraulic press
THE WEDGE
The wedge is a combination of two inclined planes >It is used to separate bodies which are held together by large force .Examples of wedge type of machines are axes chisels knives etc
PULLEY
A simple pulley is a fixed wheel hung on a suitable support with a rope passing round its groove. For a set of pulley, the velocity ratio is the number of pulley in the system.
BLOCK AND TACKLE (PULLEY )
This is the more practical system of pulleys in which one or more pulley are mounted on the same axle with one continuous rope passing all round the pulleys
INCLINED PLANE : This is in form of a sloping plank commonly used to raise heavy load such as barrels of oil with little applied effort than by lifting it vertically.
THE SCREW
Geometrically speaking the screw is an inclined plane wrapped round a cylinder to form a thread . The distance between successive threads on a screw is called its pitch. For one complete revolution of screw through an effort , the load moves a distance equal to its pitch e.g screw jack nut and bolt
In a screw jack where length of the operating handle is a , the effort moved a distance equal to the pitch P. If frictional forces are negligible
Thus V.R= [sup]2πa[/sup]/[sub]P[/sub] = [sup] 2πr[/sup]/[sub]P[/sub] …………………….. 10
EFFECTS OF FRICTION ON MACHINE
Work is always wasted in machines to overcome the frictional forces present between the moving parts and also to lift to part of the machine. The greater the friction , the greater the effort required and the smaller the M.A . M.A depends on friction but depends on the geometry of moving parts .
In practical machines the efficiency is usually less than 100% because of friction in the moving parts of the machine.
https://youtu.be/ybpFEB6Mt88
https://youtu.be/Qjf9esG76WM
ASSIGNMENT
1. A machine with a velocity ratio of 30 moves a load of 3000N when an effort of 200N is applied. The efficiency of the machine is (a) 30% (b) 50% (c) 60% (d) 75%.
2. The efficiency of a wheel and axle system is 80% and the ratio of radius of wheel to radius of the axle is 4 : 1, In order to lift a mass of 20kg,the effort required is (a) 60N (b) 62.5N (c) 32.5N (d) 250 (e) 50N.
3. The velocity ratio of an inclined plane whose angle of inclination is Ɵ is
(a) sin Ɵ (b) cos Ɵ (c) tan Ɵ (d) 1/sin Ɵ (e) 1/cos Ɵ.
4. Which of the following is not an example of levers of the first order (a) crow bar (b) Nutcracker (c) scissors (d) pliers (e) claw hammer.
5. Draw a block and tackle system of pulleys with a velocity ratio of 5.
THEORY
1. Show that efficiency E, the force ration (MA) and the velocity ratio (VR) of a machine are related by the equation E = MA/VR X 100.
2. (a) What is meant by a machine?
(b) Explain why a machine can never be 100% efficient.
GENERAL EVALUATION QUESTION
1. A body travels from rest over a distance x in time t. if it has a uniform acceleration a, the value of t expressed in terms of a and x is?
2. A uniform meter rule of mass 0.42Kg is balanced at the 60cm mark when a mass of m is placed at the 90cm mark. Calculate the value of m.