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# Chapter 6

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### Chapter 6

1. 1. Jaydeep PatelSchool of Technology,6
2. 2. Machine – a tool that helps us do work Machines help us by: 1. Changing the amount of force on an object. 2. Changing the direction of the force.6-2
3. 3. What is a Simple Machine? A simple machine has few or no moving parts. Simple machines make work easier. Simple machine is a device in which effort is applied at one place and work is done at some other place. Simple machines are run manually, not by electric power.6-3
4. 4. Have you ever tried to unscrew a nut, bolt, or screw from something with your bare hands and discovered that it was just too tight to loosen even if you had a good grip?6-4
5. 5. 6-5
6. 6. You got the proper tool, such as a screw driver or wrench, and unscrewed it!6-6
7. 7. Why is it that its so easy to unscrew with a tool when you cant with your bare hands?6-7
8. 8. The wrench and screw driver are examples of a wheel and axle, where the screw or bolt is the axle and the handle is the wheel. The tool makes the job easier by changing the amount of the force you exert. Wheel Axle6-8
9. 9. All of the simple machines can be used for thousands of jobs from lifting a 500-pound weight to making a boat go. The reason why these machines are so special is because they make difficult tasks much easier.6-9
10. 10. What is a Compound machine? Simple Machines can be put together in different ways to make complex machinery. If a machine, consists of many simple machines, it is called compound machine. Such machines are run by electric or mechanical power. Such machines work at higher speed. Using compound machines more work is done at less effort. For Ex: scooter, Lathe, crane, grinding machine etc.6 - 10
11. 11. What is a Lifting machine ? Lifting machine is a device in which heavy load can be lifted by less effort. e.g. - simple pulley - simple screw jack - lift - crane. etc.6 - 11
12. 12. Technical terms Related to Simple Machines Mechanical advantage (MA) : The ratio of load lifted (W) and effort required (P) is called Mechanical advantage. Load Lifted W MA = ∴ MA = Effort required P Where, W= Load and P= Effort Velocity ratio (VR) : The ratio of distance moved by effort and the distance moved by load is called velocity ratio. Distance moved by effort y VR = ∴ VR = Distance moved by load x6 - 12
13. 13. Input Input = effort x distance moved by effort Input = p.y Output: Output = load x distance moved by load Output = W.x • Efficiency ( η ) : The ratio of work done by the machine and work done on the machine is called efficiency of the machine. output Efficiency = × 100 % input Output = W . x & input = P . y W.x W/P ∴η = × 100 = × 100 P.y y/x MA = × 100 %6 - 13 VR
14. 14. Ideal machine : A machine having 100% efficiency is called an ideal machine. In an Ideal machine friction is zero. For Ideal machine, Output = input or MA=VR Effort lost in friction (Pf): In a simple machine, effort required to overcome the friction between various parts of a machine is called effort lost in friction. Let, P = effort • effort lost in friction. Po = effort for Ideal machine Pf=P - Po Pf = effort lost in friction For Ideal machine,VR = MA VR=W/Po Po=W/VR Pf = P-Po Pf= P-(W/VR)6 - 14
15. 15. Reversible machine : If a machine is capable of doing some work in the reverse direction, after the effort is removed is called reversible machine. For reversible machine, η ≥ 50% Non-reversible machine or self-locking machine If a machine is not capable of doing some work in the reverse direction, after the effort is removed, is called non-reversible machine or self-locking machine. For non-reversible machine, η < 50% A car resting on a screw jack does not come down on the removal of the effort. It is an example of non-reversible machine.6- 15
16. 16. Condition for reversibility of machine : W = load lifted P = effort required x = distance moved by load y = distance moved by effort P.y = input W.x = output Machine friction = P.y – W.x for a machine to reverse, output > machine friction ∴ W.x > P.y – W.x ∴ 2 W.x > p.y W. x 1 ∴ ≥ P. y 2 Output ∴ ≥ 0 .5 Input ∴ η ≥ 50%6 - 16 For a machine to reverse, η ≥ 50%
17. 17. Law of machine The law of machine is given by relation, P= mW+C Where, P = effort applied W= load lifted m = constant (coefficient of friction) = slope of line AB C= Constant = Machine Friction= OA Following observations are made from the graph : On a machine, if W = 0, effort C is required to run the machine. Hence, effort C is required to overcome machine friction. If line AB crosses x-x axis. without effort (P), some load call be lifted, which is impossible. Hence, line AB never crosses x-x axis. If line AB passes through origin, no effort is required to balance friction. Such a graph is for Ideal machine.6 - 17
18. 18. Maximum mechanical advantage W MA = P from law of machine P = mW + C W 1 C ∴ MA = = (Q neglecting ) mW + C C W m+ W 1 Maxi. MA = m Maximum efficiency (η max ) W MA = P from law of machine P = mW + C MA ∴η = VR 1 m 1 ∴η = (MA = MA max = ) VR m 1 ∴ η max =6 - 18 m x VR
19. 19. Relation Between Load Lifted and the Mechanical Advantage As the load increases, the effort also increases and the M. A. increases The maximum M. A. is equal to 1/m. Relation Between Load Lifted and the Efficiency As the load and effort increases, efficiency also increases. The maximum efficiency is equal to 1/(m x VR)6 - 19
20. 20. Simple Machine • Following are the simple machines. Simple Wheel and Axle Differential wheel and axle Worm and Worm Wheel Single purchase Crab Double Purchase Crab Simple Screw Jack lever Simple Pulley6 - 20
21. 21. Simple Wheel and AxleWHEEL AND AXLE : A wheel andaxle is a modification of a pulley.A wheel is fixed to a shaft.Large wheel fixed to smaller wheel (orshaft) called an axleBoth turn togetherEffort usually on larger wheel, movingload of axle
22. 22. 6 - 22
23. 23. When either the wheel or axle turns, the other part also turns. One full revolution of either part causes one full revolution of the other part.6 - 23
24. 24. DIFFERENTIAL WHEEL AND AXLE • In this machine load axle is made in two parts having two different diameters d1 and d2. • When effort is applied to rotate the assembly at that time string is wound over larger axle (d1) and unwound from the smaller axle (d2).6 - 24
25. 25. WORM AND WORM WHEEL • In worm and worm wheel machine, effort wheel and worm are on the same shaft and rotates in two bearings as shown. • Similarly worm wheel and load drum are also on the same shaft and rotates in two bearings. Two axes are at right angles.6 - 25
26. 26. CRAB WINCH Winch crabs are lifting machines in which velocity ratio is increased by a gear system. If only one set of gears is used, the winch crab is called a single purchase winch crab and if two sets are used it is called double purchase winch crab.6 - 26
27. 27. SINGLE PURCHASE CRAB WINCH6 - 27
28. 28. DOUBLE PURCHASE CRAB WINCH • In this machine to increase the V.R. one more pair of gears is used in comparison to single purchase crab. • Since there are totally two pairs of gears it is known as Double Purchase Crab Winch. Similarly in Triple Purchase CrabWinch there will be three pairs of gears. • Construction is similar in all the cases6 - 28
29. 29. SIMPLE SCREW JACK Screw Jack is a simple machine used for lifting heavy loads, through short distances, with the help of small effort applied at its handle. The most common application of screw jack is the raising of the front or rear portion of a vehicle for the purpose of changing the wheel or tyre. when one rotation is given to the handle. distance moved by effort = 2πR distance through which load is lifted = p6 - 29
30. 30. LEVERS The lever is simple machine made with a bar free to move about a fixed point called fulcrum. It enables a small effort to overcome a large load. VR = dE/dL6 - 30 ME = FL/FE
31. 31. First Kind of lever In a first Kind lever the fulcrum is in between of load and effort. load and effort is on either side.6 - 31
32. 32. Second Kind of lever In a second kind lever the fulcrum is at the end, with the load is in between fulcrum and effort.6 - 32
33. 33. Third Kind of lever In a third kind lever the fulcrum is again at the end, but the effort is in the middle.6 - 33
34. 34. Summary of LEVER CLASSES 1st Class 2nd Class 3rd Class Fulcrum is between the load and Load is between fulcrum and effort •Effort is between the fulcrum and effort load. • Mechanical advantage • MA = b/a •MA = b/a • MA = effort arm/load arm • MA is always greater than 1. • MA is always less than 1 MA= b/a • MA can be more than 1, equal to 1 or less than 1. When MA is greater than 1, less Since. MA is always greater than 1. Since, MA is always less effort would be required to lift a lever of second kind is an effort than 1. lever of the third heavy load. Such type of lever is multiplier lever. kind is only a speed multiplier called effort multiplier lever. lever. Such levers cannot lift heavy loads but provide increase in speed of lifting.6 - 34
35. 35. Simple Pulley PULLEY: A pulley is a simple machine made with a rope, belt or chain wrapped around a grooved wheel. A pulley works two ways. It can change the direction of a force or it can change the amount of force. A fixed pulley changes the direction of the applied force. ( Ex. Raising the flag ) . A movable pulley is attached to the object are moving.6 - 35
36. 36. Direction of Effort In Simple Pulley Pulley can change the direction of a Effort(force).6 - 36
37. 37. TYPES OF PULLEYS FIXED PULLEY (like flagpole) Pulley stays in one position Moves LOAD up, down or sideways Changes DIRECTION of force Does not reduce EFFORT6 - 37
38. 38. TYPES OF PULLEYS MOVABLE PULLEY (for lifting or lowering heavy objects) Moves along with LOAD Reduces EFFORT Increases DISTANCE6 - 38
39. 39. System OF PULLEYS First system of pulleys Second system of pulleys Third system of pulleys6 - 39
40. 40. First system of pulleys First system of pulley : VR = 2n Where, n = no. of moving Pulley6 - 40
41. 41. Second system of pulleys Second system of pulley: VR = n Where, n =total no. of Pullies.6 - 41
42. 42. Third system of pulleys Third system of pulley : VR = 2n - 1 Where, n = total no. of Pullies.6 - 42