Chapter 6

6

Jaydeep Patel

School of Technology,

Machine – a tool that helps us do

work

Machines help us by:

1. Changing the amount of force on an object.1. Changing the amount of force on an object.

2. Changing the direction of the force.

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What is a Simple Machine?

� A simple machine has fewor no moving parts.

� Simple machines makework easier.

� Simple machine is a devicein which effort is appliedin which effort is appliedat one place and work isdone at some other place.

� Simple machines are runmanually, not by electricpower.

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Have you ever tried to unscrew a nut, bolt, Have you ever tried to unscrew a nut, bolt, Have you ever tried to unscrew a nut, bolt, Have you ever tried to unscrew a nut, bolt, or screw from something with your bare or screw from something with your bare or screw from something with your bare or screw from something with your bare hands and discovered that it was just too hands and discovered that it was just too hands and discovered that it was just too hands and discovered that it was just too tight to loosen even if you had a good grip? tight to loosen even if you had a good grip? tight to loosen even if you had a good grip? tight to loosen even if you had a good grip? tight to loosen even if you had a good grip? tight to loosen even if you had a good grip? tight to loosen even if you had a good grip? tight to loosen even if you had a good grip?

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You got the proper tool,

such as a

screw driver or wrench,

and unscrewed it! and unscrewed it!

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Why is it that it's so easy to unscrew with a tool when you can't with your bare hands?

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The wrench and screw driver are The wrench and screw driver are The wrench and screw driver are The wrench and screw driver are examples of a wheel and axle, where the examples of a wheel and axle, where the examples of a wheel and axle, where the examples of a wheel and axle, where the screw or bolt is the axle and the handle is screw or bolt is the axle and the handle is screw or bolt is the axle and the handle is screw or bolt is the axle and the handle is the wheel. The tool makes the job easier the wheel. The tool makes the job easier the wheel. The tool makes the job easier the wheel. The tool makes the job easier by changing the amount of the force you by changing the amount of the force you by changing the amount of the force you by changing the amount of the force you exert.exert.exert.exert.

Axle

Wheel

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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 making a boat go. The reason why these machines are so special is because they make difficult tasks

much easier.

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� Simple Machines can be put together in different ways to make complex machinery.

What is a Compound machine?

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� If a machine, consists of many simple machines, it is called compoundmachine.

� 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.

Lifting machine is a device in which heavy load can be lifted by less effort.e.g. - simple pulley

What is a Lifting machine ?

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e.g. - simple pulley- simple screw jack- lift- crane. etc.

Technical terms Related to Simple Machines

� Mechanical advantage (MA) :

� The ratio of load lifted (W) and effort required (P) is called Mechanical advantage.

Where, W= Load and P= Effort

P

W MA

MA =∴=

requiredEffort

LiftedLoad

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� Velocity ratio (VR) :

� The ratio of distance moved by effort and the distance moved by load is called velocity ratio.

x

y VR

loadby moved Distance

effortby moved DistanceVR =∴=

� Input� Input = effort x distance moved by effort

� Input = p.y

� Output:� Output = load x distance moved by load

� Output = W.x

• Efficiency ( ) :� The ratio of work done by the machine and work done on the machine is called

η

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� The ratio of work done by the machine and work done on the machine is called efficiency of the machine.

%VR

MA

y/x

W/P

P.y

W.xη

yPinputxWOutput

%input

outputEfficiency

100

100100

. & .

100

×=

×=×=∴

==

×=

� 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

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� In a simple machine, effort required to overcome the friction betweenvarious parts of a machine is called effort lost in friction.

� Let, P = effort

Po = effort for Ideal machine

Pf = effort lost in friction

• effort lost in friction.

Pf=P - Po

� For Ideal machine,VR = MA

VR=W/Po

Po=W/VR

Pf = P-Po

Pf= P-(W/VR)

� 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,

� 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,

%50≥η

%50<η

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� For non-reversible machine,

� 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.

%50<η

� 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,

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� for a machine to reverse,

output > machine friction

50% reverse, tomachine aFor

50%

5.0

2

1

y P.

xW.

p.y W.x 2

– W.xP.y W.x

≥

≥∴

≥∴

≥∴

>∴

>∴

η

η

Input

Output

� The law of machine is given by relation,

� P= mW+C

� Where,P = effort appliedW= load liftedm = constant

(coefficient of friction)= slope of line AB

Law of machine

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= slope of line ABC= 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 requiredto 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 forIdeal machine.

Maximum mechanical advantage

m

1MA Maxi.

)( 1

CmW

WMA

CmWP machine of law from

P

WMA

=

+

=+

=∴

+=

=

W

Cneglecting

W

Cm

Q

Maximum efficiency ( )η

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Maximum efficiency ( )maxη

VR x m

1

)1

maxMA (MA

1

MA

CmWP machine of law from

P

WMA

max =∴

===∴

=∴

+=

=

η

η

η

mVR

m

VR

Relation Between Load Lifted and the Mechanical Advantage

As the load increases, the effort also increases and the M. A. increasesThe maximum M. A. is equal to 1/m.

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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)

Simple MachineSimple MachineSimple MachineSimple Machine

• Following are the simple machines.

� Simple Wheel and Axle

� Differential wheel and axle

� Worm and Worm Wheel

� Single purchase Crab

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� Single purchase Crab

� Double Purchase Crab

� Simple Screw Jack

� lever

�Simple Pulley

Simple Wheel and AxleSimple Wheel and AxleSimple Wheel and AxleSimple Wheel and Axle

� WHEEL AND AXLE : A wheel and axle is a modification of a pulley.

� A wheel is fixed to a shaft.

� Large wheel fixed to smaller wheel (or shaft) called an axle

� Both turn together

� Effort usually on larger wheel, moving load of axle

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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.

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DIFFERENTIAL WHEEL AND AXLEDIFFERENTIAL WHEEL AND AXLEDIFFERENTIAL WHEEL AND AXLEDIFFERENTIAL WHEEL AND AXLE

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• 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).

WORM AND WORM WHEELWORM AND WORM WHEELWORM AND WORM WHEELWORM AND WORM WHEEL

• In worm and worm wheel machine, effort wheel and worm are on the same shaft and rotates intwo bearings as shown.• Similarly worm wheel and load drum are also on the same shaft and rotates in two bearings. Twoaxes are at right angles.

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� Winch crabs are lifting machines in which velocityratio is increased by a gear system.

� If only one set of gears is used, the winch crab iscalled a single purchase winch crab and if two setsare used it is called double purchase winch crab.

CRAB WINCHCRAB WINCHCRAB WINCHCRAB WINCH

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SINGLE PURCHASE CRAB WINCHSINGLE PURCHASE CRAB WINCHSINGLE PURCHASE CRAB WINCHSINGLE PURCHASE CRAB WINCH

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DOUBLE PURCHASE CRAB WINCHDOUBLE PURCHASE CRAB WINCHDOUBLE PURCHASE CRAB WINCHDOUBLE PURCHASE CRAB WINCH

• In this machine to increase the V.R. one more pair of gears is used in comparison to singlepurchase crab.• Since there are totally two pairs of gears it is known as Double Purchase Crab Winch. Similarly inTriple Purchase CrabWinch there will be three pairs of gears.• Construction is similar in all the cases

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SIMPLE SCREW JACKSIMPLE SCREW JACKSIMPLE SCREW JACKSIMPLE SCREW JACK

� Screw Jack is a simple machine used for lifting heavyloads, through short distances, with the help of smalleffort applied at its handle.

� The most common application of screw jack is theraising of the front or rear portion of a vehicle forthe purpose of changing the wheel or tyre.

when one rotation is given to the handle.� when one rotation is given to the handle.

� distance moved by effort = 2πR

� distance through which load is lifted = p

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LEVERSLEVERSLEVERSLEVERS

� The lever is simple machine made with a barfree to move about a fixed point calledfulcrum.

� It enables a small effort to overcome a largeload.load.

� VR = dE/dL� ME = FL/FE6 - 30

First Kind of leverFirst Kind of leverFirst Kind of leverFirst Kind of lever

� In a first Kind lever the fulcrum is inbetween of load and effort.

� load and effort is on either side.

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� In a second kind lever the fulcrum is at theend, with the load is in between fulcrumand effort.

Second Kind of leverSecond Kind of leverSecond Kind of leverSecond Kind of lever

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� In a third kind lever the fulcrum is again atthe end, but the effort is in the middle.

Third Kind of leverThird Kind of leverThird Kind of leverThird Kind of lever

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1st Class 2nd Class 3rd Class

Summary of LEVER CLASSESSummary of LEVER CLASSESSummary of LEVER CLASSESSummary of LEVER CLASSES

Fulcrum is between the load and effort

Load is between fulcrum and effort •Effort is between the fulcrum and load.

• Mechanical advantage • MA = b/a •MA = b/a

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• Mechanical advantage• MA = effort arm/load arm

MA= b/a• MA can be more than 1,equal to 1 or less than 1.

• MA = b/a• MA is always greater than 1.

•MA = b/a• MA is always less than 1

When MA is greater than 1, less effort would be required to lift aheavy load. Such type of lever is called effort multiplier lever.

Since. MA is always greater than 1. lever of second kind is an effort multiplier lever.

Since, MA is always lessthan 1. lever of the thirdkind is only a speed multiplier lever. Such levers cannot lift heavy loads but provide increase in speed of lifting.

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

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� 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.

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Direction of Effort In Simple Pulley

� Pulley can change the direction of a Effort(force).

TYPES OF PULLEYSTYPES OF PULLEYSTYPES OF PULLEYSTYPES OF PULLEYSTYPES OF PULLEYSTYPES OF PULLEYSTYPES OF PULLEYSTYPES OF PULLEYS

FIXED PULLEY(like flagpole)

� Pulley stays in one position

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� Pulley stays in one position

� Moves LOAD up, down or sideways

� Changes DIRECTION of force

� Does not reduce EFFORT

MOVABLE PULLEY

(for lifting or lowering heavy objects)

Moves along with LOAD

TYPES OF PULLEYSTYPES OF PULLEYSTYPES OF PULLEYSTYPES OF PULLEYSTYPES OF PULLEYSTYPES OF PULLEYSTYPES OF PULLEYSTYPES OF PULLEYS

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� Moves along with LOAD

� Reduces EFFORT

� Increases DISTANCE

System OF PULLEYSSystem OF PULLEYSSystem OF PULLEYSSystem OF PULLEYSSystem OF PULLEYSSystem OF PULLEYSSystem OF PULLEYSSystem OF PULLEYS

� First system of pulleys

� Second system of pulleys

Third system of pulleys

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� Third system of pulleys

First system of pulleys

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First system of pulley : VR = 2n

Where, n = no. of moving Pulley

Second system of pulleys

Second system of pulley: VR = nWhere, n =total no. of Pullies.

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Third system of pulleys

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Third system of pulley : VR = 2n - 1Where, n = total no. of Pullies.