SIMPLE MACHINES

Machine Is any device by means of which a force applied at one point can

be used to overcome a force at some other point

OR

Is any device which is used to simplify work

.

OR

Is any device that uses energy to perform some activity (work) by

making an applied force larger

Examples are screw driver, pulley, inclined plane, bicycle, typewrite,

car. etc

Types of Machine

•

Simple machine

Complex machine

Simple Machine

•

Is any device that requires the application of a single force to do work

OR

Is a mechanical device that helps to make work easier

•

Examples are Screw driver, Crowbar, See-saw, Pulleys, Inclined plane,

Hydraulic systems ,Levers ,wheel and axle etc

Complex Machine

•

A Complex Machine is a combination of more than one simple machine.

Examples are Bicycle, Typewriter, Car, Sewing machine etc

Terms Used

Effort (E)

•

OR

Is a force which is applied to the machine so as to lift an object.

is the force used to operate a machine

•

Its SI unit is Newton (N)

Load (L)

•

Is the resistance which a machine over comes

OR

Is the object to be moved from one place to another

•

Its SI is Newton

Mechanical Advantage (MA

)

•

Mechanical advantage is the ratio of the load to the effort.

It has no SI unit

Example

1. A man of mass 100 kg lifts a box weight 500 kg by standing on one end of a

lever. How much mechanical advantage did the lever provide to the man

while lifting the box?

Solution:

Given: Effort, E = 1000kg = 1000N

Load, L = 500kg = 5000N

Mechanical advantage, MA =?

From: MA = L/E

ퟓퟎퟎퟎ

∴ 푴푨 =

= 5

ퟏퟎퟎퟎ

Velocity Ratio (VR)

•

Velocity ratio is the ratio of the distance moved by the effort to the distance

moved by load.

푬풅

푳풅

→ 푽. 푹 =

푳풐풂풅 풅풊풔풕풂풏풄풆

•

Velocity Ratio has no SI unit.

Velocity ratio does not affected by friction

Example

1. When a machine pressed by effort moved down a distance of 100 cm, while

the load is raised through 25 cm at the same time. Find the velocity ratio’

Solution:

Given:

Distance moved by effort, Ed = 100 cm

Distance moved by load, Ld = 25 cm

Required: Velocity ratio, VR =?

From: VR = = ^ퟏퟎퟎ= ퟒ

푬풅

푳풅

ퟐퟓ

Work Output (WO)

•

Work output is the product of load and distance moved by the load.

Work output = L × Ld

Work Input (WI)

•

Is the product of effort and distance moved by the effort

Work Input = E x Ed

Efficiency of a machine

❖

Is the ratio of the useful work derived from a machine to the energy put into it

OR

Is the ratio of the work output to the work input

❖

NB: This ratio is always expressed as a percentage.ie

푾풐풓풌 풐풖풕 풑풖풕

풙 ퟏퟎퟎ%

푾풐풓풌 풊풏풑풖풕

Since: Work Out put = L × Ld

Work Input

= E × Ed

푳

풙 ^푳풅

푬풅

푳 × 푳풅

× ퟏퟎퟎ% =

Now, Efficiency =

풙 ퟏퟎퟎ%

푬 × 푬풅

푬

푳

푳풅

ퟏ

풂풏풅

But:

=

= 푴. 푨

푽.푹

푬풅

푬

On Substituting:

푴. 푨

∴ 푬풇풇풊풄풊풆풏풄풚 =

풙 ퟏퟎퟎ %

푽. 푹

NB:

•

The mechanical efficiency of a machine is always less than 100% .This is

because some energy is lost as heat due to friction

A frictionless (ideal/perfect) machine would have an efficiency of 100%

Example

1. A machine having a velocity ratio of 5 requires 600 J of work to raise a load of

400 N if the load moved though a distance of 0.5 m. calculate the mechanical

advantage and efficiency of the machine

Solution:

Given: Velocity ratio, VR = 5

Work input, WI = 600 J

Load, L = 400 N

Load distance, Ld = 0.5 m

Mechanical advantage, MA =?

Efficiency, Eff =?

푊푂

From: Eff =

푥 100%

푊퐼

Since: WO = L × Ld = 400 × 0.5 = 200

200

∴

Efficiency =

푥 100% = 33.33%

600

푀퐴

But: Efficiency =

× 100%

33.33% = (MA/5) × 100%

푉푅

∴

MA = (33.33% × 5) /100% = 1.67

Individual Task – 1

2. In a certain machine a force of 10N moves down a distance of 3cm in order to

raise a load of 10N through a height of 0.5cm. Calculate the velocity ratio of

the machine. (ANS: 6 )

3. A certain machine is designed in such a way that a force of 150N is used to

lift load of 600N. What is the mechanical advantage (ANS: 4)

4. An athlete exerts a force of 100 N while running 100 m race, if he uses

50,000 J of food energy. Calculate his efficiency (ANS: 20%)

5. A simple machine was used to raise a load of weight 3920N through a height

of 3.5m by applying an effort of 980N, if the distance moved by the effort was

found to be 20m, find.

(i) The mechanical advantages (ANS: 4 )

(ii) The velocity ratio

(

ANS: 5.71

)

(iii) The efficiency of the machine (ANS: 70)

Types of Simple Machine

There are different types of simple machines but here we shall discuss the common

forms of machines. This include

o

Levers

Pulley

Inclined planes

Screw jack

Wheel and axle

Hydraulic press

Levers

•

A lever is a rigid bar (board or rod) that is supported on a single point around

which it rotates

OR

A Lever is a rigid body which when in use turns about a fixed point

•

A lever has three main parts, these are Fulcrum, Load arm and Effort arm

NB

:

➢

The lever is used to lift heavy weights with the least effort (the longer the bar

the easier it is to lift the load)

➢

The fixed point is called Pivot (Fulcrum)

Fulcrum is the fixed point about which the bar moves

Examples of levers are wheel barrow, a pair of scissors, a shovel etc

.

Classes of Levers

❖

First class levers

Second class levers

Third class levers

First Class Levers

✓

In a first class lever ,the pivot is located between the effort and the load

Examples are crowbars, scissors, pliers, see-saws etc. See the fig below

Second Class Levers

✓

In a second class lever ,the load is located between the pivot and the effort

Examples are wheelbarrows, nutcrackers, bottle openers etc

Third Class Levers

✓

In a third class lever ,the effort is applied between the pivot and the load

Examples are shovel (spade), tweezers, fishing rod, tongs, etc

Mechanical Advantage of Levers

✓

Is the ratio of effort arm (E_A) to the load arm, (L_A)

푬_푨

푴. 푨 =

푳_푨

NB:

o

Effort arm (Ea) is a distance between fulcrum and effort

Load arm (La) is a distance between fulcrum and load

MA of second class is greater than fist class lever

MA of third class is less than fist class lever

Example,

1. A force of 30 N is applied at one end of a crowbar and adjust overcomes a

resistance of 150 N at the lid of a case. Find mechanical advantage

Solution:

Given:

Load, E = 30 N

Effort, E = 150 N

Required: Mechanical advantage, MA =?

From:

MA = L/E = 150/30 = 5

Velocity Ratio of Lever

푳풅

Where: Ed = distance moved by effort,

Ld = distance moved by load

Efficiency of Lever

풘풐풓풌 풐풖풕풑풖풕

풙 ퟏퟎퟎ%

푬풇풇풊풄풊풆풏풄풚 =

풘풐풓풌 풊풏풑풖풕

Individual Task – 2

1. In a certain machine , a force of 10 N moves down a distance of 5 cm in order to

raise a load of 100 N through a height of 0.5 cm. calculate velocity ratio of the

lever (ANS: V.R = 10)

2. A machine with velocity ratio of 6 required 800J of work to raise a load of 600 N

through a vertical distance of 1 m. Find efficiency and mechanical advantage

(ANS: Eff = 75%, M.A = 4.5)

3. A certain first class lever of length 2.5 m has a velocity ratio of 12 and an efficiency of

85%. Find

a) Distance moved by effort

(

ANS: 30 m

)

b) Force/effort required lifting a load weighing 75N

(ANS: 7.4 N)

Uses of Lever in Daily Life

•

Used in pair of scissors and tong

Used in wheelbarrow to carry sand

Spanner types like (wrenches) used by plumbers, electrician etc

Crowbar to remove nails from piece of wood

Fishing rod

Pulley

•

Is a simple machine that consists of a wheel that rotates around a point called axle

T

he tension in the rope is the same at all points in an ideal pulley

Types of Pulley

•

Single fixed pulley

Single movable pulley

Combination pulley

The block and tackle pulley system

Single Fixed Pulley

•

A single pulley is a fixed wheel with a rope passing round a groove in the

wheels. Circumference,

It is used to raise flag to the top of a flag – pole and builders use this type of

pulley to lift cement bricks.

For single fixed pulley

➢

Neglecting the weight of the rope and friction of the pulley, the tension in the

rope is equal to the effort and the load is equal to the effort applied on it.

Effort (E) = tension (T) = load (L), that is E = L

푳

∴ 푴. 푨 = =

= ퟏ

푬

푳

From this type of pulley the load and effort all move the same distance.

푬풅

푳풅

푬풅

푻풉풂풕 풊풔 푬풅 = 푳풅

∴ 푽. 푹 =

=

= ퟏ

Single movable Pulley

It consists of one pulley which is free to move.

For single movable pulley

푳

푴푨 =

푬

o

The tension (T) in the string is equal to the effort applied, so the total upward pull on

the pulley is twice the effort 2E (E = T). The load L = 2T, T is the tension in the

string so load 2 = 2E (neglecting the friction losses and weight of the pulley and

string the mechanical advantage is given by;

•

When the effort moves a distance x, the two sections of the string each are

shortened a length half x, Therefore the load moves upwards through a distance half x.

푫풊풔풕풂풏풄풆 풎풐풗풆풅 풃풚 풕풉풆 풆풇풇풐풓풕

푫풊풔풕풂풏풄풆 풎풐풗풆풅 풃풚 풕풉풆 풍풐풂풅

풙

=

푽. 푹 =

= ퟐ

ퟏ

풙

ퟐ

•

Therefore: Velocity ratio = 2

Combined Pulley

It consists of fixed and movable pulleys.

For combined pulleys

푳

• 푴푨 =

푬

•

From the diagram above, the effort, E, moves a distance equal to nx while the

Load, L moves a distance equal to

bearing the Load ,L moves a distance equal to

x

(This is because each of the two ropes

푥

.Then the distance moved

2

by the effort is 2x , ie for n =2)

•

Whereby:

x = distance moved by load and effort

n = number of pulley (number of rope pull the road)

• Now, Ed = nx and Ld = x Thus: 푽푹 = ^푬풅= ^풏풙= 풏

푳풅

풙

Therefore:

VR = n (number of pulleys/ number of ropes pull the load)

From the diagram above: n = 2, therefore its VR = 2

The Block and Tackle Pulley

•

Is a combination pulley that consists of several fixed and movable pulleys

It is used in sailing ships to lift heavy sails

Individual Task – 3

1. A pulley system is made up of 8 pulleys. An effort of 200 N is applied on the

pulley system, if the pulley system has an efficiency of 80%. Find the maximum

load

(

ANS: L =1280 N)

2. A block and tackle pulley system has a VR of 4, if a load of 100 N is raised by

using a force of 50 N. find the mechanical advantage and Efficiency

(ANS: M.A = 2, Eff = 50%)

3. A simple pulley system has velocity ratio of 3, if its efficiency is 90%. Find the

load which can be raised by an effort of 100 N (ANS: L= 270 N)

Uses of Pulleys in Daily Life

❖

Applicable in winches for building works

Uses as transport tourist up mountain slopes

Used by fisher man to lift heavy clothes which used to move their boat as

done at Mtwara coast

❖

Used in garage to lift car engine

Used for fetching water in the well

Inclined Planes

❖

An inclined plane is a smooth flat rigid surface slanted at an angle to the

horizontal.

❖

Examples of inclined planes are staircases, winding roads and ramps

.

Whereby:

Vertical height = Load distance (Ld)

Slanted height = Effort distance (Ed)

Therefore:

푳

•

M

.A =

푬

•

V.R = ^푬풅

푳풅

(

)

푙표푎푑 푑푖푠푡푎푛푐푒

ℎ

•

B

ut 푆푖푛휃 =

=

(

)

퐸푓푓표푟푡 푑푖푠푡푎푛푐푒

푑

ퟏ

풉

ퟏ

V.R =

=

풅

푆푖푛휃

푴.푨

• 푬풇풇풊풄풊풆풏풄풚 =

× ퟏퟎퟎ%

푽.푨

N.B:

For smooth (frictionless) inclined plane

ퟏ

푺풊풏휽

푳풅

Example

A force of 600 N is used to move a load of 3000 N up an inclined plane. Given that

the slanted height and vertical height of the plane are 18 m and 3m respectively. Find

a) Velocity ratio of the plane

b) Mechanical advantage

c) Efficiency of the plane

Data given

Effort, E = 600 N

Load, L = 3000 N

Slanted height, Ed = 18 m

Vertical height, Ld = 3 m

Velocity ratio, VR =?

Mechanical advantage, MA =?

Efficiency, Eff =?

Solution

a) MA = = ^ퟑퟎퟎퟎ= ퟓ

푳

푬

ퟔퟎퟎ

^ퟏퟖ= ퟔ

푬풅

b) VR =

=

푳풅

ퟑ

ퟓ

(^푴푨) × ퟏퟎퟎ% =

c) Efficiency

=

풙 ퟏퟎퟎ% = ퟖퟑ. ퟑ%

푽푹

ퟔ

Individual task – 4

1. A loaded wheelbarrow weighting 800 N is pushed up an inclined plane by a

force of 150 N parallel to the plane, if the plane rises 50 cm for every 400 cm

length of the plane. Find the velocity ratio, mechanical advantage and

efficiency

(ANS: V.R = 8, M.A = 5.3, Efficiency = 66.7%)

Screw and Screw Jack

A screw is a form of an inclined plane in which the plane is wrapped around a rod

•

Screw jack consists of a rod in which there is a thread

The distance between two successive threads is referred to as PITCH

T

he M.A of a screw jack depends on its pitch

풍풆풏품풕풉 풐풇 풕풉풆 풓풐풅 풊풏 풄풎

• Pitch =

풏풖풎풃풆풓 풐풇 풕풉풓풆풂풅풔

Mechanical advantage and Velocity ratio of a screw jack

푳

•

MA

=

푬

푬풅

퐜퐢퐫퐜퐮퐦퐟퐞퐫퐞퐧퐜퐞 퐨퐟 퐚 퐜퐢퐫퐜퐥퐞 퐦퐚퐝퐞 퐛퐲 퐭퐡퐞 퐭퐮퐫퐧퐢퐧퐠 퐚퐫퐦

퐏퐢퐭퐜퐡 퐨퐟 퐭퐡퐞 퐬퐜퐫퐞퐰

ퟐ훑퐑

퐏

• VR =

=

푳풅

ퟐ훑퐑

∴ 푽. 푹 =

퐏

But:

푴푨

a) Efficiency =

× ퟏퟎퟎ%

푽푹

NB:

•

There is always much friction in a jack. In practice, more than half of the work

done is wasted by friction. A jack without friction is useless because the

load or car would fall down as soon as the effort was removed

Example,

A screw jack has 5 threads per centimeter, if the length of the turning lever is 20 cm.

find the velocity ratio (π = 3.14)

Solution:

Given:

Length of the turning, R = 20 cm

Length of the rod, x = 1 cm

Number of thread, y = 5

Pitch, P =?

Velocity ratio, VR =?

From: P = x/y

풍

P

=

= ^ퟏ= ퟎ. ퟐ 풄풎

풏풐.풐풇 풕풉풓풆풂풅풔

ퟓ

^{ퟐ풙ퟑ.ퟏퟒ풙ퟐퟎ}= ퟔퟐퟖ

ퟐ흅푹

Also: VR =

=

푷

ퟎ.ퟐ

Individual Task – 5

1. A screw jack which has a 5 thread per centimeter is used to lift a car weighting

20000 N, if the length of the turning lever is 40 cm and the efficiency of the

screw jack is 90%. Find Velocity ratio, Mechanical advantage, Minimum effort

and maximum effort

.

(ANS: V.R = 1256 , M.A =1130.4 , E_min= 17.7 N E_max= 19.7 N)

2. The handle of the screw jack is 35 cm long and the pitch of the screw is 0.5

cm. what force must be applied to the end of the handle when lifting a load of

2200 N, when efficiency of the jack is 40%(ANS: E = 12.5 N)