SIMPLE MACHINES-ENGINEERING SCIENCE.pptx

SIMPLE MACHINES
ENGINEERING SCIENCE

Concept of Simple machines
What is simple machine?

3
Simple machine
The basic purpose of designing simple machine is to
reduce the effort (force) required to perform a task.
A simple machine is any device with few or no
moving parts that is used to modify motion and
magnitude force in performing work.
Simple machines help people to move objects from one
point to another by:
a) Increasing the applied force
b) Changing the direction of force
c) Changing the magnitude of force
d) Multiplying speed

4
Simple machine
There are six types of simple machines. These include
Levers, hydraulic press, the wheel and axle, the
screw, the inclined plane and pulley.
Common Terms
Common terms used in describing simple machines are;
a) Load (L) – the weight of an object being moved by a
simple machine
b) Effort (E) – the force applied in moving the load
c) Mechanical Advantage (M.A)
d) Velocity Ratio (V.R)
e) Efficiency ()

Simple machine
Mechanical advantage (MA)
The machine is said to have offered mechanical
advantage is it enables us to use less force to perform the
same amount of work.
Mathematically, mechanical advantage of a simple
machine is the ratio of the load moved to effort applied.
Mechanical Advantage =
Mechanical advantage indicates the factor to which to which
the machine will increase or reduce the effort. For example, a
machine with a mechanical advantage of 4 will multiply a force
of 10 N four times. Therefore, the force applied on the load will
be 40 N.

Simple machine
Example
A person whose mass is 100 kg lift a box of mass 500kg by standing
on one end of the lever. How much mechanical advantage does the
lever provide to the person as he/she lifts the box?
Solution
Give that,
Load = weight of box
= mass x acceleration due to gravity
= 500kg x 10m/s2
= 5000 N
Effort = Weight of a man
= mass x acceleration due to gravity
= 100kg x 10m/s2
= 1000 N

Simple machine
Mechanical Advantage =
=
= 5
The lever offered a mechanical advantage of 5 while
lifting the box. In other words, the lever as a simple
machine magnified the person’s weight (effort) 5 times
to lift the box
Velocity Ratio (VR)
Velocity ratio of a simple machine is the ratio of distance
moved by the effort to the distance moved by the load.

Simple machines
Example
The effort arm of a simple machine moves down a distance
of 100 cm, resulting to the load being raised by 25 cm. What
is the velocity ratio of the machine?
Solution
Give that,
Distance moved by effort = 100 cm or 1 m
Distance moved by load = 100 cm or 0.25m
VR =
 = 4
Velocity Ratio (VR) =

Simple machines
Therefore, velocity ratio of a simple machine is 4.
Velocity of simple machine is not affected by the presence
of friction.
Efficiency ()
Efficiency is the measure of the effectiveness of a
machine in transforming the work input for the machine to
work output.
Mathematically, efficiency is given by the ratio of work
output to the work input. This ratio is usually expressed
as percentage.
Efficiency () =

Simple machines
Since work done = force x distance moved, then efficiency
can be written as:
Efficiency () =
= MA x x 100%
= x 100%
Therefore, Efficiency () = x 100%
The efficiency of a simple machine is always less than
100%.This is because some of the effort is used to overcome
frictional forces in the moving parts of the system. That means
the mechanical advantage numerically is always less than
velocity ratio.

Simple machines
Example.
A certain machine with force of 10N moves down a
distance of 5cm in order to raise a load of 100N through
a height of 0.5cm. Calculate the values for the
following;
a) Mechanical advantage (M.A) of the machine
b) Velocity ratio (V.R) of the machine
c) Efficiency () of machine of the machine
Solution:
Given that:
Effort = 10N
Load = 100N

Simple machines
Distance moved by effort = 5cm
Distance moved by load= 0.5cm
Efficiency machine?

Simple machines
As we have seen earlier, there are different
types of simple machines which include the
following;
a) Levers
b) Screw Jack
c) Pulley
d) Wheel and Axle
e) Inclined plane
 Hydraulic press

Simple machines
Levers
It consists of a rigid bar that moves about a fixed point.
A lever has three main parts namely. Fulcrum, Load
and effort. The fulcrum is the fixed point abut which the
rigid bar moves.

Simple machines
The distance between the load and fulcrum is called the
load arm while the distance from the load to the effort is
called effort arm. The longer the effort arm the easier it
is to lift to lift the load. Leavers always act as magnifier
of the effort (force).
Classes of Lever
There are three classes or groups of levers depending
on the position of the load, effort and fulcrum:
a) First class lever
b) Second class lever
c) Third class lever

Simple machines
First Class Levers
A first-class lever has the fulcrum located between the
load and the effort. As you can see in the figure below,
the effort applied in the downward direction results in an
upward movement of the load.
Mechanical advantage of the lever depends of the
position of fulcrum. The closer the fulcrum is to the load,
the less the effort needed to move the load.

Simple machines
The Examples of first-class levers are: see-saw, crowbar,
pair of scissors, pliers and claw hammer.

Simple machines
Second Class Levers
A second-class lever has the load located between the
fulcrum and the effort as shown in the figure below. The
load moves in the same direction as the applied while the
effort is multiplied

Simple machines
Just like in the first-class lever, the closer is the load to
the fulcrum, the easier it is to move the load. Examples
of second-class levers include: Wheelbarrow, nutcracker,
bottle opener.

Simple machines
Third Class Levers
A third-class lever has the effort located between the
fulcrum and the load as shown in the figure below. The
load moves in the same direction as the applied while the
effort is multiplied.

Simple machines
In the third-class lever, the load moves in the same
direction as the applied force and does not multiply the
applied force.
Examples of third-class levers include: tweezers and
shovel.

Simple machines
Mechanical Advantage of levers
The mechanical advantage of a lever is the ratio of the
effort arm to (EA) to the load arm (LA). It is calculated
by dividing the length of the effort arm by the length of
the load arm. Mechanical advantage is given by:
MA = or MA =
Where:
Effort Arm Length:
the distance from the fulcrum to where the force is
applied.
Load Arm Length:
the distance from the fulcrum to the load.

Simple machines
Velocity Ratio of Levers
From the definition of velocity ratio of a machine,
the velocity ratio of the lever is given by the ratio
of the effort arm to the load arm.
Velocity Ratio (VR) =
In simpler terms, velocity ratio tells you how
many times faster the effort moves compared to
the load.

Simple machines
Efficiency of Levers
The efficiency of a lever is the ratio of mechanical
advantage (MA) to its Velocity ratio (VR), expressed as a
percentage. Efficiency of a lever can be calculated using
the formula:
Efficiency () = x 100%
Efficiency represents how much of the input energy is
converted into useful output energy.
Take away points:
A mechanical advantage greater than 1 means the lever
multiplies the input force, making it easier to lift a heavy object.
A mechanical advantage less than 1 means the lever requires
more force to lift the object than it would without the lever.

Simple machines
Pulleys
A pulley is a simple machine composed of a wheel
mounted on an axle. The outer rim of the pulley is
grooved to enable a rope, cable or belt to run inside the
groove as shown in the figure below

Simple machines
Types of Pulleys
Pulleys are classified into different types
depending on the number of ropes and
arrangement. There are three basic types of
pulleys:
a) Fixed pulleys
b) Movable pulleys
c) Compound pulleys
d) Block and tackle system.

Simple machines
Fixed Pulleys
A fixed pulley is attached (hinged) to a stationary or
fixed point, like a wall or ceiling, such that it cannot
move up and down with the rope and load.

Simple machines
The effort applied is equal to the weight of the
load moved. This means that there is no
multiplication of force. Thus, a fixed pulley has a
mechanical advantage of 1. The figure below
shows the fixed pulley.
It changes the direction of the force applied, the
effort and the load move in opposite directions
making it easier to pull down on a rope to lift the
load.

Simple machines
Movable Pulley
A movable pulley is the one that is free to move up and
down along with the load as shown in the figure below

Simple machines
Movable Pulley
In a movable pulley the effort (applied force) and the load
moves in the same direction. The movable pulley
multiplies the effort applied. The mechanical advantage of
a movable pulley is greater than 1.
Compound pulley system
A compound pulley system comprises of fixed and
movable pulleys. A compound pulley consists of two or
more pulleys. The number of pulleys varies from one
pulley system to another as demonstrated in the figures
below.

Simple machines
The block and Tackle system
A block and tackle is a pulley configuration that
consists of two or more drums or blocks used to
increase pulling force.
Each drum or block contains one or more wheels
rotating on the same axle. The rope loops back
and forth between the drums passing through the
individual wheels within the drum as shown in the
figure below:

Simple machines
Mechanical Advantage of Pulleys
The mechanical advantage (MA) of a pulley
system is is calculated by comparing the output
force (the weight being lifted) to the input force
(the force applied to lift the weight).
For a simple pulley, the mechanical advantage is
given by the formula:
MA = =

Simple machines
Mechanical Advantage of Pulleys
The mechanical advantage of a pulley system can
also be determined by counting the number of rope
segments supporting the load. For example:
 A single fixed pulley has an MA of 1 (it changes
the direction of the force but does not provide
any mechanical advantage).
 A single movable pulley has an MA of 2 (the
load is supported by two segments of rope).
 A block and tackle system (a combination of
fixed and movable pulleys) can have a higher
MA, depending on the number of pulleys used.

Simple machines
Velocity Ratio of pulleys
The velocity ration of a pulley is given by:
VR =
In a simple pulley system (one fixed and one movable
pulley), the velocity ratio is equal to the number of ropes
supporting the load
For example, if there are two ropes supporting the load, the
velocity ratio is 2.
For compound pulley systems (multiple pulleys), you can
calculate it by counting the number of supporting ropes
For instance, a system with four ropes supporting the load has a
velocity ratio of 4.

Simple machines
Velocity Ratio of pulleys
For systems involving different sized pulleys, the velocity
ratio can be calculated as the ratio of the diameters of the
driven pulley to the driver pulley
For example, if the driven pulley has a diameter twice that
of the driver pulley, the velocity ratio is 2.
Note: A single movable and compound pulley consisting
of a single fixed pulley and a single movable pulley have
the mechanical advantage of 2.

Simple machines
Inclined Plane
An inclined plane is a smooth flat rigid surface slanted at an angle 
to the horizontal. The inclined plane makes it easy to move a load from
a lower to a higher position. This is achieved by reducing the effort and
increasing the distance through which the effort is applied as shown in
the figure below

Simple machines
Mechanical Advantage of an inclined plane
The mechanical advantage of an inclined plane is equal to
the ratio of the slanted Length (Ed) to the vertical height
(Ld) of the plane
MA =

Simple machines
Velocity Ratio of an inclined plane
The velocity ratio of the inclined plane is given by:
VR =
Example
A force of 600N was used to move a load of 3000N up an
inclined plane. Given that a slanted height and the vertical
height of the plain are 18m and 3m respectively,
determine;
(a) the velocity ratio of the plane
(b) the mechanical advantage of the plane
(c) the efficiency of the plane

Simple machines
Solution
Given that,
Effort = 600 N
Load = 3000 N
Slanted length = 8 m
Vertical Height = 3 m
a) The velocity ratio (VR) of the plane
VR =
=
VR = 6

Simple machines
a) The mechanical Advantage of the plane
Mechanical Advantage (MA) =
=
= 5
c) The efficiency of the plane
Efficiency =
=
= 83.33 %

Simple machines
a) Screw jack
The screw jack consists of a rod that is usually made up of a hard
metal. The contains spiral grooves that are separated by raised
bands known as threads. There are two types of screws:
- Fastening screw: example is the screw jack that is used to lift a
car when changing tyres.
- Lifting screw. An example of fastening screw. An example of
fastening screw is a bolt and nut.
Threads

Simple machines
The distance between two successive threads is
known as a pitch. The pitch of a screw jack is given
by:
Pitch =
For example, if there are 10 threads in 1 cm of the rod,
then the pitch of the screw jack is:
Pitch =
= 0.1 cm

Simple machines
Mechanical Advantage of a screw
Mechanical advantage of a screw depends on its
pitch. Without considering friction, the mechanical
advantage of a screw jack is the ratio of the
circumference of the circle made by the turning
arm to the pitch of the screw.
MA =
The mechanical advantage a screw jack is very
large because the pitch is very small compared
to the length of the arm.

Simple machines
Velocity Ratio (VR) a screw jack
VR of a simple machine =
Hence, the velocity ratio of a screw jack is given by:
VR =
VR = or VR =
where R is the radius of the circle made by the turning arm
(Length of the effort lever)
Therefore, VR = where P is the distanced moved by
the screw

Simple machines
Example
A screw jack has 5 threads per centimetre. If the length of
the turning arm is 20 cm, determine the velocity ratio of
the screw jack. (Take =3.14)
Solution
Given that,
Number of threads = 5 cm
Length of turning arm (R) = 20 cm
 = 3.14
Velocity Ratio (VR) = ?
VR =

Simple machines
But
circumference = 2 R
= 2 x 3.14 x 20cm
= 125.6 cm
Pitch =
=
= 0.2 cm
VR =
VR = 628

Simple machines
Example
A screw jack which has 5 threads per centimetre is used to
lift a car weighing 2000 N. If the length of the turning arm
is 40cm, and the efficiency of the screw jack is 90% find:
a) the velocity ratio of the jack
b) the mechanical advantage of the jack
c) the minimum force required to raise the car
Solution
Number of threads = 5 cm
Length of turning arm (R) = 40 cm
Load = 2000 N
Efficiency = 90%
 = 3.14

Simple machines
a) Velocity Ratio (VR)
VR =
Circumference = 2R
= 2 x 3.14 x 40
= 251.2
Pitch =
= 0.2 cm
VR =
= 12.5

Simple machines
b) Mechanical Advantage of the screw jack
From
Efficiency =
MA = VR x Efficiency
= 12.56 x
= 1130.4
The mechanical advantage of the screw jack is
1130.4,

Simple machines
c) Minimum force required to raise the car
MA =
Effort =
=
= 17.7 N

Simple machines
Wheel and Axle
A wheel and axle is a simple machine that consists of a
wheel and a rod (axle) that rotates with it. When you apply
a force to the wheel, it rotates the axle, which can then
move a load or perform a task. The wheel has a larger
radius than the axle.

Simple machines
 The wheel and axle allow for a smaller force applied to the
wheel to move a larger load attached to the axle.
 The wheel and axle can act as a force multiplier or a
speed multiplier, depending on how it's used.
 Applying a force to the wheel can result in a greater force
on the axle (force multiplier), or a force on the axle can
result in a greater distance of movement of the wheel
(speed multiplier).
 Examples include steering wheels, doorknobs, and
screwdrivers,
Examples:
o Steering Wheel: A small force on the steering wheel (wheel)
can move the car's wheels (axle) with greater ease.

Simple machines
o Doorknob: Turning the doorknob (wheel)
rotates the spindle (axle) to open or close
the door.
o Screwdriver: Turning the handle (wheel) of
a screwdriver rotates the shaft (axle) to drive
screws

Simple machines
Mechanical Advantage of a Wheel and axle:
The mechanical advantage of a wheel and axle is given
by:
Mechanical Advantage (MA) =
Velocity Ratio of a Wheel and axle
As already seen, one complete turn of the wheel results in
one complete turn of the axle. Since the effort is applied at
the wheel.
VR of wheel & Axle =

Simple machines
VR =
VR =
Therefore, the velocity ratio of a wheel and axle
machine is the ratio of the radius of the wheel to
the radius the axle.
Example
A wheel and axle has a velocity of 6. Determine the
radius of the wheel if the radius of the axle is 12.

Simple machines
Solution
Given that,
Velocity ratio (VR) = 6
Radius of the axle (r) = 12cm
Radius of the wheel (R) = ?
VR of wheel =
R = VR x r
R = 6 x 12 cm
= 72 cm

Simple machines
Example
A wheel and axle with efficiency of 90% is used to
raise a load of 10000 N. The radius of the wheel
is 40 cm while that of the axle is 5 cm. Calculate,
i) the velocity ratio of the wheel and axle
ii) the mechanical advantage of the wheel and
axle
iii) the effort required to raise the 10000N load
Solution
Given that,

Simple machines
Load = 10000 N
Radius of the wheel (R) = 40 cm
Radius of the axle (r) = 5 cm
Efficiency = 90%
i) Velocity Ratio (VR) of the wheel and axle
VR =
=
VR of wheel & axle = 8

Simple machines
ii) Mechanical Advantage
Efficiency = =
MA = VR x Efficiency
= 8 x
= 7.2

Simple machines
iii) Effort Required to raise 10000N load
MA =
Effort =
=
Effort = 1388.9 N

SIMPLE MACHINES-ENGINEERING SCIENCE.pptx

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