PHYSICS FORM TWO-Topic 5: SIMPLE MACHINE

 

Simple MachinesTOPIC 5: SIMPLE MACHINES

A simple machine is a non-powered mechanical device that changes the
direction or magnitude of a force. In general, they can be defined as
the simplest mechanisms that use mechanical advantage (also called
leverage) to multiply force. A simple machine uses a single applied
force to do work against a single load force. Ignoring friction losses,
the work done on the load is equal to the work done by the applied
force.Concept of Simple MachinesNowadays
man can do many things without necessarily using much of his own
energy. Many can fly by using aeroplane, raise a heavy load, and drive a
nail into wood by using a hammer. All of these are achieved using
machines.The Concept of a Simple MachineExplain the concept of a simple machineMachine:Machine
is any device, which is used for simplifying work. Examples of machines
are: a crowbar, a seesaw, a claw hammer, a pulley and an inclined
plane.Types of machine:There are two types of machines

1. Simple machine
2. Complex machine

What is simple machine?Simple
machine is any device, which requires single force in operation to
simplify work e.g. Claw hammer, a pulley, and an inclined plane. In a
simple machine, a force is applied at one convenient point to overcome
another force acting at another point.Simple Machine

The
diagram above shows a stone being shifted. Force is applied at one end
of the bar in order to exert an upward force on the stone. The down ward
force is called effort and the weight of the stone is called load.Effort is the force used to operate a machine. And Load is the resistance, which machines overcome.The terms Applied in Simple MachineExplain the terms applied in simple machineTerms used in simple machineMechanical AdvantageMechanical advantage (M.A) is the ratio of load and effortMathematically:–

Mechanical advantage has no SI unit.Example 1Example 1A simple machine raises a load of 100N by using a force 50N. Calculate the mechanical advantage.Solution;–

Example 2Example 2.A force of 20N raises a load of 100kg. Calculate mechanical advantage of the machine.Solution

Velocity ratioVelocity
ratio is the ratio of distance travelled by effort and distance
travelled by load. Or Velocity ratio is the distance moved by effort per
distance moved by load.–

Example 3

ExampleIn
a certain machine a force of 10N moves down a distance of 5cm in order
to raise a load of 100N through a height of 0.5cm calculated the
velocity ratio (V.R) of the machine.Solution:Distance by Effort = 5cmDistance moved by load = 0.5cm.From–

Efficiency of MachineEfficiency of machine is the ratio of work output and work input.Work output = Load x Distance moved by LoadWork input = Effort x Distance moved by Effort–

A perfect machine has 100% Efficiency. Therefore M.A is equal to V.R.Note:
most machines are imperfect machines since efficiency is less than 100%
this is due to the friction and heat and loss of energy.Example 4Example1: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:

1. M.A
2. V.R
3. Efficiency of machine

Solution:Date given:

Effort = 10NLoad = 100NDistance moved by effort = 5cmDistance of load= 0.5cmEfficiency machine?Efficiency of machine () = M.A x 100%–

Different Kinds of Simple MachineIdentify the different kinds of simple machinesDifferent Kinds of Simple MachinesTypes of Simple Machines

• LEVERS
• PULLEYS
• INCLINED PLANE
• THE SCREW AND SCREW JACK
• WHEEL AND AXLE
• HYDRAULIC PRESS

LeversA lever is a rigid body, which when used turns about a fixed point called a fulcrum or pivot. It is used to shift heavy loads.The Three Classes of LeversIdentify the three classes of leversClasses of LeversThere are three classes of levers:

1. First class lever
2. Second class lever
3. Third class lever

First Class LeverIs
the class lever whereby the pivot is between load and effort. Examples
of first class levers are: see-saw, crowbar, pair of scissors and claw
hammer.First Class Lever

Second Class LeverIs the class lever where by load is between pivot and load. eg, wheel barrow, tongs, nutcracker, bottle opener.Second Class Lever

Third Class LeverIs the class lever whereby Effort is between load and pivot. Eg, fishing load.Third Class Lever

The Mechanical Advantage, Velocity Ratio and Efficiency of LeverDetermine the mechanical advantage, velocity ratio and efficiency of leverMechanical Advantage of LeverM.A =X/YM.A =Load arm/Effort armLevers in Daily LifeUse of levers in daily lifeThe reason for a lever is that you can use it for amechanical advantagein lifting heavy loads, moving things a greater distance or increasing the speed of an object.

• Increase force:You can increase the applied force in order to lift heavier loads.
• Increase distance moved
• Increase speed: You can increase the speed that the load moves with Class 1 or Class 3 levers.

PulleysA pulley is a grooved wheel, which is free to turn about an axle that is fixed in a frame.Different Pulley SystemIdentify different pulley systemsTypes of Pulleys

1. Single fixed pulley
2. Single movable pulley
3. The block and tackle system of pulley

Single fixed pulleyThis
is the type of pulley whereby effort is applied at one end of the tape
in order to raise the load. Single fixed pulleys are used to raise small
objects e.g. Flags. Consider the diagram below:-Single fixed Pulley

M.A and V.R of single fixed pulley

Single Movable PulleySingle movable pulley is the one which load is multiple of Effort.Load = 2EConsider the following diagramSingle movable pulley

M.A and V.R of single movable pulley

The block and tackle system of pulleyWhen
two or more pulleys are fixed in a frame, a block is formed. The
pulleys in each block are fixed independently on separate axles.
Consider the diagram below:-Block and tackle system of pulley

Note; mechanical advantage = Load/EffortVelocity ratio of Block and tackle system is equal to the number of pulleys.Example 5Example 1A
block and tackle pulley system has a velocity ratio of 4. If a load of
200N is raised by using a force of 75N. Calculate the mechanical (i)
Advantage of the system (ii) efficiency of the system.Solution;Data givenVelocity ratio (V.R) = 4Load = 200NEffort = 75NM.A =?M.A and Efficiency of block and tackle pulley system

Mechanical Advantage, Velocity Ratio and Efficiency of Pulley SystemDetermine mechanical advantage, velocity ratio and efficiency of pulley systemVR of block and tackleWhen
the lower two pulleys move up a vertical distance y, corresponding to
movement y of the load L, each pulley releases a length y of the rope on
each side giving a total length 2y.With
all this movement of pulleys, the effort E is moved down a distance of 2
x 2y or 4y.Thus, VR = (distance moved by effort)/(distance moved by
load at the same time) = 4y/y = 4VR = Number of pulleys of the system.Efficiency of block and tackleFrom, ε = MA/VR X 100%ε = (number of pulleys )/(number of pulleys) x 100%Note:Then, for a perfect block and tackle pulley system, ε = 100%.But
in practical case the MA is less than the number of pulleys, hence the
efficiency of pulleys system is less than 100% due to friction losses.MA of block and tackle.From MA = load/effortMA = (Effort x Number of pulleys of the system)/EffortMA = Number of pulleys of the system.Pulley in Daily LifeUse of pulley in daily lifeUses of PulleysPulleys
have been used for lifting for thousands of years. The most prevalent
and oldest example are their uses on ships and boats. The block and
tackle have been a key tool for raising sails and cargo. Another major
use for pulleys is withcranes.Pulleys
have been used also in modern times with various machines and systems.
Even in the space age, pulleys have been an important aspect for the
construction and operations of spacecraft and aircraft. It is with a
pulley system that rudders for an aircraft are controlled.Pulleys are used in everyday life, from vehicles to moving equipment such as cranes.Inclined PlaneThe Concept of Inclined PlaneState the concept of inclined planeAn
inclined plane is a sloping plane surface, usually a wooden plank used
to raise heavy load by pulling or pushing them along the surface of the
plane.An inclined plane

Mechanical Advantage, Velocity Ratio and Efficiency of Inclined PlaneDetermine mechanical advantage, velocity ratio and efficiency of inclined planeMechanical advantage of the inclined planeM.A = Load/EffortV.R of inclined plane = Length of the plane/Height of the planeExample 6Example:A
loaded wheelbarrow of weight 800N is pushed up an inclined plane by a
force of 150N parallel to the plane. If the plane rises by 50cm for
every 400cm distance measured along the plane, find the velocity ratio,
mechanical advantage and efficiency of the plane.Solution:Data givenLoad = 800NEffort = 150NLength of plane = 400cmHeight of the plane = 50cmV.R =?M.A=?=?M.A, V.R and Efficiency of Inclined Plane

Inclined Plane in Daily LifeApply inclined plane in daily lifeApplication of Inclined PlaneInclined planes are widely used in the form ofloading rampsto
load and unload goods on trucks, ships, and planes.Wheelchair rampsare
used to allow people inwheelchairsto get over vertical obstacles without
exceeding their strength.Escalatorsand slantedconveyor beltsare also
forms of inclined plane.In
a funicular or cable railway a railroad car is pulled up a steep
inclined plane using cables. Inclined planes also allow heavy fragile
objects, including humans, to be safely lowered down a vertical distance
by using the normal force of the plane to reduce the gravitational
force. Aircraft evacuation slides allow people to rapidly and safely
reach the ground from the height of a passenger airliner.Screw JackThe Structure of a Screw JackDescribe the structure of a Screw JackStructure of Screw JackA
screw Jack consist of a cylinder with a spiral ridge runs round it. The
spiral is called the thread (T) and the distance between two adjacent
threads is called the pitch (p) of the screw.Consider the following diagram.The bolt and screw

The Screw Jack

The Mechanichal Advantage, Velocity Ratio and Efficiency of a Screw JackDetermine the mechanical advantage, velocity ratio and efficiency of a Screw JackMechanical advantage of the screw jackM.A = Load/EffortVelocity ratio (V.R)V.R = Circumference of circle of radius (R)/Pitch of screwV.R = 2pR/PExample 7Example 1A screw jack with a pitch of 0.2cm and a handle of length 50cm is used to lift a car of weight 1.2 x 104N. If the efficiency of the screw is 30%, find:

1. The velocity ratio and mechanical Advantage of the machine
2. The effort required to raise the car

Solution;Date givenPitch = 0.2cmRadius= 50cmLoad = 1.2 x104NEfficiency of jack =30%V.R=?M.A=?Effort+?–

The Screw Jack in Daily LifeUse the Screw Jack in daily lifeScrew
jacks are used to lift heavy loads despite the large friction they
produce. The heavier the load the higher the friction force. They are
self-locking, meaning that when the applied force is removed, they do
not rotate backwards. They are used in adjusting workplace chairs and
tables. They also help in pulling and pushing machine equipment as well
as tightening mechanical parts.Wheel and AxleThe Structure of a Wheel and AxleDescribe the structure of a wheel and axleStructure of Wheel and AxleA
wheel and axle is a simple machine that consists of a wheel and axle
mounted with the same axis of rotation. The radius of the wheel is
always greater than that of the axle.Consider the diagram below:Wheel and Axle

The Mechanical Advantage, Velocity Ratio and Efficiency of a Wheel and AxleDetermine the mechanical advantage, velocity ratio and efficiency of a wheel and axleMechanical advantage of Wheel and AxleM.A = Load/EffortVelocity ratio ( V.R)= radius of wheel (R)/radius of axle (r)Example 8Example 1A
wheel and axle of efficiency 80% is used to raise a load of 2000N. If
the radius of the wheel is 50cm, and that of the axle is 2cm, calculate

1. The velocity ratio and mechanical Advantage of machine
2. The effort required to overcome the load

SolutionData givenEfficiency = 80%Load = 2000NRadius of wheel (R)= 50cmRadius of axle (r) = 2cmV.R=?M.A=?Effort?–

The Wheel and Axle in Daily LifeUse the wheel and axle in daily lifeApplication of Wheel and AxleWheels
help people do work in two ways. First, likeleversorinclined planes,
wheels allow you to do something easy for a longer time, instead of
doing something hard for a shorter time. If you turn a large wheel fixed
to an axle, the axle will also turn. You can turn the large wheel
easily (but it takes a lot of turning to go all the way around).The
axle will go around a much shorter distance, but with more force. So
you can use a wheel to create a mechanical advantage – you can turn
something heavy, by spinning a large wheel attached to an axle that is
attached to the heavy thing.That’s
how a pencil sharpener works. Or, you can do it the other way around –
use a lot of force to turn the axle, and that will spin the wheels
really fast. That’s what cars do.Wheels are the most important part of
pottery wheels, wagons and cars, but also ofwheelbarrows,spinning
wheels, water wheels, windmills, andpulleys.Also,
wheels on a wagon only touch the ground at one spot at a time, keeping
the rest of the wagon off the ground. This makes lessfriction, so that
the wagon is easier to move than if you were pulling it along like a
sled.Hydraulic pressThe Structure of Hydraulic PressDescribe the structure of Hydraulic PressStructure of Hydraulic PressA
hydraulic press is a machine that has a bed or a plate in which the
metallic material is placed so that it can be crushed, straightened or
moulded.Mechanical Advantage, Velocity Ratio and Efficiency of a Hydraulic PressDetermine mechanical advantage, velocity ratio and efficiency of a Hydraulic PressIn
hydraulic press small force (Effort) applied on the small piston is
used to overcome a much greater force (load) on the large piston.When
a small effort (E) is applied downwards on the effort piston of radius
(r) the load piston of radius (R) lifts the load (L).Consider the diagram below:Hydraulic Press

By the principle of transmission of pressure in liquid, the pressure on effort piston is equal to the load piston.–

VELOCITY RATIO OF HYDRAULIC PRESSIf
friction is neglected the work done by the effort E is equal to the
work done on the load (L). So if the effort piston is moved by distance x
and the load piston raised up by a corresponding distance Y, it
follows:–

Note: Due to friction, efficiency of the hydraulic press is not 100%The Hydraulic Press in Daily LifeUse the Hydraulic Press in daily lifeUses of a Hydraulic PressA
hydraulic press is used for almost all industrial purposes. But
basically it is used for transforming metallic objects into sheets of
metal. In other industries, it is used for the thinning of glass, making
powders in case of the cosmetic industry and for forming the tablets
for medical use. The other common uses of the hydraulic presses are as
follows:For crushing carsA
hydraulic press is the heart of any car crushing system. In this
process, a hydraulic motor applies a large pressure on the fluids into
the cylinders. The fluid pressure makes the plates rise and with a large
force, the plate is driven on the car thereby crushing it.Fat-free cocoa powderWhile
processing the cocoa beans, a liquid known as chocolate liquor is
derived. For making fat-free cocoa powder, this liquid is squeezed out
in a hydraulic press. After this stage, this liquid is processed further
to make a powder. The powder thus derived is cocoa powder, which is
fat-free.For sword makingIn the process of making swords, a hydraulic press is used to give a flat shape to the raw steel.