TOPIC 5: SIMPLE MACHINE - PHYSICS NOTES FORM 2

Welcome to our website scholars.co.tz. In this article, are you looking for TOPIC 5: SIMPLE MACHINE – PHYSICS NOTES FORM 2, Download Full Notes Physics Notes Form Two Topic 3

SIMPLE MACHINE

WHAT IS MACHINES?

A machine is any device which is used to simplify work.

In a machine, a force is applied at one convenient point to overcome force acting at another point.

Simple Machine and complex Machine
A simple Machine is the one which involve one movement example; inclined plane

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

Six types of Simple Machine are;

Levers
Pulley
Inclined Plane
The Screw Jeck
Wheel and axle
Hydraulic Press

$C:\thlb\cr\tz\__i__images__i__\u1.jpg$

The figure above shows a load being lifted by using a crowbar. A downward force is applied at one and point of the crowbar in order to extend an upward force on the stone.

The upward force shifts the stone by one crowing its weight. The down ward force applied on the crowbar is called the effort and the weight of the stone is the load.

Effort – is defined as the force used to operate a machine.

Load – is the resistance which a machine overcomes.

Mechanical Advantage

In general a machine is designed in such a way that the applied force effort is less than the load.

The action of the load to the applied effort is a measure of usefulness of mechanical advantage (M.A) of a machine.

$C:\thlb\cr\tz\__i__images__i__\uu.jpg$

Since mechanical Advantage is a ratio of two forces it has no unit.

Example

1. 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.

Solution

Effort = 150N

Load = 600N

$C:\thlb\cr\tz\__i__images__i__\uuuu1.jpg$

Mechanical advantage = 4

Velocity Ratio:

In any machine, the movement of the effort causes the corresponding movement of the Load. The distance moved by each of these forces are measured with the ratio of the distance moved by effort to the distance moved by the load,it is called the velocity ratio (V.R of the machine)

$C:\thlb\cr\tz\__i__images__i__\v.jpg$

V.R is the ratio of two lengths (it has not unit)

Example:

1. In a certain machine a force of 10N moves down a distance of 2cm in order to raise a load of 10N through a height of 0.5cm. Calculate the velocity ratio of the machine.

$C:\thlb\cr\tz\__i__images__i__\vv.jpg$ Velocity ratio = 4

EFFICIENCY OF A MACHINE

Work input

Work input is the total workdone by effort

Work input = Effort x Effort distance

Work output

Work output is the total workdone on load

Work output = load x load distance

Efficiency is the ratio of work output to work input usually expressed in percentage.

efficiency is always less than 100%

This is due to energy loses due to friction.

$C:\thlb\cr\tz\__i__images__i__\neutral_1.jpg$ Neutral equilibrium

Application of equilibrium

1. Vehicles used in a car race have tyres wide apart to increase stability

2. Buses have luggage compartments on their lower parts so as to lower the centre of gravity

All practical machines have losses due to friction. Therefore in such case the work output will be less than the work in put.

$C:\thlb\cr\tz\__i__images__i__\vvv.jpg$

But work = force x Distance moved

$C:\thlb\cr\tz\__i__images__i__\ml.jpg$

Example

1. 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.

The mechanical advantages
The velocity ratio
The efficiency of the machine

Solution

Load = 3920N

Effort = 980N

Distance moved by the effort = 20m

Distance moved by the load = 3.5m

$C:\thlb\cr\tz\__i__images__i__\vvvvv.jpg$
Mechanical Advantage = 4

$C:\thlb\cr\tz\__i__images__i__\w.jpg$

velocity ratio = 5.71

$C:\thlb\cr\tz\__i__images__i__\ww2.jpg$

Efficiency = 70 %

TOPIC 5: SIMPLE MACHINE – PHYSICS NOTES FORM 2

LEVERS

Levers is a rigid body which when in use turns about a fixed point called a fulcrum or pivot.

It is used to shift heavy loads. A lever is designed such that a small force applied at one point overcomes a large force at another point. A lever is therefore a simple machine.

Classes of lever

Levers are divided in to three classes or orders namely, first class lever, second class lever and third class levers.

Classification of levers depends on the position of the fulcrum, load and effort.

1. First class lever

This is a class of lever whereas fulcrum between the load and effort.

Examples: claw hammer, crow bar and pair of scissors.

$C:\thlb\cr\tz\__i__images__i__\www1.jpg$

2. Second class lever

This is a class of lever whereas load is between the fulcrum and the effort.

Examples: wheel barrow, a bottle opener, nutcracker etc

$C:\thlb\cr\tz\iimagesi\wwww1.jpg$
3. Third class levers

This is a class of lever whereas effort between the fulcrum and the load.

Examples: tongs, fishing rod and a spade.

$C:\thlb\cr\tz\iimagesi\x.jpg$ Mechanical advantages of a lever

By considering the moments of the applied effort and load which is overcomed by the effort about the fulcrum.

$C:\thlb\cr\tz\__i__images__i__\xx.jpg$ From the figure above, the effort is first overcoming the load. From the principles of moments, it follows that;

The sum of clockwise moment = the sum of anti clockwise moment

Effort x Distance from Fulcrum to effort = load x Distance from fulcrum to load

$C:\thlb\cr\tz\__i__images__i__\xxx.jpg$
But

$C:\thlb\cr\tz\__i__images__i__\xxxx.jpg$

Pulleys

A pulley’s block consists of two or more pulleys in a wooden or metal frame.

A pulley is a grooved wheel which is free to turn about an axle fixed in a frame. There are about four types of pulleys which are;

The single fixed pulley
Single movable pulley
Movable pulley
Block and tackle system.

1. The 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.

$C:\thlb\cr\tz\__i__images__i__\single_pulley.JPG$

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 = tension (T) = load
$C:\thlb\cr\tz\__i__images__i__\y.jpg$

But load = effort = tension (T)

$C:\thlb\cr\tz\__i__images__i__\yy.jpg$

M.A = 1

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

$C:\thlb\cr\tz\__i__images__i__\yyy.jpg$

V.R = 1

2. The movable pulley

The pulley is free to move and can be in two arrangements show in figures (a) and (b) shown below. The first arrangement consists of single movable pulley the second arrangement consists of two pulleys in which one is fixed.

$C:\thlb\cr\tz\__i__images__i__\FIGURE_A_AND_B.png$

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;

$C:\thlb\cr\tz\__i__images__i__\yyyyyy.jpg$
M.A = 2

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.

$C:\thlb\cr\tz\__i__images__i__\z.jpg$

Velocity ratio = 2

3. Block and tackle

Block is made up of two of more pulleys fixed in a wooden or metal frame. The pulleys in each block are fixed on separate axles. One string is used.

It is tied to the top of the block and then passes around each of the pulleys. In block and tackle system pulleys, it is only the lower block which is free to move.

$C:\thlb\cr\tz\__i__images__i__\zz.jpg$

Figure, the tension in each section of the rope is equal the effort applied at the free end. The total tension in the rope sections supporting the movable block is equal to the load. That is load L=4T since there are four sections.

The tension (T) in the string equals to the load applied effort (E), that is E = T, then it follows that:-

Load (L) = 4 x Effort, which means that the load is equal to the effort multiplied by a number of rope sections.

In figure (b)

Load = number of rope sections that supports the load x Effort (number of pulley)

Load = 3 x effort

$C:\thlb\cr\tz\__i__images__i__\zzz.jpg$

M.A. = 3

Efficiency of block and tackle system

The efficiency (e) of a machine is given as;

$C:\thlb\cr\tz\__i__images__i__\zzzz.jpg$

For block and tackle system

M.A = Number of pulleys and

V.R = Number of pulleys of the system

Example

1.A block and tackle pulley system has a velocity ratio of 4. If a load of 100N is raised by using a force of 50 N. Calculate the mechanical advantage and efficiency of the system.

Solution

Data given

Velocity ratio = 4

Load = 100N

Effort = 50N

$C:\thlb\cr\tz\__i__images__i__\ab1.jpg$ M.A = 2
$C:\thlb\cr\tz\__i__images__i__\abb.jpg$

Efficiency = 50%

Example 2

2. A simple pulley system has velocity ratio of 3. Its efficiency is 90%, what load can it raise by an effort of 100N.

Solution

Data given

V.R = 3

E = 90%

E = 100N

M.A =?

$C:\thlb\cr\tz\__i__images__i__\abbbb.jpg$ M.A = 2.7

Load = M.A x Effort

= 2.7 x 100

Load = 270N

The inclined plane

An inclined plane is the simple machine formed by a sloping plane surface, used to raise heavy loads by pulling, pushing or dragging along the surface of the plane.

Force is applied parallel to the plane, hence the effort moves a distance equal to the length of the plane.

$C:\thlb\cr\tz\__i__images__i__\bb3.jpg$

The load rises up a distance equal to the vertical height of the plane, which is AB.

$C:\thlb\cr\tz\__i__images__i__\BBB2.jpg$

Neglecting the friction, the work done by effort is equal to the work done on the load.

Then E x length of inclined plane = L x height of inclined plane
$C:\thlb\cr\tz\__i__images__i__\BBBB2.jpg$

Example

1. A loaded wheel barrow weight 800N is pushed up an inclined plane by a force of 150N parallel to the plane. If the plane rises 50cm for every 400cm length of the plane, find the velocity ratio, mechanical advantage and efficiency of the plane.

Solution

Data given

L = 800N

E = 150N

Height of inclined plane = 50cm

Height of inclined plane = 400cm

$C:\thlb\cr\tz\__i__images__i__\CCC3.jpg$ $C:\thlb\cr\tz\__i__images__i__\CCCC2.jpg$

Efficiency = 66.25

The screw jack

A screw jack consists of a rod in which there is thread. The thread of the screw is regarded as continuous inclined plane mapped round a cylinder. The distance between two successive threads is called the pitch of the screw.

$C:\thlb\cr\tz\__i__images__i__\CCCCC22.jpg$

The thread of a screw jack threads into base is turned by means of handle. The load acts on top of the screw, at the same time effort is applied to the handle. When the handle makes one complete turn, the distance moved 2R. The effort raises the load through the distance equal to the pitch p of the screw, making the length of the handle then velocity ratio can be found as follows;

$C:\thlb\cr\tz\__i__images__i__\dd3.jpg$

R = Radius

P = Pitch

Example

1. The handle of a screw jack is 35cm long and the pitch of the screw is 0.5cm. What force must be applied at the end of the handle when lifting a load of 2200N? If the efficiency of jack is 40%

Solution

Data given

R = 35cm

P = 0.5cm

L = 2200N

E = 40%

$C:\thlb\cr\tz\__i__images__i__\e2.jpg$

V.R = 440

$C:\thlb\cr\tz\__i__images__i__\ddd4.jpg$ M.A = 176

$C:\thlb\cr\tz\__i__images__i__\dddd6.jpg$

Effort = 12.5N

WHEEL AND AXLE

A wheel and axle is a simple machine which 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.

When in operation, the effort E is applied to a string wound round the wheel while the load is attached to a string round the axle in opposite direction to that of the string in the wheel.

$C:\thlb\cr\tz\__i__images__i__\ddddd2.jpg$
R = 5 and r = 1

In figure, R is the radius of the wheel r is the radius of axle. When the wheel completes one turn the axle rotates once. Thus the effort and the load moves the distances.

2πR and 2πr

E = 2πr wheel

C = 2πr axle

$C:\thlb\cr\tz\__i__images__i__\ee3.jpg$ V.R = R/r

Example

1. A wheel and axle of efficiency of 80% is used to raise a load of 2000N. If the radius of the wheel is 50cm and that of the axle is 20m. Calculate:-

The velocity ratio and mechanical advantage of the machine.
The effort required to overcome the load

Data given

Load = 2000N

E = 80%

R = 50cm

r = 2cm

V.R =?

M.A =?

Effort =?
$C:\thlb\cr\tz\__i__images__i__\eee4.jpg$

Velocity ratio = 25

$C:\thlb\cr\tz\__i__images__i__\eeee2.jpg$

Mechanical advantage = 20

b) M.A = 20

Load = 2,000N

Effort = ?

M A = Load
Effort

Effort = Load
MA

Effort = 2000
20

Effort = 100N

MECHANICAL ADVANTAGE, VELOCITY RATIO, AND EFFICIENCY OF HYDRAULIC PRESS

In a hydraulic press a small force (effort) applied on the small piston is used to overcome 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 lift the load L.

By principle of transmission of pressure in liquids, the pressure on effort piston equal to that on the load piston.

$C:\thlb\cr\tz\__i__images__i__\ff4.jpg$ $C:\thlb\cr\tz\__i__images__i__\Rr1.png$