# MACHINES

Machines make our work simpler. It is a force producing device by which a large force called load can be overcome by a small applied force called effort

## Terminologies Used In Machines

1. FORCE RATIO (MECHANICAL ADVANTAGE )
2. VELOCITY RATIO
3. EFFICIENCY

We define effort as the force applied to a machine and load as the resistance overcome by the machine. The ability of a machine to overcome a large load through a small effort is known as its mechanical advantage .It is given by

The mechanical advantage of a machine is influenced by friction in parts

## VELOCITY RATIO (V.R)

The velocity ratio is the ratio of distance moved by the effort and load in the same interval

V.R = Distance moved by effort

The velocity ratio depends on the geometry of the machine

## EFFICIENCY (E)

The efficiency of a machine is defined as

Ef =Useful work done by the machine X 100

Work put into the machine

Work = force xÂ  distance

Effort x distance moved by effort

Then V.R =M.A

## TYPES OF MACHINES

1. LEVER

This is the simplest form of machine. ItÂ  consistÂ  of a rigid rodÂ  pivoted about aÂ  pointÂ  called the fulcrum F with a smallÂ  effort applied at one endÂ  of theÂ  lever to overcomeÂ  a largeÂ  load LÂ  at the other end . There are various types of lever depending on theÂ Â  relative positions of the load, effort and fulcrum.

E x a = L x bÂ Â  which is given

L =Â  aÂ  =M.A

EÂ Â Â Â  b

a/b = V.R

Examples of first class lever are the crowbar, pair of scissors or pincers, claw hammer, see-saw ,pliers etc

In second order lever , the load is between the fulcrum and effort

Examples are wheel barrow, nut cracker tarp door , an oar etc .

In the third order lever, the effort is between the fulcrum and the load . Human fore arm ,Â  laboratory tong etc.

## 2.Â Â Â Â  WHEEL AND AXLE

It consists ofÂ  a largeÂ  wheelÂ  to which a rope or string is attached and an axleÂ  or small wheelÂ  with the ropeÂ  or stringÂ  wound roundÂ  itÂ  inÂ  opposite direction . The load to be lifted is hung at the free end of the rope on the axle whileÂ  the effortÂ  is applied at the end of the rope on the wheel . For each complete rotation the load and the effort move through distance equal to the circumference of the wheel and axle respectively.

The principle of wheel and axle is used in brace screw driver but spanner windless and gear-boxes

1. GEAR WHEELS

InÂ  gear boxes , thereÂ  are toothed wheels of differentÂ  diameter interlockedÂ  to give turning forceÂ  at low speedÂ  depending on whichÂ  gearÂ  is the driverÂ  and which is the driven

V.R = No of teeth on driven wheel ( A)

No of teeth on driving wheel (B)

## 4.Â Â Â Â  THE HYDRAULIC PRESS

TheÂ  machine isÂ  widely usedÂ  forÂ  compressingÂ  wasteÂ  paper and cottonÂ  intoÂ  compact balesÂ  forging different alloys intoÂ  desirable shape etc .It s work is based on Pascalâ€™s principle whichÂ  statesÂ  thatÂ  pressure is transmitted equally in fluid Oil isÂ  the liquidÂ  normallyÂ  used in hydraulic press

## 5.Â Â Â Â  THE WEDGE

The wedge is a combination of two inclined planes. It is usedÂ  to separate bodies whichÂ  are held together by largeÂ  force .Examples of wedge type of machines are axes chisels knives etc.

M.A = Â X1 =Â Â  Slant height of wedge

X0Â Â Â Â Â  Thickness of wedge

## 6.Â Â Â Â  PULLEY

A simple pulley is a fixed wheel hung on a suitable support with a rope passing round its groove.

BLOCK AND TACKLE (PULLEY)

This isÂ Â  theÂ  more practicalÂ  systemÂ  of pulleys in which one orÂ  moreÂ  pulleyÂ  are mounted onÂ  the same axleÂ  withÂ  one continuous ropeÂ  passingÂ  all-round the pulleys

## EFFECTS OF FRICTION ON MACHINE

Work is always wasted in machines to overcome the frictional forces present between the moving parts and also to liftÂ  to part of the machine. The greater the friction, the greater the effort required and the smaller the M.A. M.A depend on friction but depend on the geometry of moving parts.

The efficiency of nearly all the machines varies with the load and the load and effort are related by : E = al + b ( a and bÂ  are constant ).ThisÂ  is called linear law forÂ  a machine .ItÂ  followsÂ  that E is proportional to L .TheÂ  valueÂ  to give us the effort required toÂ  operateÂ  theÂ  machineÂ  moving part onlyÂ  if no load isÂ  presentÂ  whileÂ  A gives usÂ  the measureÂ  of the friction present

= Â M.A xÂ  100

V.R

In practical machines the efficiency is usually less than 100% because of friction in the moving parts of the machine.

(1)INCLINED PLANE: ThisÂ  is in form of a slopingÂ  plank commonly used to raise heavy load such asÂ  barrels of oil withÂ  little applied effort thanÂ  by liftingÂ  it vertically .

V.R = Distance moved by effort

= x /h ; V.R = 1/ sin Î¸

## THE SCREW

Geometrically speaking the screw is an inclined plane wrapped round a cylinder to form aÂ Â  thread. The distance between successive threads on a screw is called its pitch. For one complete revolutionÂ  ofÂ  screwÂ  throughÂ  anÂ  effort ,Â  the loadÂ  moves a distance equalÂ  to itsÂ  pitchÂ  e.g.Â  screwÂ  jackÂ  nutÂ  and bolt

In a screw jack where length of the operating handle is a, the effort moved a distance equal to the pitch P.

Thus V.R= -2Ï€a

P

= 2Ï€r

P

If frictional forces are negligible

## ONLINE WORK

1. (a) What is a machine? (b) Explain why a machine can never be 100% efficient.
2. Define the following terms as applicable to machine (a) velocity ratio (ii) mechanical advantage (iii) efficiency
3. A pulley with velocity ratio of 5 is used to lift a load of 400N through a vertical height of 8m by exerting an effort of 100N. Calculate the: (a) work done by the effort (b) efficiency of the pulley system

## ASSIGNMENT

SECTION A

1. The statement that the mechanical advantage of machine is 3 means that the (a) efficiency is 33 (b)Â  effort is three times as large as the load (c) mechanical advantage is three times as large as velocity ratio (d) ratio of effort to load is 1:3
2. In the diagram below XY represents a plank used to lift a load from a point X on the ground onto a horizontal platform YP.

What is the velocity ratio of the plank? (a) Â (b) (c) Â (d)

1. A machine with a velocity ratio of 30 moves a load of 3000N when an effort of 200N is applied. The efficiency of the machine is (a) 30% (b) 50% (c) 60% (d) 75%
2. The efficiency of a wheel and axle system is 80% and the ratio of radius of wheel to radius of the axle is 4 : 1, In order to lift a mass of 20kg,the effort required is (a) 60N (b) 62.5N (c) 32.5N (d) 250
3. The velocity ratio of an inclined plane whose angle of inclination is ÆŸ is (a) sin ÆŸ (b) cos ÆŸ (c) tan ÆŸ (d) 1/sin ÆŸ
4. Which of the following is not an example of levers of the first order? (a) crow bar (b) Nutcracker (c) scissors (d) pliers
5. A body of mass 7.5kg is to be pulled up along a plane which is inclined at 300 to the horizontal. If the efficiency of the plane is 75%, what is the minimum force required to pull the body up the plane? [g=10ms-2] (a) 5.0N (b) 20.0N (c) 50.0N (d) 200.0N
6. Calculate the velocity ratio of a screw jack of pitch 0.3cm if the length of the tommy bar is 21cm (a) (b) 14Ï€(c) 70Ï€ (d) 140Ï€
7. A machine with a velocity ratio of 5 is used to raise a load with an effort of 500N. If the machine is 80% efficient, determine the magnitude of the load (a) 2500N (b) 2000N (c) 1200N (d) 625N
8. A block and tackle system of pulley has 6 pulleys. If the efficiency of the machine is 60%, determine its mechanical advantage (a) 12.0 (b) 10.0 (c) 3.6 (d) 1.8

SECTION B

1. Show that efficiency E, the force ration (MA) and the velocity ratio (VR) of a machine are related by the equation
2. (a) Draw a diagram of a system of pulleys with a velocity ratio of 5 (b) A man pulls up a box of mass 70kg using an inclined plane of effective length 5m onto a platform 2.5m high at uniform speed. If the frictional force between the box and plane is 100N, draw the diagram of forces acting on the box when in motion and calculate the; (i) minimum effort applied in pulling up the box (ii) velocity ratio of the plane (iii) mechanical advantage of the plane (iv) efficiency of the plane (v) energy lost in the system (vi) work output of the man (vii) total power developed by the man given that the time taken to raise the box onto the platform is 50seconds [g=10ms-2]
3. A screw jack, 25% efficient and having a screw of pitch 0.4cm is used to raise a load through a certain height. If in the process the handle turns through a circle of radius 40cm, calculate the (a) velocity ratio of the machine (b) the mechanical advantage of the machine (c) effort required to raise a load of 100N with the machine [Ï€=3.14]