# 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 x  distance

Effort x distance moved by effort

Then V.R =M.A

## TYPES OF MACHINES

1. LEVER

This is the simplest form of machine. It  consist  of a rigid rod  pivoted about a  point  called the fulcrum F with a small  effort applied at one end  of the  lever to overcome  a large  load L  at the other end . There are various types of lever depending on the   relative positions of the load, effort and fulcrum.

E x a = L x b   which is given

L =  a  =M.A

E     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 ,  laboratory tong etc.

## 2.     WHEEL AND AXLE

It consists of  a large  wheel  to which a rope or string is attached and an axle  or small wheel  with the rope  or string  wound round  it  in  opposite direction . The load to be lifted is hung at the free end of the rope on the axle while  the effort  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

In  gear boxes , there  are toothed wheels of different  diameter interlocked  to give turning force  at low speed  depending on which  gear  is the driver  and which is the driven

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

No of teeth on driving wheel (B)

## 4.     THE HYDRAULIC PRESS

The  machine is  widely used  for  compressing  waste  paper and cotton  into  compact bales  forging different alloys into  desirable shape etc .It s work is based on Pascal’s principle which  states  that  pressure is transmitted equally in fluid Oil is  the liquid  normally  used in hydraulic press

## 5.     THE WEDGE

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

M.A =  X1 =   Slant height of wedge

X      Thickness of wedge

## 6.     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 is   the  more practical  system  of pulleys in which one or  more  pulley  are mounted on  the same axle  with  one continuous rope  passing  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 lift  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 b  are constant ).This  is called linear law for  a machine .It  follows  that E is proportional to L .The  value  to give us the effort required to  operate  the  machine  moving part only  if no load is  present  while  A gives us  the measure  of the friction present

=  M.A x  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: This  is in form of a sloping  plank commonly used to raise heavy load such as  barrels of oil with  little applied effort than  by lifting  it vertically .

V.R = Distance moved by effort

= x /h ; V.R = 1/ sin θ

## THE SCREW

Geometrically speaking the screw is an inclined plane wrapped round a cylinder to form a   thread. The distance between successive threads on a screw is called its pitch. For one complete revolution  of  screw  through  an  effort ,  the load  moves a distance equal  to its  pitch  e.g.  screw  jack  nut  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= -2πa

P

= 2πr

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)  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)  (b) (c)  (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 Ɵ is (a) sin Ɵ (b) cos Ɵ (c) tan Ɵ (d) 1/sin Ɵ
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 30 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) 14π(c) 70π (d) 140π
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 [π=3.14]