This document discusses simple machines and their characteristics. It defines simple machines as devices that make work easier by transmitting force through a mechanical advantage. Examples of simple machines discussed include levers, pulleys, gears, inclined planes, screws, and the wheel and axle. Key terms like effort, load, mechanical advantage, velocity ratio, and efficiency are defined and the relationships between them are explained mathematically. Several examples and quiz questions are provided to illustrate concepts.

1. SIMPLE MACHINES
● Is a device use to make work easier
● In a machine,force applied at one point produces
a force at another point in order to overcome a
load

2. Examples of simple machines
1)Lever
2)Pulleys
3)Pulley belts
4)Gears
5)Hydraulic press
6)Screw
7)Inclined planes
8)The wheel and axle

3. Terms used in the study of
machines
Effort
● Force applied on the machine
Load
● Force exerted by the machine
NB: The SI unit of effort and load is Newton(N)

4. Mechanical Advantage (M.A)
● The ratio of load to effort
Mathematically,
M.A is a ratio of two units hence it has no unit
M.A depends on:
1)Friction between the moving parts of the
machine
2)The weight of the parts of the machine that
have to lifted when operating it.
Therefore, M.A cannot be 100%
M . A=
Load
Effort

5. Velocity Ratio (V.R)
● The ratio of effort distance to load distance
Mathematically,
V.R is a ratio of two distances hence it has no unit
NB: If two machines have velocity ratios VR1 and
VR2 then, the resultant VR is given by;
VR = VR1 x VR2
V . R .=
Effort distance
Load distance

6. Efficiency (E)
● The ratio of work output to work input
● E is always expressed as a percentage
Mathematically,
● Work output is the work done on the load
● Work input is the work done by the effort
Therefore,
E=
Work output
Work input
∗100
0
0
E=
Work doneon the load
Work done by the effort
∗100
0
0
E=
Load∗Load distance
Effort∗Effort distance
∗100
0
0

7. Efficiency (E)
E=(
Load
Effort
)∗(
Load distance
Effort distance
)∗100
0
0
E=
M . A
V . R
∗100
0
0

8. Efficiency (E)
● E of a machine is always less than 100%
because some energy is lost in overcoming the
friction force and the weight of the parts that
have to be lifted

9. Quiz
● In a machine, an effort of 20N is applied to move
a load of 80N through a distance of 2cm. Given
that effort moves through 0.5m, determine:
(a)MA
(b)VR
(c)E

10. levers
● They work on the principle of moments
Effort arm
Load
Load arm
V .R=
Effort arm
Load arm

11. The inclined plane
● Can be used to ease the loading of a heavy
luggage on the back of a lorry.
● The load is moved thro' “h” by an effort which
covers a distance “x”
L
h
E
0
x
V .R=
Effortdistance(x)
Loaddistance(h)
=
x
xsin0
=
1
sin0
sin0=
h
x
h=xsin0

12. In this case;
● Work output/work done on the load is given by;
● Work input/work done by the effort is given by;
Workoutput=Load∗distance=mgh
Workinput=Effort∗distance=E∗x=
Eh
sin0

13. Quiz
● In the previous figure, take L=50kg, h=4m,
θ=30 and determine;
a)V.R
b)The effort if the incline is 72% efficient
c)The work done against friction in raising the
load through the height of 4m

14. The wheel and Axle
● It consists of a large wheel of radius R attached
to an axle of radius r
● A car steering wheel, screw driver and some
water taps are example of wheel and axle.
● The effort is applied on the wheel while the load
is attached on the axle.

15. ● R-radius of the wheel, r-radius of axle
Wheel Load
r
R
Axle
Effort
V .R=
Effort distance
load distance
V .R=
Circumferenceof thewheel
Circumferenceof axle
V .R=
2( pie)R
2( pie)r
V .R=
R(radiusof wheel)
r (radiusof axle)

16. Quiz
● A wheel and axle is used to raise a load of 28kg
by a force of 40N applied to the rim of the
wheel. If the radius of the wheel is 0.7m while
that of axle is 5cm, calculate:
(a)M.A
(b)V.R
(c)Efficiency

17. The screw
●
R
pitch
Pitch−isthedistancebetweentwosuccessivethreads
V .R=
Circumferenceof screwhead
pitch
V . R=
2( pie)R
pitch

18. Quiz
● A car whose weight is 16000N is lifted with a
jack-screw of 11mm pitch. If the handle is
0.28m from the screw and the force applied by
the jack is 110N, find:
(a)V.R
(b)M.A
(c)E

19. Gears
● Is a wheel that can rotate about its centre
● Driver-the effort wheel (where the effort is
applied
● Driven wheel-is the load wheel
24
12
Effort
Load
V .R=
no of teethof drivenwheel
no of teethof driving wheel
V .R=
revolutionsmadeby driverwheel
revolutionsmadeby drivenwheel

20. Quiz
● A driving gear wheel having 25 teeth engages
with a second wheel with 100 teeth. If the gear
system is 85% efficient, find:
(a)V.R
(b)M.A

21. Pulley belts
● Has both industrial domestic uses e.g. in posho
mills, sewing machines, and motor engines
Driving
pulley
Effort Load
belt
Driven
pulley
R r
V .R=
radiusof driven pulley
radiusof driving pulley
V . R=
r
R

22. Pulleys
● Is a wheel with a groove to accommodate a
string.
● Three common pulley systems include:
(a)Single fixed
(b)Single movable
(c)Block and tackle
-In determining V.R of pulleys, count the # of-In determining V.R of pulleys, count the # of
ropes supporting the loadropes supporting the load oror the # of upwardthe # of upward
arrows.arrows.

23. Single fixed
● Pulley is fixed
● Effort and load moves thro' the same distance
hence;
V.R = 1, Effort=Load
Load
Effort

24. Quiz
● Refer previous figure, a pulley used to raise a
load of 50N
● What is the V.R of the system
● Determine the M.A

25. Single movable
● Pulley is movable
V.R = 2
Load
Effort

26. Block and tackle
● Has more than two pulleys
V.R=4

27. Graph of M.A vs Load for pulleys

28. Graph of Efficiency vs Load for pulleys

29. Quiz 1
● Determine the V.R of the following pulley
systems

32. Quiz 2
● A pulley system having a velocity ratio of 4 is
used to raise a load of 80N through height of
0.6m at a constant speed using an effort of 20N
in a time of 15seconds.
(a)Draw the diagram to show the pulley system.
(b)Calculate the M.A of the pulley system
(c)Find the efficiency
(d)Calculate the power developed by the effort.

33. Assignment
● A pump can raise 120kg of water to height of
10m every minute.
(a)What is the power output of the pump
(b)If the efficiency is 80%, what power must be
supplied to the pump.
Hint: Efficiency=
power output
powerinput
∗100

34. Hydraulic press
● x