subject: Phyics Topic: work, energy, power and machines sub-topic: Simple machines

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