Page 178 - WCS - Electrical

WORKSHOP CALCULATION & SCIENCE - CITS

EXERCISE 17 : Simple Machines

Heat & Temperature
Introduction

- Simple machines are basic mechanical devices that facilitate the performance of work by amplifying, redirecting,
or transmitting force.
- They are fundamental building blocks in the design of more complex machines and systems.

Load (or) Weight
The force overcome by the effort is called load or weight (W).
Effort (or) power
The force applied to lift the load is called effort or power (P)
Fulcurm

It is a fixed point in the machine around which the machine rotates (F).
Concept of Mechanical Advantage (MA)
- Mechanical Advantage is the ratio of the output force (load) to the input force (effort) applied to a machine.
- It quantifies the amplification of force achieved by using a machine. A higher MA means the machine can lift or
move a heavier load with less effort.
- Mathematically,

Load = 15000 = 8
MA =
Effort 2π ∗ 300
Velocity Ratio (VR)
Distance moved by effort 8∗ 7
15000 ∗
V.R. =
- Velocity Ratio is the ratio of the distance moved by the effort to the distance moved by the load in a machine. 8
=

Distance
load

by
moved
2∗

22∗
Load
3008
MA =
- It quantifies how the speed of the load compares to the speed of the effort. = 15000 = 2π ∗ 300
Effort
Output work
- Mathematically, Efficiency = × 100% Distance moved by load
Iutput work =

Distance moved by effort Distance moved by load
15000 ∗
7
8∗
V.R. =
work
Distance moved by load = 2∗ 22∗ 3008
Output
Efficiency = D
=
Output and Input Iutput work πD =
Output work πd d
100%
×
Efficiency =
Distance
moved

The product of load and distance moved by load is known as output. Whereas the product of effort and distance by load
Iutput
work
=
moved by effort is known as input D Distance moved by load
Load× Distance moved by load
=
Output =Load X Distance moved by load moved DistanceEffort × Outpu workt by effort d
Efficiency = 1  1 2  D
− πd
 8

Input = Effort X Distance moved by effort Iutput work = of  πd πD = d
Load
=

 15000 =
2=
MA =
πd
Effort
Efficiency Load × Distance moved by load 8 1  1 2π ∗ 300
=

2
MA = Load Effort Distance moved by effort = 15000 = = π d − d 
 D
2
2π ∗
300

load
- Efficiency is a measure of how well a machine converts input work or energy into useful output work. 
Distance

by
moved
Load×
Effort
=
d

by
effort

Distance

moved
moved


effort
Distance
Effort ×
by

1

- It’s expressed as the ratio of output work to input work, multiplied by 100% to give in a percentage.ddπ 15000 2   7∗ 2 
− 8∗
1
V.R. =
1

=
=
Advantage =
Mechanical

 1
Distance

by
load
moved
of
− πd
 πd
Ratio
Velocity
Distance
moved

effort
- Mathematically, by Load Distance moved by load 15000 ∗ 8∗ 7 = = 2∗ 22∗ 3008  
2

2
V.R. =
1

moved

by
Distance
= load
moved

Distance 1
work
Output
× Distance moved 100% = 2∗ 22∗ = 3008 Ratio = = 2 π  d − d 2 b    loady by Load
Velocity
effort
by
Efficiency
Effort =
×
 moved
Distance
Load
moved
Load

by
Distance
work
Iutput
Efficiency = Output work × 100% MA = Effort = Distance moved by load

2 

1

Distance
1
πD
work
Iutput
Relations between Mechanical Advantage, Velocity Ratio, and Efficiency: moved by load = = π  d − d  
Advantage =
=
Mechanical
=
work

Output
moved
by
load
Ratio
Velocity
Distance
1200
 1
d 2
d
Efficiency = Iutput work = π πD - D 2   
=

=
Output work 300 Ratio = πd Distance moved by Load
d
Efficiency =

Efficiency = Load D = Velocity  1 2 
Iutput work MA = πD = π  d - Distance moved by Load
d 
=

Effort
Load× Distance moved by load πd d = πD/ D = d 2 πD
Mechanical
Advantage

=
Ratio
Velocity
1200

by
2 d
load

Load× Distance moved Effort × Distance moved by effort D 1  π 1  1 -2 d 2  
=
=
= d = πD of ∗  πd − πd  

Effort × Distance moved by effort 300 165 2  π.  1 - d 2  
d
4


Load × Distance moved by load 1 of   πd 1 − πd 2   1 π  1 − d 1 - d 
 
 
2
=
=
=
π
d 2
d
=


by
moved
Effort
Distance
effort
Load Distance moved by load 5 Advantage 2   = 2 πD/  2D   
=
Mechanical
= × Load 1  1 2  1 2 2
d 2 
Effort Distance moved by effort Ratio 1 = 2 π d − d   π  d − - d 
d 1
MA = Velocity


Advantage =
= Mechanical Effort Velocity Ratio =  ∗  2
= πD
2 
2
 1
1
=
1 4 π  d − d  D = dπ. 15 - d 2  
= Mechanical Advantage = =   Distanc 6  moved e  by Load
d
75
Velocity Ratio 5 = = Velocity Ratio =
=

MA = Load 2 Load = 2D moved by Load
Distance
25
150
=
Load = Velocity Ratio = Distance moved by Load d = 1 - d 2
Effort
Effect
MA = Load MA = Effort Distance moved by Load πD x
3
=
=
Effort 1200 4 πD = 75 D 21 = d- = =  15
15
15 

d
π
×
=

1200 300 75 = π  1 - d 2   100 d 15 d- 6 d  8 6
=
d

2 
1
=
25
300 = Velocity Ratio = Distance moved by effort   = πD/ π Load   = 150
= 
8
moved
Distance

2 
Mechanical Advantage by Load π  d 1 - d  Effect x
2
3
Velocity 2π = = πD/   150 = 15 15
Ratio
l
75
15

Mechanical Advantage = p 4 2 = πD ∗ = x 2 × 8 =

Velocity Ratio 4 2 π. 100 1 - d 6 2   8
d
15 
=

= Velocity 5 Distance moved by effort = πD ∗ 150x8
Ratio =
d
4 = Velocity Ratio = Distance moved by effort = 2ππ π.  1 - d 2   = 2D 8 8
moved

by
Load
Distance

= Distance moved by Load 1 2  
2
5 MA = Load 2π l p − p 2D d 1 - 150 = 15
d
Load Effort = p = d 1 - d 2 D x 15 8
MA = = =
Effort = F × / 75 of screw d 150x8
Pitch
6
D
=
= Velocity Circumferetanc e m screw by oved effort = 2ππ = = 15 Load 150
2
Dis
of
nce
Ratio = 25
8
75 Distance moved by Load p − p 2 d 6 = Effect = x
1
=
25 3 Load = 150
=
=
75
3 4 Pitch of screw Effect x = 100 × 15 = 15
8
6
= = F × /
75
2
screw

nce
4 = Velocity Ratio = Distance moved of by effort = 100 × 15 = 15 15
Circumfere

8
6
Distance
= Velocity Ratio = Distance moved by effort moved by Load 15 150 8 15
2π
Distance moved by Load = l 8 x = 8
2π l p 150 = 15
= x 8
p 150x8
= Velocity Ratio = Distance moved by effort = 2ππ 8

Distance
1
= Velocity Ratio = Distance moved by effort = 2ππ moved by Load p − p 2 150x8
8
Distance moved by Load p − p 2
1
Pitch of screw
= F × /
2
= F × / Pitch of screw Circumfere nce of screw
2 Circumfere nce of screw