Page 184 - WCS - Electrical

8

Load
8
Load
=
15000 =
15000 =
=
MA

8
=

Load Load
MA =
300
2π ∗
150
=
15000 =00 ==
Effort
300
2π ∗

MA = MA = Effort
8
Load

8 300 300∗
2π ∗2π
Load
Load

=
=
Effort Effort
15000 =
15000 =
MA =
15000 =
=
MA =
MA =
2π ∗
2π ∗

Effort
2π ∗
Effort
Load
Effort
15000 =
=

moved
Distance
300
2π ∗
by
effort

Distance

moved
15000 ∗
8∗
Effort
7
V.R. =
7
15000 ∗
V.R. =
by

ved
mo
Dista
moved

nce
effort effortby
Distance
=
Distance

load

moved
by
15000 ∗00
=
78∗
150
7
8∗∗
moved

by
load
V.R. = V.R. = Distance
22∗
2∗
3008

moved
Distance
Distance
=

by

3008
= 2∗
22∗
by load by d
m ce
move
D
moved oved
by

Distance istance
effort
load
Distan
8∗
15000 ∗
7
8∗
15000 ∗ 15000 ∗
7
V.R. =
7
V.R. =
8∗ 3008∗
2∗
22∗222∗
V.R. =
=
=
by
moved
by
load

Distance

=

load Distance
moved
by
effort
Distance
load
moved

by
Distance

2∗
22∗
Output
work
22∗

3008
7
15000 ∗
3008
8∗
22∗

2∗
work
Output
100%
Efficiency =
=

moved
load
Distance

by
work worktput
Output
Ou

×
Efficiency =
100%
moved

load

by
Distance
load
moved

Distance
by

8
work
Iutput
2∗

3008
22∗
Load
Efficien
100% 100%×
×
work
mo
Dista
by
Distance
nce

=
ved
= =
moved
loadloadby
Output
work
Output

work
8
MA =

load
Distance

moved

by

Output workIutput
work
work
Iutput
=

moved

Load
by
load
×iency

Effic Load
100%
100%=
Efficiency =
by
=
moved
by 15000 == =
15000
Efficiency =

moved
Distance Distance
Effort
100% =
× MA
Distance
Dista
by load b d
MA =
move
m e
nc
moved oved
work
Iutput
Iutput
work
=
300

300
Output
= 2π ∗
work
work
2π ∗
Iutput
=
Effort
Effort
Efficiency =cy = Iutput by × effort V.R. = MA = effort moved moved by × effort = 15000 = Distance 3002π ∗ 3008 8∗ 8 2∗ by 300 load loady 15000 = 300 load Distance 8 8 3008 8 300 load
work
by 8

Output
load
100%
moved
×
by
Efficiency =
load Distance

Distance
moved

work

Distance
load
Load

by
moved
Output
moved 8
Distance
by
load

Efficiency = Load

=
Ou
15000 =
Iutput
work

Output
=
work worktput MA =
=
Efficiency =
D
MA =
Iutput
300
work
2π ∗
D
Efficien
Effort
Efficiency =cy = Iutput
=
=
work
Distance mo Effort effortby ved Output workIutput work Output Output work πD πD D 2π ∗ 300 Distance moved by load
πD πD==
D
work
d
Efficiency =
V.R. = Efficiency = Iutput work Efficiency = effort 15000 = πd 78∗∗ = = πd =d

by d
move

moved

Distance
by
D
Distance moved Iutput V.R. Distance Output work effort = πD dπd πd D πD = 15000 ∗ 8∗ 7 πD 7 = D WORKSHOP CALCULATION & SCIENCE - CITS

by
load
work
Iutput
work
Iutput
d
15000 ∗
work=
8∗
V.R. =
=
=
=
Efficiency =
Load Distance move by d loa d load 2∗ 22∗ 3008 = 8 πd = d = πd d
by
Distance
moved
15000 =
=
d
MA =

2∗
Distance
D

Load× Distance moved moved by effoby load rt load moved b Iutputrty effo work D πd 2π ∗ 300 15000 ∗ 22 πD 222∗ 3008∗ = ∗ D 3008
Distance
= 7∗
8
moved
Distance
V.R. =

by
Load×Effort
Efficiency = Distance movee movedd nce mo ved loadlby oadmoved nce by load 1 D D 85000 ∗ ∗ 7 = 2∗ 22∗ 3008 πd d
= V.R. =Output
work
d
moved
Lo
Load×ad×
Distance
Dista
=
=
by Dista
d
×
Effort × Distanc
effort
by loadby
100%
D

moved
=

= Effort ×

work
moved
effortOutput
by
d ∗
2
1 d

loa

by
moved

Load×
Distance
by
moved
Iutput
work


=
Eff
×
100%
byciency =
Load× DistanceEffort ×ort Distance nc× Distance moved oved Effi by effort b d Efficien Load load Distance× Output work × 100% Distance 2 1  πdof D d300822∗ 1 by load D Dist Distance by moved ance moved d load
load effy
m e
move
Dista
2
ortcy =
d = Diameter of smaller load axle
1 1
loa

of
=
=
by
 − πd
 πd
=
2

d
=
b
Dis
1 − loady
1= moved tance
Iutput
work

d 1 
Distance

effort

Effort ×
Load× by moved ce
Effort × Distance by ed Distan effort Effort × Iutput work moved by effort = 2 of = 2   πd πdof  − πd − 2 πd 2 d    = = D loa

mov
Distance
effort
by
work

load
Output

moved

Distance
by
 πd 
moved
work
Output
Distance moved by effort = πD 1 moved Distance by moved Distance

8∗
1
V.R.
Load= Distance movedi cie loa by % × 100% 15000 ∗ 1 = 7  2 of  πd loadby Distance  d = by ed of load 1 by d 2 load
2
by ncy

Eff
=d=

2
 

1  2
− πd mov
1
100

moved ×

=
load
Efficiency =
Distance

= Load Distance nce workut mo ved loadloadby Effort × workIutput moved by effort 1Dista  πd  moved nce 2 − πd    πd − πd 
× Distance workOutput
of 
by

load
moved
= 1 1
Distance
  =
moved
Dista

Load Load×=
by
Iutp
d 22
1 
== 2∗
− d 3008∗
1 
Efficiency = × Distance moved by Output work work load πD π =   1  1 − ddπ  1   2  2 2 2     Distance moved 2 1 by load 
Effort

by

Distance

moved
effort
2 1 1 
Output
2
×

Distance moved by load = of (πd - πd )
=
effort
2
 D
= Effort
Lo
movedad
− d moved
of
Load
Distance
π = 2
d dπ 
loadorty Efficiency =
=
Distance mo nc
by ort effb
Dista
Load DistanceEffort Effort Iutput work moved by ved eff Efficiency = by load Distance moved by = = 2Distance  − d    by load 2 = 2 πD  πd − πd   1 2 
moved e
1
1
=
D
×

2
12
×
 1 
2 
 πD
=
 D
 1
Iutput
work
Iutput
= × Ou Effort worktput movedrkput Distance moved Eff by Distanceort work work by effor t πd = 1 d π d 2  − d  =  π d − d  = = = = = π d − d 
moved

effort

Load Output
effort
Ou
by

Distancet
 d

Effic
= Mechanical Advantage = wo × 100% × 1 Distance moved by load = Dista 2 π moved nce d  d     by 2  load πD 1 π  1 2 2 d    
2 
iency
1
d −
Effort =
πd
1 
d
π
πd
Efficiency =
1 d
=
 d −
Efficiency =
2 
2 

= D
Iutput
1  
work
d
− d

1

work
Effort 1 Iutput
−d − D
=

dπ π  πD
Iutput
work

Ratio
=
Velocity
=
=
Mechanical
Distance
2 
Advantage =
1 load
Mechanical
=

Advantage =Velocity
Ratio
 1
2 

by
Distance
moved

load
Load× Mechanical Advantage = Velo 1 Ratio Ratiocity Distance 1 moved by effort 1 = D =  = = =  2 1  = moved − 2 d  by  d − d  πd D 2 D π  d − d 

2  π
d

Velocity
d 
dππd
=
Advantage =
Mechanical
=

Mechanical
Advantage =
=

d


Mechanical

 2
Load×
moved
load
Distance
=

Load
by
2 
 =
1=
mo

wo effort
Distance
Effort × Efficiency = Advantage =Load× Distance move by d loa = by d effort Ratio = = Distance 2 moved mo 2 Loadby by ved by Load  d − d  2 
Output by ved
1 Velocity
Velocity
Ratio

Ratio
Distance
moved
=rk

=
Ratio
Velocity
Velocity
d
= 1
π d
2 Distance
Load

Distance

moved

Velocity 
=ort ×

Advantage = by moved stance by moved e
Eff
Distanc
Load
Load D
Ra D πd

by
= =
−
Ratio =tiocity πD 
Velo
Load
=

=
Distance
1
work
by
= Distance

Iutput
moved
Ratio
Velocity
by

moved
Load MA Dis× =tance Load× Mechanical DiEffort × moved by load effort Velocity  πdof  Ratio = 21 Distance D moved move by by Load by d = d of Load   by 2 Distance moved by Load

load

moved
Distance 
Load 21 

=
=
2
Load Load
1 1
Load
2 πd
Distance stance
m e
moved oved
=  πd
MA = =
Di Distanc
Load of−

Ratio = − πdπd 
Velocity 
=
=
=
Velocity dπd
Distan
Load × Effort × MA = MA = Effort loadby moved ce Effort Effort × Distance moved by effort = Velocity Ratio = d 2 Ratio = Distance moved  by Load moved moved by Load

2


Load
2
Load moved
Distance
Distance
Load
effort
by
1

Effort Effort
Distance
=
by
Load
Distance
by
moved 1
Load
πD 

 1
πD
MA = loadby ved


mo

Distance
MA = Load
2

1
 
Ratio = πdd
2
= =

1
by
effort


Effort Distance MA = Effort Load Effort × Distance moved by load = 2 π =  = 1 d =  1  πdof − d = πD πD  Velocity πof 1 − Distance 2 d moved by Load
2 
moved
= ×
− πd
=
Effort
 1 


Load

1 1
1200

2

d
d 
-
by

MA =nce by moved ce
Efforttan

moved
Dis
Effort loady
b
Load× Distanc 1200 moved e moved by Distance Dista Effort effort effort 2 π D =  1  2 d- 2 2     2 πD =  2 π  = d 2 π − d  d = − πD
=
d
π

moved
by

1200 1200 Load
πD 


load
=
 1  1 
load
=
Distance
d d
- π 
1
300
=  
= dπ d 2 
=
1
1
=

 
moved
Load × Distance = 300 by 1 × effort 1200 π  d − d   1  − d  d- 2  π  1 π  1 − d 2   πD  1 2 
= Effort ×
 1
2
 d
=


1200
π
-
2
π 1 d
=
1200 300 Effort
d
1 

300 =
 1
= Mechan Effort Advantageical Distance moved = effortby Distance moved by = effort 1 1 = 1 o π 2   -  d 2  2   2  d 2 d  d −  d − d π 2  - d  
 2
-

d 


 d
d
= π d 
π
=
1
 
1 


−
1 d- 
300
π
Mecha
Mechanicantagen
300ical
=
2 
=
=
 1  
300 Velocity Ratio Adva 1200tagel = Advan = Velocity Ratio = =  πdf   π  dπ d πd   2     =  = π   1  - d 2   
πD/ 2 2
d
d  d-d
- 
1 
πD/
=
2 
1



Advantage by moved
Dist
MechanicalanceLoad Mechanical load 1 300 1 Velocity Ratio Distance  2 d − move 1  2  2  π Loadby d   π d  2 2   2 π   1 - d 
 1
d −
d
2  d 
-
πD/πD/
Advantage
d
d
=π
= 1
= = Effort Velocity Advantage = by effort Advantage = Velocity Ratio Ratio = = = π  d 2 − d -2  πD/  =  Distance 1tan 2  moved ce by ved Load Load
×
Mechanical
=
d 

d 2

π 1
Velocity
=
M
Mechanical Advantageechanical

Advantage
Mechanical


2  


= Dis
πD/ mo

by

Ratio moved ce
Distan

=
Load
Ratio
Load
Dis
2 =  by oved
Velocity
Ratio Velocity
-
d
d 
= 2
Velocity = 2
=
Mechanical Mechanical Advantage Mechanical Advantage = πD πD/  tance ∗ 2 m 2 Velocity Ratio Ratio = π  ce move by d 2 Load Load
MA =
2
2 2

Velo
Velocity
Advantage
Ratio Ratiocity
Load


Load
∗

Distan
moved
Distance
by
= πD
Effort

2
=
πD/

MA =

MA =
Velocity

Ratio
by
Load
Velocity
Distance
Mechanical

∗ πD  1 21
Velocity
-
2

d
d Veloc= d
∗  1 ity
= πD = π. dπ πD
= Mechanic = Advantageal 4 Ratio Ratio Load Advantage = Velocity = Ratio = −  1  dπ.  2 2 2 1   moved -  d 2 Ratio = 2 Distance moved by Load
Effort
4

2
1
Effort
 


2
= πDd
∗ by
Distance
Load
4 4 Load =
move
d  
-


= πD d-d moved
by
∗  
πD
= πD π Distan
Load
Velocity
5
 
2
= MA =
Ratio
1200 = = 5 4 MA = Effort Ratio π =  1 - d ∗ d. π. ce d   2  π.  1 = d = πD 1 ∗  1  πD  1 - d 2  
Velocity


2
 =
d
2 π.
-
d
2D 
d
 1
4
2
=

π.
-
5
4 5 Effort
d 2D


2

1200

 d

2D
=
=
=
2 πD moved ce
=
 1
Load
300 5 Load = 5 1200 = 5  = Distan  2D 2  by Load π πD  - π d d  - - d d 2 2       
1
d 
= -d
=
π. 
d
4

= 1
MA = MA = Load 1200 300 300 = Velocity Ratio = 1 = 2  2D 2 1 - d 2 2D  1 2   2D
1 d



=
Load Load
d
-

= by d
d an
d 
d 
d -d 2 move ce
Load
Dist
π
-
d
Effort 1200
π
d

- 1
1 
d
-
π
MA


MA = MA = Effort Load = 5 Load = πD/  Velocity Radio of diff.wheel and axle 1  = 2 1  2
= d 
 2
= =

d
Load

2D d-d 
π d- 
2 π
1
Effort Effort
D
1 15
2 

Effort
d 15
MA =
300

d =
MA =
Mechanical Advantage MA = Effort 300 Load Effort EXAMPLES 15D== - D 15 d = - d  = πD/ =   2 d  - d
= 2
πD/
D
πD
2 
1
6
Effort
d
=
= 6
Velocity Ratio 75 Mech Mechanicalntageanical Adva Advantage = π d 1 = =d 2  D π d 1 - d 2  d - d 2 D 15
MA =
75
15
-
d 
15 6
= = 1200 = Velocity Ratio Ratio = πD = ∗ πD/ dπ  2  D 6d 1 2 d   = = πD/ =   = =
1 In a wheel and axle, the diameter of the wheel is 15cm and that of the axle is 6cm. If the efficiency of the
Effort
= d-
75 75
=
Velocity
25
6
150
2
2
Lo

Advantage
machine is 75%, what should be the effect required to lift a load of 150 kg
Mechanical = = 25 Mechanical Advantage 75 Load 2 dad  6 150 d = πD 2 D = 15 d 6
75
300
= 2 
=  1
= πD
= ∗
∗
25
4 7525 = = π. Load Load==d-d  x 150 150

Effect
= Velocity = Velocity Ratio 25 Solution : Diameter of wheel D = 15cm Load dπ. dπ.  1 - d 1  6 2  150
2
= x
= Effect
1 
= 

Ratio
= 2 
d
-
d
x
25 4
-
d
d
Load 2
π
5 3 25 = 5 4 75 = πD/ 2D Effect Effect x 150 Load = ∗ 1502  =   Effect  = x
3
= = πD
=
=
= 
= ∗ 
=
= πD
3 3
=
15
75
15
x
Effect

4
x 15
2

2
π.
-
2D d
=
Effect 1575  1
d
= 
= 4
Mechanical
×
=
75 = π. 2
2D
15 15× d-d
7 
15 155= 
3
MA = Load 4 Advantage 4 5 25 3 = = d 1 Diameter of axle d = 6cm  1 Load = 150 15 15
2
= 
=
3 4
4
= 
8
6
= d-
100
=
×
=
= × 6 
x
= 8
= 100
=
Effect
=
Load = 150kg
4 Load
Ratio
75
15 1
5
15
Velocity
2
1
75 2
75 6
3
4
2
MA =
MA =
= 152D

Effort 5 Distance moved Effort Load 4 = πD D 100 100 15 8 6 = = 15 8 × = =2D d - d d = d- 100 × 6 = 8
Distance
moved

effort
by
× 15
=
∗
by
= 15
= Velocity Ratio = Load Dista nce moLoad effort Effort 4 = Effect = say x kg= To find 86100 d 1 d- = D 75 15 × 15 15 15
8
100 15
6 15
Distance
effort effortby
moved
Ratio =
=
Velocity
ved
by
=
2 
2
2
81  1
=

Load

moved
Distance
by

π.
- -
d d
D
8 
Ra
Ratio =tiocity 4
Velo
=
Load
=Distance MA =
=
by

6
d

MA =
by Distance
Velocity ratio of wheel and axle =
=

effort
moved

Distance
15 8
8
= 75
Velocity Ratio = Distance stance m ce moved Velocity Ratio = moved by effort  d d 150 15 15 = d 100 6 d 6 = 6 8 15
byo
Di Distan
move
Load
effort
by Load by drt
moved ovedEff
15
150
Ratio =
Velocity
=Effort
=
=
Velocity 5
=
=
75
75
by Distance
Distance
moved
Load

by
150 1 15D

25 2π l 2π l l moved = Velocity Ratio = Distance moved moved by Load 2D = x = 815 1550= = 8 8 D = 15 15 8
Load
x 150
Distance

effort Load
=
8
=
by =
=
=
l =
2π 2π
=
8 150
150

25
Load = p = p l 75 25 Distance moved by Load Effect d = = 1 150 8xd d 2 x 6 15 8 150 15 Load 6d Load 150 = 15
-x
l
2π
= =
= =
=
p 75
=
MA = 2π lp 2π = = Mechanical Advantage = ….(1) but
x
3 = = = p 25 p 150x8 8 x 8 Effect 150ct 15 x 8
Effex
Effort
x
=
150
l
2π
150x8
25
p
3
3
15
D
=
4 Distance moved by effort effort 2ππ = 2ππ = 75 Load 1515 150x8 150 Load = x = 8
=
=
=
150x8
=
Distance
moved

by
= =
×

8 =
75 15
75
15 x
Effect
15
= Velocity Ratio = Distance moved mo ved effort effortby by 3 = 1 4 = 2ππ2ππ 100 Mechanical Advantage = Efficiency * velocity ratio
15
p
8x
6
by

Ratio =
Dista
=
Velocity
Distance
moved
nce
Effect 8
4
6
150x8
150x8
d
= ×
× =
=
by
Load

=
2
8
150x8 8
Velo
=
Ra
Velocity
=
=Distance

Ratio =tiocity 75
Load pp
= 1
= −
3

6 8
2ππ 21 p Distance
6

2ππ
p
Distance
effort
=

=
move
by
by Load by d
Load
15
moved 1
Distance stance
effort
moved oved
Di Distan
15
= Velocity Velocity Distance = mo Ratio = effortby ved m ce moved Velocity p − by 2 − p 2 = 1 moved e moved by effort 75 = 1 × 2ππ 2 = = 8 75 100 15 = 100 150x8 8 8
Ratio
15
=
=
p p − =
Velocity

8 15
4
15
=
=
Ratio = 25
4
Load
150
×
Ratio =
Distanc
Load
Distance

by =
Distance
by Distanc
1 Loadby move e

Distance
by effortby

2
Load
2ππ p − =
Distance moved moved = = Velocity RatioVelocity = moved Distance moved moved − effortby d p p 2 effort = =8 Effect 6 p x 8 100 6 8 15 8
by
Load
Ratio = p −
p
=
Velocity
Ratio
100
=
move

Distance
2
Distance
screw
of
Pitch Pitch of screw Distance Distance moved moved Loadby d effort by Loadby Load 150 1 p 15 15 8 8

p −
3
moved

by
15

moved
l
F ×
=
=
/ 2π

= Velocity = / = Distance screw screw of Ratioity screw by effort x Mechanical Advantage = ……(2) 15
h
15
F ×
of
Veloc
=
Pitch
150
Pitc
=
150
=
Ratio =
15
2
15

F ×F ×= 2 Circumfere
nce
of
75 8
=
4
/
8
l
nce

=
/ Circumfere
Load
=
×
8 =
screw
Distance
Pitch d
by
Load

of
=
2 2 p Circum nce move of screw 2π moved Distance l 2π by Pitch of screw = By comparing Eq.(1) and Eq (2) we can write
scr screw of
x 8
=
Circumferef
x
ofe
screwew of
nce
Pitcher
8
/
=
6
F ×
=
8
F ×
/
100
= F × / 2 Circumfere nce l of 2 p screw Circumfere nce of screw 150 15 150 15
p
of

2
screw
Pitch

of
nce
screw 2π
l
2π
15

Circumfere moved by = = / 150x8 = x = 8
Distance
effort
F ×
=
Velocity
= Velocity Ratio = Dist Distance moved by = 2 p 2ππ nce of screw 8 x 8 8 150x8

Circumfere
moved
by
effort

Ratio =ance
=
150x8
p
Load
move
Distance

by
moved

Distance moved by Velocity = p − p 2 Distance by d effort effort 2ππ 2ππ 15 8 8
1
Load
=
=
Ratio
Velocity
=
=
Ratio =
150
Load
move

Distance
2 150x8
2
Distance
moved
1
1
=
2π l Distance moved by by d effort by Load p X= =80kg 150x8
p −
p
p −
2ππ

by
=
= Velocity Ratio = p Velocity Ratio = effort = 2ππ = x 8 8
moved

Distance
8
=

1 move
1
Load
screw
of

= F × / Pitch Distance moved by Distance p − p 2 by d Load p − p 2 X=80kg

of
Pitch

Distance
= by d
2ππ
move
2 Circumfere nce of screw F × = / effort / Pitch of screw screw 150x8
F ×
8
Circumfere screw of ncefere
= Velocity Ratio = 2 Circum nce of screw Effect required = 80 kg Ans.
2
=
Pitch
2
= F × / Distance of = m screw by oved / Load of 1 screw - The differential wheel and axle consist of two wheels of different diameters connected by an axle.
Pitch

p
p −
F ×
Circumfere
2 Circumfere nce 2 of screw nce of screw
- When force is applied to the larger wheel, it rotates the smaller wheel at a different speed, allowing for speed
Pitch of screw and torque adjustments.
= F × /
2 Circumfere nce of screw
171
CITS : WCS - Electrical - Exercise 17