Week - 1 - Consistency of Units
Consistency of Units
OBJECTIVE:-
To write the given measurements in the above different system of units and also mention the conversion factors.
- MASS 1kg
- LENGTH 1m
- TIME 1s
- FORCE 1N
- STRESS 1Pa
- ENERGY 1Nm
- DENSITY 1Kg/m3
- YOUNG'S Modulus 210GPa
- VELOCITY 56.33KMPH
- GRAVITY 9.8m/s2
- Kg cm ms
- Kg cm s
- gm mm ms
- kg m s
- g cm s
- g cm us
- g mm s
- ton mm s
- slug ft s
- kg mm s
- g cm ms
- kg mm ms
PROCEDURE:-
Important Conversions:-
1 Kilogram = 1000 grams = 0.001 tonne = 0.068 slug
1 meter = 1000 millimeters = 100 centimeters = 3.28 feets
1 second = 1000 milliseconds = 1000000 microseconds
Conversion of SI unit values into g,mm,ms system -
|
In SI Unit system (kg, m, s) |
In g, mm, ms system |
|
MASS = 1kg |
1000g |
|
LENGTH = 1m |
1000mm |
|
TIME = 1s |
1000ms |
|
FORCE = 1N |
1N = 1mass*1acceleration = 1kg*1 m/s2 = (1000g*1000mm)/(1000ms)2 = 106*10-6 (g*mm)/ms2 = 1 (g*mm)/ms2 Conversion factor = 1 |
|
STRESS = 1Pa |
1 Pa = 1N/m2 = {1kg*(1 m/s2)}/m2 = 1 kg/ (m* s2) So, 1 kg/ (m* s2) = 1000g/{1000mm*(1000ms)2} = 10-6 g/ (mm*ms2) Conversion factor = 10-6 |
|
ENERGY = 1Nm |
1 J = 1Nm = (1kg*1 m/s2) * m = 1 (kg*m2/s2) Now, 1 (kg*m2/s2) = {1000g * (1000mm)2}/(1000ms)2 = (109 g*mm2) / (106 ms2) = 103 (g*mm2/ ms2) Conversion factor = 103 |
|
DENSITY = 1Kg/m3 |
1Kg/m3 = 1000g/(1000mm)3 = 10-6 g/mm3 Conversion factor = 10-6 |
|
YOUNG'S MODULUS = 210GPa |
210 GPa = 210e+9 kg/(m*s2) Here we already have 1 kg/ (m* s2) while calculating the stress 1 kg/ (m* s2) = 1000g/{1000mm*(1000ms)2} = 10-6 g/(mm*m s2) Therefore, 210e+9 kg/(m*s2) = 210e+9 * 10-6 g/ (mm*m s2) = 210e+3 g/ (mm*m s2) = 210*103 g/ (mm*m s2) Conversion factor = 103 |
|
VELOCITY = 56.33Kmph |
56.33 Kmph = 56.33 * {106mm/(3600*1000ms)} = 15.647 mm/ms Conversion factor = 1 |
|
GRAVITY = 9.8m/s2 |
9.8m/s2 = 9.8 * 1000mm/(1000ms)2 = 9.8* 10-3 mm/ms2 Conversion factor = 10-3 |
SI system (kg m s)
Force : 1 kg*m/s2
conversion factor = 1
Stress : 1 kg/(m*s2)
conversion factor = 1
Energy: 1 kg*m2/s2
conversion factor = 1
Density: 1 kg/m3
conversion factor = 1
Young's Modulus: 210 e+9 kg/(m*s2)
conversion factor = 109
Velocity: 15.647 m/s
conversion factor = 1
Gravity: 9.8 m/s2
conversion factor = 1
kg cm ms
Force : 10-4 kg*cm/ms2
conversion factor = 10-4
Stress : 10-8 kg/(cm*ms2)
conversion factor = 10-8
Energy: 10-2 kg*cm2/ms2
conversion factor = 10-2
Density: 10-6 kg/cm3
conversion factor = 10-6
Young's Modulus: 2100 kg/(cm*ms2)
conversion factor = 10
Velocity: 1.5647 cm/ms
conversion factor = 1
Gravity: 9.8*10-4 cm/ms2
conversion factor = 10-4
kg cm s
Force : 102 kg*cm/s2
conversion factor = 102
Stress : 10-2 kg/(cm*s2)
conversion factor = 10-2
Energy: 104 kg*cm2/s2
conversion factor = 104
Density: 10-6 kg/cm3
conversion factor = 10-6
Young's Modulus: 210e+7 kg/(cm*s2)
conversion factor = 107
Velocity: 1564.7 cm/s
conversion factor = 1
Gravity: 9.8*102 cm/s2
conversion factor = 102
g cm s
Force : 105 g*cm/s2
conversion factor = 105
Stress : 10 g/(cm*s2)
conversion factor = 10
Energy: 107 g*cm2/s2
conversion factor = 107
Density: 10-3 g/cm3
conversion factor = 10-3
Young's Modulus: 210e+10 g/(cm*s2)
conversion factor = 1010
Velocity: 1564.7 cm/s
conversion factor = 1
Gravity: 9.8*102 cm/s2
conversion factor = 102
g cm us
Force : 10-7 g*cm/us2
conversion factor = 10-7
Stress : 10-11 g/(cm*us2)
conversion factor = 10-11
Energy: 10-5 g*cm2/us2
conversion factor = 10-5
Density: 10-3 g/cm3
conversion factor = 10-3
Young's Modulus: 2.10 g/(cm*us2)
conversion factor = 10-2
Velocity: 15.647*10-4 cm/us
conversion factor = 10-4
Gravity: 9.8*10-10 cm/us2
conversion factor = 10-10
g mm s
Force : 106 g*mm/s2
conversion factor = 106
Stress : 1 g/(mm*s2)
conversion factor = 1
Energy: 109 g*mm2/s2
conversion factor = 109
Density: 10-6 g/mm3
conversion factor = 10-6
Young's Modulus: 210 e+9 g/(mm*s2)
conversion factor = 109
Velocity: 15647 mm/s
conversion factor = 1
Gravity: 9.8*103 mm/s2
conversion factor = 103
ton mm s
Force : 1 ton*mm/s2
conversion factor = 1
Stress : 10-6 ton/(mm*s2)
conversion factor = 10-6
Energy: 103 ton*mm2/s2
conversion factor = 103
Density: 10-12 ton/mm3
conversion factor = 10-12
Young's Modulus: 210 e+3 ton/(mm*s2)
conversion factor = 103
Velocity: 15647 mm/s
conversion factor = 1
Gravity: 9.8*103 mm/s2
conversion factor = 103
slug ft s
Force : 0.2246 slug*ft/s2
conversion factor = 1
Stress : 0.0208 slug/(ft*s2)
conversion factor = 1
Energy: 0.7366 slug*ft2/s2
conversion factor = 1
Density: 1.93*10-3 slug/ft3
conversion factor = 10-3
Young's Modulus: 4.368 e+9 slug/(ft*s2)
conversion factor = 109
Velocity: 51.322 ft/s
conversion factor = 1
Gravity: 32.144 ft/s2
conversion factor = 1
kg mm s
Force : 103 kg*mm/s2
conversion factor = 103
Stress : 10-3 kg/(mm*s2)
conversion factor = 10-3
Energy: 106 kg*mm2/s2
conversion factor = 106
Density: 10-9 kg/mm3
conversion factor = 10-9
Young's Modulus: 210 e+6 kg/(mm*s2)
conversion factor = 106
Velocity: 15647 mm/s
conversion factor = 1
Gravity: 9.8*103 mm/s2
conversion factor = 103
g cm ms
Force : 10-1 g*cm/ms2
conversion factor = 10-1
Stress : 10-5 g/(cm*ms2)
conversion factor = 10-5
Energy: 10 g*cm2/ms2
conversion factor = 10
Density: 10-3 g/cm3
conversion factor = 10-3
Young's Modulus: 210 e+4 g/(cm*ms2)
conversion factor = 104
Velocity: 1.5647 cm/ms
conversion factor = 1
Gravity: 9.8*10-4 cm/ms2
conversion factor = 10-4
kg mm ms
Force : 10-3 kg*mm/ms2
conversion factor = 10-3
Stress : 10-9 kg/(mm*ms2)
conversion factor = 10-9
Energy: 1 kg*mm2/ms2
conversion factor = 1
Density: 10-9 kg/mm3
conversion factor = 10-9
Young's Modulus: 210 kg/(mm*ms2)
conversion factor = 1
Velocity: 15.647 mm/ms
conversion factor = 1
Gravity: 9.8*103 mm/ms2
conversion factor = 103
CONCLUSION:-
Table showing Fundamental units and their respective derived units in verious unit systems.
