Week - 1 - Consistency of Units
Objective: The objective of this challenge is to convert the given SI unit values of the given quantities to gm/mm/ms units and to prepare consistent unit system table for different unit system.
Before converting the given values into different unit system the definitions of Fundamental quantities and the derived quantities are established just as a ritual.
Fundamental quantity: A fundamental quantity is that which is independent of any other quantity (length (m), mass (kg) and time (s))
Derived quantity: A quantity which is dependent on Fundamental quantity is called derived quantity say (density (kg/m3), acceleration (m/s2) and velocity (m/s))
For the convenience the fundamental quantities (mass, length and time are converted to different unit measurement)
1 kg => 1000g = 0.001tonne = 0.06852 slug
1 m => 100 cm = 1000 mm = 3.2808 feet
1 s => 1000 ms = 1000000 µs
Conversion factor for all three aove =10^3
|
SI Unit system (kg, m, s) |
Conversion to (g, mm, ms) |
|
MASS (1kg) |
1000g |
|
LENGTH (1m) |
1000mm |
|
TIME (1s) |
1000ms |
|
FORCE (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) |
= 1N/m2 = {1kg*(1 m/s2)}/m2 = 1 kg/ (m* s2) Hence, 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 (E = 210GPa) |
210 GPa = 210e+9 kg/(m*s2) Here we already have 1 kg/ (m* s2) while calculating the stress, so 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 |
The Conversion factor for parameters in other unit system are as follows:
1. kg, m, s
Force: 1kg*m/s2
Conversion factor = 1
Stress: 1kg/ (m*s2)
Conversion factor = 1
Energy: 1kg*m2/s2
Conversion factor = 1
Density: 1kg/m3
Conversion factor = 1
Young's Modulus: 210 e+9 kg/ (m*s2)
conversion factor = 10^9
Velocity: 15.647m/s
conversion factor = 1
Gravity: 9.8 m/s2
onversion factor = 1
2. 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: 15.647 cm/ms
conversion factor = 1
Gravity: 9.8*10-4 cm/ms2
Conversion factor = 10-4
3. kg, cm, s
Force: 10^2 kg*cm/s2
Conversion factor = 10^2
Stress: 10-2 kg/ (cm*s2)
Conversion factor = 10-2
Energy: 10^4 kg*cm2/s2
Conversion factor = 10^4
Density: 10-6 kg/cm3
Conversion factor = 10-6
Young's Modulus: 210e+7 kg/ (cm*s2)
Conversion factor = 10^7
Velocity: 15.647 cm/s
Conversion factor = 1
Gravity: 9.8*10^2cm/s2
Conversion factor = 10^2
4. g, cm, s
Force: 10^5 g*cm/s2
Conversion factor = 105
Stress: 10 g/ (cm*s2)
Conversion factor = 10
Energy: 10^7*cm2/s2
Conversion factor = 10^7
Density: 10-3 g/cm3
Conversion factor = 10-3
Young's Modulus: 210e+10 g/ (cm*s2)
Conversion factor = 10^10
Velocity: 1564.7 cm/s
Conversion factor = 1
Gravity: 9.8 * 10^2 cm/s^2
Conversion factor = 10^2
5. g, cm, ms
Force: 10-7 g*cm/µs2
Conversion factor = 10-7
Stress: 10^-11 g/ (cm*µs2)
Conversion factor = 10-11
Energy: 10^-5 g*cm2/µs2
Conversion factor = 10^-5
Density: 10-3 g/cm3
Conversion factor = 10-3
Young's Modulus: 2.10 g/ (cm*µs2)
Conversion factor = 10-2
Velocity: 15.647*10^-4 cm/µs
Conversion factor = 10-4
Gravity: 9.8*10^-10 cm/µs2
Conversion factor = 10^-10
6. gm, mm, sec
Force: 10^6 g*mm/s2
Conversion factor = 10^6
Stress: 1 g/ (mm*s2)
Conversion factor = 1
Energy: 10^9 g*mm2/s2
Conversion factor = 10^9
Density: 10^-6 g/mm3
Conversion factor = 10^-6
Young's Modulus: 210 e+9 g/(mm*s2)
Conversion factor = 10^9
Velocity: 15647 mm/s
Conversion factor = 1
Gravity: 9.8*10^3 mm/s2
Conversion factor = 10^3
7. ton, mm, sec.
Force: 1 ton*mm/s2
Conversion factor = 1
Stress: 10-6 ton/ (mm*s2)
Conversion factor = 10-6
Energy: 10^3 ton*mm2/s2
Conversion factor = 10^3
Density: 10-12 ton/mm3
Conversion factor = 10^-12
Young's Modulus: 210 e+3 ton/(mm*s2)
Conversion factor = 10^3
Velocity: 15647 m/s
Conversion factor = 1
Gravity: 9.8*10^3 mm/s2
Conversion factor = 10^3
8. slug, feet, second
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^-3slug/ft3
Conversion factor = 10^-3
Young's Modulus: 4.368 e+9 slug/ (ft*s2)
Conversion factor = 10^9
Velocity: 51.322 ft/s
Conversion factor = 1
Gravity: 32.144 ft/s2
Conversion factor = 1
9. kg, mm,s
Force: 10^3 kg*mm/s2
Conversion factor = 10^3
Stress: 10-3 kg/ (mm*s2)
Conversion factor = 10^-3
Energy: 106 kg*mm2/s2
Conversion factor = 10^6
Density: 10^-9 kg/mm3
Conversion factor = 10-9
Young's Modulus: 210 e+6 kg/ (mm*s2)
Conversion factor = 106
Velocity: 15467mm/s
Conversion factor = 1
Gravity: 9.8*10^3mm/s2
Conversion factor = 10^3
10. G, cm, ms
Force: 10-1g*cm/ms2
Conversion factor = 10-1
Stress: 10^-5g/(cm*ms2)
Conversion factor = 10^-5
Energy: 10g*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
11. kg, mm, ms
Force: 10-3 kg*mm/ms2
Conversion factor = 10-3
Stress: 10-9 kg/ (mm*ms2)
Conversion factor = 10-9
Energy: 1kg*mm2/ms2
Conversion factor = 1
Density: 10-9 kg/mm
Conversion factor = 10^-9
Young's Modulus: 210 kg/ (mm*ms2)
Conversion factor =1
Velocity: 15.647m/ms
Conversion factor =1
Gravity: 9.8*10^3 mm/ms2
Conversion factor =10^3
Conversion table:
|
Unit system |
Mass |
Length |
Time |
Force |
Stress |
Energy |
Density |
Young’s Modulus |
Velocity 56.33 Kmph |
Gravity |
|
SI Unit kg m s |
1kg |
1m |
1s |
1 N = kg*m/s2 |
1 Pa = kg/(m* s2) |
1 J = 1Nm = kg*m2/s2 |
1kg/m3 |
210 GPa = 210e+9 kg/(m*s2) |
15.647 m/s |
9.8 m/s2 |
|
kg cm ms |
1kg |
102cm |
103ms |
10-4 kg*cm/ms2 |
10-8 kg/(cm*m s2) |
10-2 kg*cm2/ms2 |
10-6 kg/cm3 |
2100 kg/(cm*ms2) |
1.5647 cm/ms |
9.8*10-4 cm/ms2 |
|
kg cm s |
1kg |
102cm |
1s |
102 kg*cm/s2 |
10-2 kg/(cm* s2) |
104 kg*cm2/s2 |
10-6 kg/cm3 |
210e+7 kg/(cm*s2) |
1564.7 cm/s |
9.8*102 cm/s2 |
|
g mm ms |
103g |
103mm |
103ms |
1 g*mm/ms2 |
10-6 g/(mm*m s2) |
103 g*mm2/ms2 |
10-6 g/mm3 |
210e+3 g/(mm*ms2) |
15.647 mm/ms |
9.8*10-3 mm/ms2 |
|
g cm s |
103g |
102cm |
1s |
105 g*cm/s2 |
10 g/(cm* s2) |
107 g*cm2/s2 |
10-3 g/cm3 |
210e+10 g/(cm*s2) |
1564.7 cm/s |
9.8*102 cm/s2 |
|
g cm μs |
103g |
102cm |
106μs |
10-7 g*cm/μs2 |
10-11 g/(cm*μ s2) |
10-5 g*cm2/μs2 |
10-3 g/cm3 |
2.10 g/(cm*μs2) |
15.647*10-4 cm/ μs |
9.8*10-10 cm/μs2 |
|
g mm s |
103g |
103mm |
1s |
106 g*mm/ s2 |
1 g/(mm* s2) |
109 g*mm2/s2 |
10-6 g/mm3 |
210 e9 g/(mm*s2) |
15647 mm/s |
9.8*103 mm/s2 |
|
Ton mm s |
10-3ton |
103mm |
1s |
1 ton*mm/s2 |
10-6 ton/(mm* s2) |
103 ton*mm2/s2 |
10-12 ton/mm3 |
210e+3 ton/(mm*s2) |
15647 mm/s |
9.8*103 mm/s2 |
|
slug ft s |
0.068slug |
3.28 ft |
1s |
0.2246 slug*ft/ s2 |
0.0208 slug/(ft*s2) |
0.7366 slug*ft2/s2 |
1.93*10-3 slug/ft3 |
4.368 e9 slug/(ft*s2) |
51.322 ft/s |
32.144 ft/s2 |
|
kg mm s |
1kg |
103mm |
1s |
103 kg*mm/s2 |
10-3 kg/(mm*s2) |
106 kg*mm2/s2 |
10-9 kg/mm3 |
210e+6 kg/(mm*s2) |
15647 mm/s |
9.8*103 mm/s2 |
|
g cm ms |
103g |
102cm |
103ms |
10-1 g*cm/ms2 |
10-5 g/(cm*ms2) |
10 g*cm2/ms2 |
10-3 g/cm3 |
210e+4 g/(cm*ms2) |
1.5647 cm/ms |
9.8*10-4 cm/ ms2 |
|
kg mm ms |
1kg |
103mm |
103ms |
10-3 kg*mm/ms2 |
10-9 kg/(mm*ms2) |
1 kg*mm2/ms2 |
10-9 kg/mm3 |
210 kg/(mm*ms2) |
15.647 mm/ms |
9.8*10-3 mm/ms2 |
Conclusion: All conversions are done in respective unit system and learnt very well.