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 also to prepare cosistent 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), time(s))
Derived quantity: A quantity which is dependent on Fundamental quantity is called derived quantity ( density(kg/m3), acceleration (m/s2), velocity(m/s) )
For the convenience the fundamental quantities (mass, length and time are converted to different unit measurement)
1kg => 1e+3 g = 0.001 tonne = 0.06852 slug
1m => 100 cm = 1000 mm = 3.2808 ft
1s => 1000 ms = 1e+6 μs
All parameters are converted to their respective unit system with SI Unit system as standard. (kg,m,s)
Calculation of the conversion from SI unit to g,mm,ms
|
SI Unit system (kg, m, s) |
Conversion to (g, mm, ms) |
|
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 |
|
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 = 1 kg*m/s2 |
1 Pa = 1 kg/(m* s2) |
1 J = 1Nm = 1 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*ms2) |
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*ms2) |
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*μs2) |
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 |
2.10 e+11 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 e+9 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 |
The Conversion factor for parameters in other unit system are as follows:
Unit 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 μs
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
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
RESULT :
Thus, all the given unit systems were converted to the respective unit system and its conversion factor has been identified.