Week - 1 - Consistency of Units
AIM :-The aim of this challenge is to convert the given SI unit values of given quantities to all different parameters & also to prepare consistent unit system table for different unit system.
In Kg Cm ms
Mass 1kg
1kg
Lenght 1m
100cm
Time 1sec
1000ms
Force 1N
F=mxa=
1 kg * 1m/s^2
(1 kg*100cm)/(1000ms)2
10-4 (kg*cm)/ms2
Stress 1pa
force/area
1N/m^2
1N=10-4 (kg*cm)/ms2
={10-1 (kg cm/ms2)} / (100 cm2)
=> 10-3 kg/cm ms2
Energy 1Nm
1N=10-4 (kg*cm)/ms2
m=100cm
10-2 kg cm2/ms2
Density 1kg/m3
1kg=1kg
m=100cm
m3=(100cm)3
1kg/(100cm)3=10-6 kg/cm3
Young's modulus 210Gpa
Young's modulus=stress/strain
stress=force/area
strain=L/ΔL (Strain has no SI unit)
1Gpa=1+e9p
210Gpa=210+e9p (conversion unit is e9)
Velocity 56.33KMPH
1km=10000cm
1hr=3600000milisec
(104 )/(36*105)
56.33 kmph = 56.33 * 0.00277 cm/ms
0.1560 cm/ms
GRAVITY 9.8m/s2
1m=100cm
9.8m=980cm
1sec=1000ms
980cm/1000ms
9.8*10-4 cm/ms2
Mass = 1 kg
1 kg
Length = 1m
100 cm
Time = 1 sec
1 s
Force = 1 N
F = mass* acceleration
= 1 kg * 1m/s2
= (1 kg*100cm)/(1s)2
= 100 kg cm/s2
Conversion factor = 100
Stress = 1 Pa
1 Pa = 1N/m2
As from the above derived 1N = 100 kg cm/s2
= (100 kg cm/s2 )/ (100 cm)2
= 10-2 kg/cm s2
Conversion factor = 10-2
Energy = 1 Nm1N *1 m100 kg cm/s2 * 100 cm
104 kg cm2/s2
Conversion factor = 104
Density = 1Kg/m^3
- 1 kg / (100 cm)3
- 1 kg/10000 cm3
- 10-4 kg/cm3
Conversion factor = 10-4
Young’s Modulus = 210 GPa
1 Pa = 10-2 kg/cm s2
1 GPa = 109 * 10-2 kg/cm s2
210 GPa = 210 * 107 kg/cm*s2
Conversion factor = 107
Velocity = 56.33 Kmph
Km/h
1Km = 10000 cm = 104 cm
1 hr = 60min*60sec
= 3600
= 3600 s
1 kmph
=> (104 )/(3600)
=> 2.77 cm/s
56.33 kmph =
=> 56.33 * 2.77 cm/s
=> 156.03 cm/s
Conversion factor =2.77
Gravity = 9.88 m/s2
1 m/s2 = 100 cm/(1s)2
= 100 cm/s2
9.8 m/s2 = 9.8*100 cm/s2
Conversion Factor = 100
- Mass = 1 kg
1000gm
- Length = 1m
1000 mm
- Time = 1 sec
1000 ms
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s^2
=> (1000gm*1000mm)/(1000ms)^2
=> 1 (gm*mm)/ms^2
Conversion factor = 1
- Stress = 1 Pa
1 Pa => 1N/m^2
As from the above derived 1N = 1(gm*mm/ms^2)
=> {1 (gm*mm/ms^2)} / (1000mm^2)
=> 1*10^-6 gm/mm*ms^2
Conversion factor = 10^-6
- Energy = 1 Nm
- 1N *1 m
- {1 gm*mm/ms^2} * 1000 mm
- 1000 gm*mm^2/ms^2
- 10^3 gm mm^2/ms^2
Conversion factor = 10^3
- Density = 1Kg/m^3
- 1000 gm / (1000 mm)^3
- 1 gm/1000000 mm^3
- 10^-6 gm/mm^3
Conversion factor = 10^-6
- Young’s Modulus = 210 GPa
1 Pa = 10^-6 gm/mm ms2
1 GPa = 109 * 10 -6 gm/mm ms2
210 GPa = 210 * 103 gm/mm ms2
Conversion factor = 103
- Velocity = 56.33 Kmph
Km/h
1Km = 1000000 mm = 106 mm
1 hr = 60min*60sec*1000
= 3600000
= 36*105 ms
1 kmph
=> (106 )/(36*105)
=> 0.277 mm/ms
56.33 kmph =
=> 56.33 * 0.277 mm/ms
=> 15.60 mm/ms
Conversion factor =0.277
- Gravity = 9.88 m/s^2
1 m/s2 = 1000mm/(1000ms2)
= 10 -3 mm/ms2
9.8 m/s2 = 9.8*10-3 mm/ms2
Conversion Factor = 10-3
4. Conversion of SI unit to kg m s
- Mass = 1 kg
1 kg
- Length = 1m
1 m
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s2
=> (1 kg*1m)/(1s)2
=> 1 kg m/s2
Conversion factor = 100
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 1 kg m/s2
=> (1 kg m/s2) / (1 m)2
=> 1 kg/m s2
Conversion factor = 1
- Energy = 1 Nm
- 1N *1 m
- 1 kg m/s2 * 1 m
- 1 kg m2/s2
Conversion factor = 1
- Density = 1Kg/m^3
- 1 kg / (1 m)3
- 1 kg/1 m3
- 10 kg/m3
Conversion factor = 10
- Young’s Modulus = 210 GPa
1 Pa = 1 kg/m s2
1 GPa = 109 * 1 kg/m s2
210 GPa = 210 * 109 kg/m s2
Conversion factor = 109
- Velocity = 56.33 Kmph
Km/h
1Km = 1000 m = 103 m
1 hr = 60min*60sec
= 3600 s
1 kmph
=> (103 )/(3600)
=> 0.277 m/s
56.33 kmph =
=> 56.33 * 0.277 m/s
=> 15.603 m/s
Conversion factor = 0.277
- Gravity = 9.88 m/s2
1 m/s2 = 1 m/(1s)2
= 1 m/s2
9.8 m/s2 = 9.8*1 m/s2
Conversion Factor = 1
5. Conversion of SI unit to g cm s
- Mass = 1 kg
1000gm
- Length = 1m
100 cm
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1000 g * 1m/s2
=> (1000 g*100cm)/(1s)2
=> 105 g cm/s2
Conversion factor = 105
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 105 g cm/s2
=> 105 g cm/s2/ (100 cm)2
=> 10 g/cm s2
Conversion factor = 10
- Energy = 1 Nm
- 1N *1 m
- 105 g cm/s2 * 100 cm
- 107 g cm2/s2
Conversion factor = 107
- Density = 1Kg/m^3
- 1000 g / (100 cm)3
- 1000 g/1000000 cm3
- 10-3 g/cm3
Conversion factor = 10-3
- Young’s Modulus = 210 GPa
1 Pa = 10 g/cm s2
1 GPa = 109 * 10 g/cm s2
210 GPa = 210 * 1010 g/cm s2
Conversion factor = 1010
- Velocity = 56.33 Kmph
Km/h
1Km = 10000 cm = 104 cm
1 hr = 60min*60sec
= 3600
= 3600 s
1 kmph
=> (104 )/(3600)
=> 2.77 cm/s
56.33 kmph =
=> 56.33 * 2.77 cm/s
=> 156.03 cm/s
Conversion factor =2.77
- Gravity = 9.88 m/s2
1 m/s2 = 100 cm/(1s)2
= 100 cm/s2
9.8 m/s2 = 9.8*100 cm/s2
Conversion Factor = 100
6. Conversion of SI unit to g cm us(micro-sec)
- Mass = 1 kg
1000 gm
- Length = 1m
100 cm
- Time = 1 sec
106 us
- Force = 1 N
F => mass* acceleration
=> 1000 g * 100 cm/(106 us)2
=> (1000 g*100 cm)/(106 us)2
=> 10-1 g cm/us2
Conversion factor = 10-1
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 10-1 g cm/us2
=> 10-1 g cm/us2/ (100 cm)2
=> 10-3 g/cm us2
Conversion factor = 10-3
- Energy = 1 Nm
- 1N *1 m
- 10-1 g cm/us2 * 100 cm
- 10 g cm2/us2
Conversion factor = 10
- Density = 1Kg/m^3
- 1000 g / (100 cm)3
- 1000 g/1000000 cm3
- 10-3 g/cm3
Conversion factor = 10-3
- Young’s Modulus = 210 GPa
1 Pa =10-3 g/cm us2
1 GPa = 109 * 10-3 g/cm us2
210 GPa = 210 * 106 g/cm us2
Conversion factor = 106
- Velocity = 56.33 Kmph
Km/h
1Km = 10000 cm = 104 cm
1 hr = 60min*60sec*106 us
= 36*108 us
= 36* 108 us
1 kmph
=> (104 )/(36*108)
=> 0.00000278 cm/ us
56.33 kmph =
=> 56.33 * 0.00000278 cm/us
=> 0.000156 cm/us
Conversion factor =0.00000278
- Gravity = 9.88 m/s2
1 m/s2 = 100 cm/(106 us)2
= 100 cm/ 1012 us2
9.8 m/s2 = 9.8*10-10 cm/us2
Conversion Factor = 10-10
7. Conversion of SI unit to g mm s
- Mass = 1 kg
1000 gm
- Length = 1m
1000 mm
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1000 g * 1m/s2
=> (1000 g*1000 mm)/(1s)2
=> 106 g mm/s2
Conversion factor = 106
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 106 g mm/s2
=> (106 g mm/s2 ) /(1000 mm)2
=> 1 g/mm s2
Conversion factor = 1
- Energy = 1 Nm
- 1N *1 m
- 106 g mm/s2 * 1000 mm
- 109 g mm2/s2
Conversion factor = 109
- Density = 1Kg/m^3
- 1000 g / (1000 mm)3
- 1000 g/1000000000 mm3
- 10-6 g/mm3
Conversion factor = 10-6
- Young’s Modulus = 210 GPa
1 Pa = 1 g/mm s2
1 GPa = 109 * 1 g/mm s2
210 GPa = 210 * 109 g/mm s2
Conversion factor = 109
- Velocity = 56.33 Kmph
Km/h
1Km = 1000000 mm = 106 mm
1 hr = 60min*60sec
= 3600
= 3600 s
1 kmph
=> (106 )/(3600)
=> 277.7 mm/s
56.33 kmph =
=> 56.33 * 277.7 mm/s
=> 15603 mm/s
Conversion factor =277.7
- Gravity = 9.88 m/s2
1 m/s2 = 1000 mm/(1s)2
= 1000 mm/s2
9.8 m/s2 = 9.8*1000 mm/s2
Conversion Factor = 103
8. Conversion of SI unit to ton mm ms
- Mass = 1 kg
0.001 ton
- Length = 1m
1000 mm
- Time = 1 sec
1000 ms
- Force = 1 N
F => mass* acceleration
=> 0.001 ton * 1m/s^2
=> (0.001 ton *1000 mm)/(1000ms)2
=> 10-6 ton mm/ms2
Conversion factor = 10-6
- Stress = 1 Pa
1 Pa => 1N/m^2
As from the above derived 1N = 10-6 (ton mm)/ms2
=> {10-6 (ton mm)/ms2} / (1000 mm)2
=> 10-12 ton/mm ms2
Conversion factor = 10-12
- Energy = 1 Nm
- 1N *1 m
- {10-6 (ton mm)/ms2} * 1000 mm
- 10-3 ton mm2/ms2
- 10-3 ton mm2/ms2
Conversion factor = 10-3
- Density = 1Kg/m^3
- 001 ton / (1000 mm)3
- 001 ton/1000000000 mm3
- 10-12 ton/mm3
Conversion factor = 10-12
- Young’s Modulus = 210 GPa
1 Pa = 10-12 ton/mm ms2
1 GPa = 109 * 10-12 ton/mm ms2
210 GPa = 210 * 10-3 ton/mm ms2
Conversion factor = 10-3
- Velocity = 56.33 Kmph
Km/h
1Km = 1000000 mm = 106 mm
1 hr = 60min*60sec*1000
= 3600000
= 36*105 ms
1 kmph
=> (106 )/(36*105)
=> 0.277 mm/ms
56.33 kmph =
=> 56.33 * 0.277 mm/ms
=> 15.60 mm/ms
Conversion factor =0.277
- Gravity = 9.88 m/s2
1 m/s2 = 1000 mm/(1000 ms)2
= 10 -3 mm/ms2
9.8 m/s2 = 9.8*10-3 mm/ms2
Conversion Factor = 10-3
9. Conversion of SI unit to slug ft s
- Mass = 1 kg
0.068 slug
- Length = 1m
3.28 ft
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s2
=> (0.068 slug*3.28 ft)/(1s)2
=> 0.22 slug ft/s2
Conversion factor = 0.22
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 0.22 slug ft/s2
=> 0.22 slug ft/s2 / (3.28 ft)2
=> 0.0205 slug/ft s2
Conversion factor = 0.0205
- Energy = 1 Nm
- 1N *1 m
- 22 slug ft/s2 * 3.28 ft
- 7216 slug ft2/s2
Conversion factor = 0.7216
- Density = 1Kg/m^3
- 1 kg / (1 m)3
- 068 slug/(3.28 ft)3
- 068 slug/ 35.29 ft3
- 0019 slug/ft3
Conversion factor = 0.0019
- Young’s Modulus = 210 GPa
1 Pa = 0.0205 slug/ft s2
1 GPa = 109 * 0.0205 slug/ft s2
210 GPa = 210 * 109 * 0.0205 slug/ft s2
210 GPa = 4.305*109 slug/ft s2
Conversion factor = 0.0205
- Velocity = 56.33 Kmph
Km/h
1Km = 1000 m = 103 m = 103 * 3.28 ft
1 hr = 60min*60sec
= 3600 s
1 kmph
=> (3.28*103 ft)/(3600 s)
=> 0.911 ft/s
56.33 kmph =
=> 56.33 * 0.911 ft/s
=> 51.316 ft/s
Conversion factor =0.911
- Gravity = 9.88 m/s2
1 m/s2 = 3.28 ft/(1s)2
= 3.28 ft/s2
9.8 m/s2 = 9.8*3.28 ft/s2 = 32.14 ft/s2
Conversion Factor = 3.28
10. Conversion of SI unit to kg s
- Mass = 1 kg
1 kg
- Length = 1m
1000 mm
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s2
=> (1 kg*1000 mm)/(1s)2
=> 1000 kg mm/s2
Conversion factor = 100
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 1000 kg mm/s2
=> (1000 kg mm/s2 )/ (1000 mm)2
=> 10-3 kg/mm s2
Conversion factor = 10-3
- Energy = 1 Nm
- 1N *1 m
- 1000 kg mm/s2 * 1000 mm
- 106 kg mm2/s2
Conversion factor = 106
- Density = 1Kg/m^3
- 1 kg / (1000 mm)3
- 1 kg/1000000000 mm3
- 10-9 kg/mm3
Conversion factor = 10-9
- Young’s Modulus = 210 GPa
1 Pa = 10-3 kg/mm s2
1 GPa = 109 * 10-3 kg/mm s2
210 GPa = 210 * 106 kg/mm s2
Conversion factor = 106
- Velocity = 56.33 Kmph
Km/h
1Km = 1000000 mm = 106 mm
1 hr = 60min*60sec
= 3600
= 3600 s
1 kmph
=> (106 )/(3600)
=> 277.78 mm/s
56.33 kmph =
=> 56.33 * 277.78 mm/s
=> 15603 mm/s
Conversion factor =277.78
- Gravity = 9.88 m/s2
1 m/s2 = 1000 mm/(1s)2
= 1000 mm/s2
9.8 m/s2 = 9.8*1000 mm/s2
Conversion Factor = 103
11. Conversion of SI unit to g cm ms
- Mass = 1 kg
1000gm
- Length = 1m
100 cm
- Time = 1 sec
1000 ms
- Force = 1 N
F => mass* acceleration
=> 1000 g * 1m/s2
=> (1000 g*100cm)/(1000 ms)2
=> 10-1 g cm/ms2
Conversion factor = 10-1
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 10-1 g cm/ms2
=> 10-1 g cm/ms2 / (100 cm)2
=> 10-3 g/cm ms2
Conversion factor = 10-3
- Energy = 1 Nm
- 1N *1 m
- 10-1 g cm/ms2 * 100 cm
- 10 g cm2/ms2
Conversion factor = 10
- Density = 1Kg/m^3
- 1000 g / (100 cm)3
- 1000 g/1000000 cm3
- 10-3 g/cm3
Conversion factor = 10-3
- Young’s Modulus = 210 GPa
1 Pa = 10-3 g/cm ms2
1 GPa = 109 * 10-3 g/cm ms2
210 GPa = 210 * 106 g/cm ms2
Conversion factor = 106
- Velocity = 56.33 Kmph
Km/h
1Km = 10000 cm = 104 cm
1 hr = 60min*60sec*1000
= 36*105 ms
= 36*105 ms
1 kmph
=> (105 cm)/( 36*105 ms)
=> 0.0277 cm/ms
56.33 kmph =
=> 56.33 * 0.0277 cm/ms
=> 1.5603 cm/ms
Conversion factor =0.0277
- Gravity = 9.88 m/s2
1 m/s2 = 100 cm/(1000 ms)2
= 10-4 cm/ms2
9.8 m/s2 = 9.8*10-4 cm/ms2
Conversion Factor = 10-4
12. Conversion of SI unit to kg mm ms
- Mass = 1 kg
1 kg
- Length = 1m
1000 mm
- Time = 1 sec
1000 ms
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s^2
=> (1 kg*1000 mm)/(1000ms)2
=> 10-3 (kg*mm)/ms2
Conversion factor = 10-1
- Stress = 1 Pa
1 Pa => 1N/m^2
As from the above derived 1N = 10-3 (kg*mm)/ms2
=> {10-3 (kg*mm)/ms2} / (1000 mm)2
=> 10-9 kg/mm ms2
Conversion factor = 10-9
- Energy = 1 Nm
- 1N *1 m
- {10-3 (kg mm)/ms2} * 1000 mm
- 1 kg mm2/ms2
- 1 kg mm2/ms2
Conversion factor = 1
- Density = 1Kg/m^3
- 1 kg / (1000 mm)3
- 1 kg/1000000000 mm3
- 10-9 kg/mm3
Conversion factor = 10-9
- Young’s Modulus = 210 GPa
1 Pa = 10-9 kg/mm ms2
1 GPa = 109 * 10-9 kg/mm ms2
210 GPa = 210 * 1 kg/mm ms2
Conversion factor = 1
- Velocity = 56.33 Kmph
Km/h
1Km = 1000000 mm = 106 mm
1 hr = 60min*60sec*1000
= 3600000
= 36*105 ms
1 kmph
=> (106 )/(36*105)
=> 0.277 mm/ms
56.33 kmph =
=> 56.33 * 0.277 mm/ms
=> 15.60 mm/ms
Conversion factor = 0.277
- Gravity = 9.88 m/s2
1 m/s2 = 1000 mm/(1000 ms)2
= 10 -3 mm/ms2
9.8 m/s2 = 9.8*10-3 mm/ms2
Conversion Factor = 10-3