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Challenge

Week - 1 - Consistency of Units

KKailash Kumar4 Aug 2023

Aim:-Write a detailed report of unit conversion because of Different industries use different system of units as per their convenience. For example, automotive industries use kg,mm,ms as their standard unit system. Construction industries are likely to use tonne,m,s as their unit system. Similarly, PCB simulation in electronic industry uses gm, micrometer,ms as their system of units.

Object:- The main object of this challege convert value in different uint system, which deal with LS-Dyna.

Value of the following measurements are given as follows:

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

Now, here are a few system of units:


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

1.Conversion of SI unit to Kg,cm,ms

  • Mass=1 Kg
  • Length=1m=100cm
  • Time=1s=1000ms
  • force=1N =1kg*m/s^2 =1kg*100cm/(1000ms)^2 =1kg*100cm/10^6ms^2 =1kg*1cm/10^4ms^2 =10^-4(kg*cm)/ms^2 Conversion factor=10^-4
  • Stress=1pa =1n/m^2 =(kg*m/s^2)/m^2 we can write it =kg*m/s^2*m^2 =kg/s^2*m =kg/(1000ms)^2*100cm =kg/10^6ms^2*100cm =10^-8kg/(ms*cm) Conversion factor=10^-8
  • Energy=1Nm =(kgm/s^2)*m =kg*m^2/s^2 =kg*(100cm)^2/(1000ms)^2 =kg*10^4cm^2/10^6ms^2 =10^-2*kg*cm^2/ms^2 Conversion factor=10^-2
  • Density=1kg/m^3 =kg/(100cm)^3 =kg/10^6cm^3 =10^-6kg/cm^3 Conversion factor=10^-6
  • Young's moduius=210Gpa we known that 1Gpa=10^9pa =210*10^9*pa =210*10^9*n/m^2 =210*10^9(kg*m/s^2)/m^2 =210*10^9kg*m/s^2*m^2 =210*10^9kg/s^2*m =210*10^9kg/(1000ms)^2*100cm =210*10^9kg/10^6ms^2*100cm =210*10kg/(ms*cm) =2100kg/(ms*cm) Conversion factor=10
  • Velocity=56.33KMPH =56.33*(1000*100*cm)/(60*60*1000ms) =56.33*10^5cm/36*10^5ms =56.33*0.0277cm/ms =1.564cm/ms Conversion factor=0.0277
  • Gravity=9.8m/s^2 =9.8*100cm/(1000ms)^2 =9.8*100cm/10^6ms =9.8*10^-4cm/ms Conversion factor=10^-4

2.Conversion of SI unit to Kg,cm,s

  • Mass=1 Kg
  • Length=1m=100cm
  • Time=1s
  • force=1N =1kg*m/s^2 =1kg*100cm/s^2 =1kg*100cm/s^2 =100kg*cm/s^2 Conversion factor=100
  • Stress=1pa =1n/m^2 =(kg*m/s^2)/m^2 we can write it =kg*m/s^2*m^2 =kg/s^2*m =kg/s^2*100cm =10^-2kg/cm*s^2 Conversion factor=10^-2
  • Energy=1Nm =(kgm/s^2)*m =kg*m^2/s^2 =kg*(100cm)^2/s^2 =10^4kg*cm^2/s^2 Conversion factor=10^4
  • Density=1kg/m^3 =kg/(100cm)^3 =kg/10^6cm^3 =10^-6kg/cm^3 Conversion factor=10^-6
  • Young's moduius=210Gpa we known that 1Gpa=10^9pa =210*10^9*pa =210*10^9*n/m^2 =210*10^9(kg*m/s^2)/m^2 =210*10^9kg*m/s^2*m^2 =210*10^9kg/s^2*m =210*10^9kg/s^2*100cm =210*10^9kg/s^2*100cm =210*10^7kg/s*cm Conversion factor=10^7
  • Velocity=56.33KMPH =56.33*(1000*100*cm)/(60*60s) =56.33*10^5cm/3600ms =56.33*27.77cm/ms =1,564.722cm/ms Conversion factor=27.77
  • Gravity=9.8m/s^2 =9.8*100cm/s^2 =9.8*100cm/s^2 =9.8*10^2cm/s^2 Conversion factor=10^2

3.Conversion of SI unit to gm,mm,ms

  • Mass=1 Kg=1000gm
  • Length=1m=100cm=1000mm
  • Time=1s=1000ms
  • force=1N =1kg*m/s^2 =1000gm*1000mm/(1000ms)^2 =10^6gm*mm/10^6ms^2 =1 gm*mm/ms^2 Conversion factor=1
  • Stress=1pa =1n/m^2 =(kg*m/s^2)/m^2 we can write it =kg*m/s^2*m^2 =kg/s^2*m =1000gm/(1000ms)^2*1000mm =1000gm/10^9 mm*ms^2 =10^-6gm/mm*ms^2 Conversion factor=10^-6
  • Energy=1Nm =(kgm/s^2)*m =kg*m^2/s^2 =1000gm*(1000mm)^2/(1000ms)^2 =10^9gm*mm^2/10^6ms^2 =10^3gm*mm^2/ms^2 Conversion factor=10^3
  • Density=1kg/m^3 =1000gm/(1000mm)^3 =10^-6gm/mm^3 Conversion factor=10^-6
  • Young's moduius=210Gpa we known that 1Gpa=10^9pa =210*10^9*pa =210*10^9*n/m^2 =210*10^9(kg*m/s^2)/m^2 =210*10^9kg*m/s^2*m^2 =210*10^9kg/s^2*m =210*10^9(1000gm)/(1000ms)^2*1000mm =210*10^12gm/10^9ms^2*mm =210*10^3gm/ms*mm Conversion factor=10^3
  • Velocity=56.33KMPH =56.33*(1000*100*10mm)/(60*60*1000ms) =56.33*10^6cm/36*10^5ms =56.33*0.277cm/ms =15.64.722cm/ms Conversion factor=0.277
  • Gravity=9.8m/s^2 =9.8*1000mm/(1000ms)^2 =9.8*10^-3mm/ms^2 Conversion factor=10^-3

4.Conversion of SI unit to Kg,m,s

  • Mass=1 Kg
  • Length=1m
  • Time=1s
  • force=1N (f=m*a) =1kg*m/s^2 =1kg*m/s^2 =1kg*m/s^2 Conversion factor=1
  • Stress=1pa =1n/m^2 =(kg*m/s^2)/m^2 we can write it =1kg*m/s^2*m^2 =1kg/s^2*m Conversion factor=1
  • Energy=1Nm =(kg*m/s^2)*m =1kg*m^2/s^2 Conversion factor=1
  • Density=1kg/m^3 =1kg/m^3 Conversion factor=1
  • Young's moduius=210Gpa we known that 1Gpa=10^9pa =210*10^9*pa =210*10^9*n/m^2 =210*10^9(kg*m/s^2)/m^2 =210*10^9kg*m/s^2*m^2 =210*10^9kg/s^2*m Conversion factor=10^9
  • Velocity=56.33KMPH =56.33*(1000m)/(60*60s) =56.33*10^3m/3600s =56.33*0.27m/s =15.64m/s Conversion factor=0.277
  • Gravity=9.8m/s^2 =9.8*1m/s^2 Conversion factor=1

5.Conversion of SI unit to gm,cm,s

  • Mass=1 Kg=1000gm
  • Length=1m=100cm
  • Time=1s
  • force=1N =1kg*m/s^2 =1000gm*100cm/s^2 =10^5gm*cm/s^2 Conversion factor=10^5
  • Stress=1pa =1n/m^2 =(kg*m/s^2)/m^2 we can write it =kg*m/s^2*m^2 =kg/s^2*m =1000gm/s^2*100cm =10gm/cm*s^2 Conversion factor=10
  • Energy=1Nm =(kgm/s^2)*m =kg*m^2/s^2 =1000gm*(100cm)^2/s^2 =10^7gm*cm^2/s^2 Conversion factor=10^7
  • Density=1kg/m^3 =1000gm/(100cm)^3 =1000gm/10^6cm^3 =10^-3gm/cm^3 Conversion factor=10^-3
  • Young's moduius=210Gpa we known that 1Gpa=10^9pa =210*10^9*pa =210*10^9*n/m^2 =210*10^9(kg*m/s^2)/m^2 =210*10^9kg*m/s^2*m^2 =210*10^9kg/s^2*m =210*10^9*1000gm/s^2*100cm =210*10^12gm/s^2*100cm =210*10^10gm/s^2*cm Conversion factor=10^10
  • Velocity=56.33KMPH =56.33*(1000*100*cm)/(60*60s) =56.33*10^5cm/3600s =56.33*27.77cm/s =1,564.722cm/s Conversion factor=27.77
  • Gravity=9.8m/s^2 =9.8*100cm/s^2 =9.8*100cm/s^2 =9.8*10^2cm/s^2 Conversion factor=10^2

6.Conversion of SI unit to gm,cm,us

  • Mass=1 Kg=1000gm
  • Length=1m=100cm
  • Time=1s =10^6us
  • force=1N =1kg*m/s^2 =1000gm*100cm/(10^6us)^2 =10^-7gm*cm/us^2 Conversion factor=10^-7
  • Stress=1pa =1n/m^2 =(kg*m/s^2)/m^2 we can write it =kg*m/s^2*m^2 =kg/s^2*m =1000gm/(10^6us)^2*100cm =10^-11gm/cm*us^2 Conversion factor=10^-11
  • Energy=1Nm =(kgm/s^2)*m =kg*m^2/s^2 =1000gm*(100cm)^2/(10^6us)^2 =10^5gm*cm/10^12us^2 =10^-7gm*cm^2/us^2 Conversion factor=10^-7
  • Density=1kg/m^3 =1000gm/(100cm)^3 =1000gm/10^6cm^3 =10^-3kg/cm^3
  • Young's moduius=210Gpa we known that 1Gpa=10^9pa =210*10^9*pa =210*10^9*n/m^2 =210*10^9(kg*m/s^2)/m^2 =210*10^9kg*m/s^2*m^2 =210*10^9kg/s^2*m =210*10^9*1000gm/(10^6us)^2*100cm =210*10^12gm/10^12us^2*100cm =210*10^-2gm/us^2*cm Conversion factor=10^-2
  • Velocity=56.33KMPH =56.33*(1000*100*cm)/(60*60*10^6us) =56.33*10^5cm/36*10^8s =56.33*0.000027cm/s =0.001564cm/s Conversion factor=0.000027
  • Gravity=9.8m/s^2 =9.8*100cm/(10^6us)^2 =9.8*100cm/10^12us^2 =9.8*10^-10cm/s^2 Conversion factor=10^-10

7.Conversion of SI unit to gm,mm,s

  • Mass=1 Kg=1000gm
  • Length=1m=100cm=1000mm
  • Time=1s
  • force=1N =1kg*m/s^2 =1000gm*1000mm/s^2 =10^6gm*mm/s^2 Conversion factor=10^6
  • Stress=1pa =1n/m^2 =(kg*m/s^2)/m^2 we can write it =kg*m/s^2*m^2 =kg/s^2*m =1000gm/s^2*1000mm =1000gm/1000 mm*s^2 =1gm/mm*s^2 Conversion factor=1
  • Energy=1Nm =(kgm/s^2)*m =kg*m^2/s^2 =1000gm*(1000mm)^2/s^2 =10^9gm*mm^2/s^2 Conversion factor=10^9
  • Density=1kg/m^3 =1000gm/(1000mm)^3 =10^-6gm/mm^3 Conversion factor=10^-6
  • Young's moduius=210Gpa we known that 1Gpa=10^9pa =210*10^9*pa =210*10^9*n/m^2 =210*10^9(kg*m/s^2)/m^2 =210*10^9kg*m/s^2*m^2 =210*10^9kg/s^2*m =210*10^9(1000gm)/s^2*1000mm =210*10^9gm/s^2*mm Conversion factor=10^9
  • Velocity=56.33KMPH =56.33*(1000*100*10mm)/(60*60s) =56.33*10^6mm/3600s =56.33*277.77mm/ms =15,647.2mm/ms Conversion factor=277.77
  • Gravity=9.8m/s^2 =9.8*1000mm/s^2 =9.8*10^3mm/s^2 Conversion factor=10^3

8.Conversion of SI unit to ton,mm,s

  • Mass=1 Kg=1000gm=0.001ton
  • Length=1m=100cm=1000mm
  • Time=1s
  • force=1N =1kg*m/s^2 =0.001ton*1000mm/s^2 =1ton*mm/s^2 Conversion factor=1
  • Stress=1pa =1n/m^2 =(kg*m/s^2)/m^2 we can write it =kg*m/s^2*m^2 =kg/s^2*m =0.001ton/s^2*1000mm =0.001ton/1000 mm*s^2 =10^-6ton/mm*s^2 Conversion factor=10^-6
  • Energy=1Nm =(kgm/s^2)*m =kg*m^2/s^2 =0.001ton*(1000mm)^2/s^2 =1ton*mm^2/s^2 Conversion factor=1
  • Density=1kg/m^3 =0.001ton/(1000mm)^3 =10^-12gm/mm^3 Conversion factor=10^-12
  • Young's moduius=210Gpa we known that 1Gpa=10^9pa =210*10^9*pa =210*10^9*n/m^2 =210*10^9(kg*m/s^2)/m^2 =210*10^9kg*m/s^2*m^2 =210*10^9kg/s^2*m =210*10^9(0.001ton)/s^2*1000mm =210*10^3ton/s^2*mm Conversion factor=10^3
  • Velocity=56.33KMPH =56.33*(1000*100*10mm)/(60*60s) =56.33*10^6mm/3600s =56.33*277.77mm/s =15,647.2mm/s Conversion factor=277.77
  • Gravity=9.8m/s^2 =9.8*1000mm/s^2 =9.8*10^3mm/s^2 Conversion factor=10^3

9.Conversion of SI unit to slug,ft,s

  • Mass=1 Kg=1000gm=0.001ton =0.068slug
  • Length=1m=100cm=1000mm =3.28ft
  • Time=1s
  • force=1N =1kg*m/s^2 =0.068slug*3.28ft/s^2 =0.223slug*ft/s^2 Conversion factor=0.223
  • Stress=1pa =1n/m^2 =(kg*m/s^2)/m^2 we can write it =kg*m/s^2*m^2 =kg/s^2*m =0.068slug/3.28ft*s^2 =0.0207slug/ft*s^2 Conversion factor=0.0207
  • Energy=1Nm =(kgm/s^2)*m =kg*m^2/s^2 =0.068slug*(3.28ft)^2/s^2 =0.068slug*10.7584ft^2/s^2 =0.731slug*ft/s^2 Conversion factor=0.731
  • Density=1kg/m^3 =0.068slug/(3.28ft)^3 =0.001927slug/ft^3 =1.927*10^-3slug/ft^3 Conversion factor=1.927*10^-3
  • Young's moduius=210Gpa we known that 1Gpa=10^9pa =210*10^9*pa =210*10^9*n/m^2 =210*10^9(kg*m/s^2)/m^2 =210*10^9kg*m/s^2*m^2 =210*10^9kg/s^2*m =210*10^9(0.068slug)/s^2*3.28ft =210*10^9*0.22304slug/s^2*ft =4.683*10^9slug/ft*s^2 Conversion factor=0.22304
  • Velocity=56.33KMPH =56.33*(328ft)/(60*60s) =56.33*3280ft/3600s =56.33*0.091ft/s =51.32ft/s Conversion factor=0.09
  • Gravity=9.8m/s^2 =9.8*3.28ft/s^2 =32.144ft/s^2 Conversion factor=3.28

10.Conversion of SI unit to Kg,mm,s

  • Mass=1 Kg
  • Length=1m=100cm=1000mm
  • Time=1s
  • force=1N (f=m*a) =1kg*m/s^2 =1kg*m/s^2 =10^3kg*mm/s^2 Conversion factor=10^3
  • Stress=1pa =1n/m^2 =(kg*m/s^2)/m^2 we can write it =1kg*m/s^2*m^2 =10^-3kg/s^2*mm Conversion factor=10^-3
  • Energy=1Nm =(kg*m/s^2)*m =10^6kg*mm^2/s^2 Conversion factor=10^6
  • Density=1kg/m^3 =1kg/10^9mm^3 =10^-9kg/mm^3 Conversion factor=10^-9
  • Young's moduius=210Gpa we known that 1Gpa=10^9pa =210*10^9*pa =210*10^9*n/m^2 =210*10^9(kg*m/s^2)/m^2 =210*10^9kg*m/s^2*m^2 =210*10^9kg/s^2*m =210*10^9kg/s^2*1000mm =210*10^6kg/mm*s^2 Conversion factor=10^6
  • Velocity=56.33KMPH =56.33*(1000*100*10mm)/(60*60s) =56.33*10^6m/3600s =56.33*277.77mm/s =15647.22mm/s Conversion factor=277.77
  • Gravity=9.8m/s^2 =9.8*10^3mm/s^2 Conversion factor=10^3

11.Conversion of SI unit to gm,cm,ms

  • Mass=1 Kg=1000gm
  • Length=1m=100cm
  • Time=1s=1000ms
  • force=1N =1kg*m/s^2 =1000gm*100cm/(1000ms)^2 =10^5gm*cm/10^6ms^2 =10^-1(gm*cm)/ms^2 Conversion factor=0.1
  • Stress=1pa =1n/m^2 =(kg*m/s^2)/m^2 we can write it =kg*m/s^2*m^2 =kg/s^2*m =1000gm/(1000ms)^2*100cm =1000gm/10^6ms^2*100cm =10^-5kg/(ms*cm) Conversion factor=10^-5
  • Energy=1Nm =(kgm/s^2)*m =kg*m^2/s^2 =1000gm*(100cm)^2/(1000ms)^2 =10^7gm*cm^2/10^6ms^2 =10gm*cm^2/ms^2 Conversion factor=10
  • Density=1kg/m^3 =1000gm/(100cm)^3 =1000gm/10^6cm^3 =10^-3gm/cm^3 Conversion factor=10^-3
  • Young's moduius=210Gpa we known that 1Gpa=10^9pa =210*10^9*pa =210*10^9*n/m^2 =210*10^9(kg*m/s^2)/m^2 =210*10^9kg*m/s^2*m^2 =210*10^9kg/s^2*m =210*10^9kg/(1000ms)^2*100cm =210*10^9(1000gm)/10^6ms^2*100cm =210*10^4gm/(ms*cm) Conversion factor=10^4
  • Velocity=56.33KMPH =56.33*(1000*100*cm)/(60*60*1000ms) =56.33*10^5cm/36*10^5ms =56.33*0.0277cm/ms =1.564cm/ms Conversion factor=0.0277
  • Gravity=9.8m/s^2 =9.8*100cm/(1000ms)^2 =9.8*100cm/10^6ms =9.8*10^-4cm/ms Conversion factor=10^-4

12.Conversion of SI unit to kg,mm,ms

  • Mass=1 Kg
  • Length=1m=100cm=1000mm
  • Time=1s=1000ms
  • force=1N =1kg*m/s^2 =1kg*1000mm/(1000ms)^2 =1000kg*mm/10^6ms^2 =10^-3kg*mm/ms^2 Conversion factor=10^-3
  • Stress=1pa =1n/m^2 =(kg*m/s^2)/m^2 we can write it =kg*m/s^2*m^2 =kg/s^2*m =1kg/(1000ms)^2*1000mm =1kg/10^9 mm*ms^2 =10^-9gm/mm*ms^2 Conversion factor=10^-9
  • Energy=1Nm =(kgm/s^2)*m =kg*m^2/s^2 =1kg*(1000mm)^2/(1000ms)^2 =10^6kg*mm^2/10^6ms^2 =1kg*mm^2/ms^2 Conversion factor=1
  • Density=1kg/m^3 =1kg/(1000mm)^3 =10^-9gm/mm^3 Conversion factor=10^-9
  • Young's moduius=210Gpa we known that 1Gpa=10^9pa =210*10^9*pa =210*10^9*n/m^2 =210*10^9(kg*m/s^2)/m^2 =210*10^9kg*m/s^2*m^2 =210*10^9kg/s^2*m =210*10^9kg/(1000ms)^2*1000mm =210*10^9kg/10^9ms^2*mm =210*kg/ms*mm Conversion factor=1
  • Velocity=56.33KMPH =56.33*(1000*100*10mm)/(60*60*1000ms) =56.33*10^6cm/36*10^5ms =56.33*0.277cm/ms =15.64.722cm/ms Conversion factor=0.277
  • Gravity=9.8m/s^2 =9.8*1000mm/(1000ms)^2 =9.8*10^-3mm/ms^2 Conversion factor=10^-3

Conclusion:- This conversion used in LS-Dyna to switch one unit system to another.

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