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  1. Home/
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  3. Week - 1 - Consistency of Units

Week - 1 - Consistency of Units

                    Consistency of Units  Objectives: -  Write the given measurements of the following different systems of units. Also, mention the conversion factors. Value of the following measurements are given as follows: MASS 1kgLENGTH 1mTIME 1sFORCE…

    • Parag Bari

      updated on 25 Feb 2022

                        Consistency of Units 

    Objectives: -  Write the given measurements of the following different systems of units. Also, mention the conversion factors.

    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 systems 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

    Procedure:- 

    Mass: - 

    1 tonne = 1000kg ,

    1 kg = 1000 gram = 0.001 tonne = 0.068 slug ,

    1 gram = 1000 mg (milligram)

    Length: - 

    1 km = 1000 m ,

    1 m = 100 cm = 1000 mm = 3.28 ft ,

    1 mm = 100 μm.

    Time: - 

    1 Hour = 3600 s , 

    1 s = 1000 ms = 10^6 μs

    SI unit to gm mm ms 

    Mass: - 

    1 kg = 1000 gram

    Length: - 

    1 m = 1000 mm

    Time: - 

    1 s =1000 ms

    Force: - 

    F = m.a

      = 1 kg * m/s2

      = (1000 g )*(1000 mm)/ (1000 ms)^2

      = 10^6 g mm/ 10^6 ms^2

    F=1N = 1 g mm/ms^2 

    Conversion Factor = 1

    Stress: -

    1Pa = 1 N/m^2

          = (1 g mm/ ms^2) /(1000 mm)^2

          = (1 g mm/ ms^2) / (10^6 mm^2)

    1Pa = 10^-6 g /mm ms^2 

    Conversion Factor = 10^-6

    Energy: - 

    Nm = 1 g mm/ ms^2 * 1 m

          = 1 g mm/ms^2 * 10^3 mm

    Nm = 10^3 g mm^2 / ms^2

    Conversion Factor = 10^3 

    Density: - ρ: - 

                    = kg/m^3

                    = 10^3 g /( 10^3 mm)^3

                    = 10^3 g / ( 10^9 mm ^3)

                ρ  = 10^-6 g /mm^3

    Conversion Factor = 10^-6

    Young's Modulus = 210 GPa

    • 1 Pa (N/m2) = 1x10-6 N/mm2 
    •  1 MPa = 106 Pa (N/m2) 
    • 1 GPa = 109 N/m2 = 106 N/cm2  = 103 N/mm2 

     GPa = 10^9 * 10^-6 g/mm ms^2

    210 GPa =  210*10^3 g/mm ms^2

    Conversion Factor = 10^3

    Velocity = 56.33 kmph

    km = 10^6 mm 

    1 Hour = 3600 s = 3600000 ms 

    kmph = 56.33*10^6 mm / 3.6*10^6 ms

            V = 15.60 mm/ms 

    Conversion Factor = 1

    Gravity: - 9.8 m/s^2

             = 9.8*10^3 mm/ 10^6 ms^2 

             = 9.8*10^-3 mm / ms^2

    Conversion Factor = 1 

     

    SI unit to g mm s 

    Force  N = 10^6 g mm/s^2

    Conversion Factor = 10 ^6

    Stress: - Pa = 1* g/mm s^2

    Conversion Factor = 1 

    Energy Nm = 10^9 g mm^2/s^2 

    Conversion Factor = 10^9

    Density ρ = 10^-6 g/mm^3 

    Conversion Factor = 10^-6 

    Young's Modulus = 210 GPa = 210* 10^9 g/ mm s^2 

    Conversion Factor = 10^9

    Velocity = 56.33 kmph = 15647 mm/s

    Conversion Factor = 1

    Gravity = 9.8*10^3 mm/s^2

    Conversion Factor = 10^3

     

    SI unit to g cm s 

    Force  N = 10^5 g cm /s^2

    Conversion Factor = 10^5

    Stress: - Pa = 10 g /cm s^2

    Conversion Factor = 10  

    Energy Nm =10^7 g cm^2/s^2

    Conversion Factor = 10^7

    Density: - ρ = 10^-3 g /cm^3

    Conversion Factor = 10^-3 

    Young's Modulus = 210 GPa = 210*10^10 g/cm s^2

    Conversion Factor = 10^10

    Velocity = 56.33 kmph = 1564.72 cm/s

    Conversion Factor = 1

    Gravity = 9.8*10^2 cm/s^2

    Conversion Factor = 10^2

     

     

    SI unit to g cm ms

    Force  N = 10^-1 g cm /ms^2

    Conversion Factor = 10^-1

    Stress: - Pa = 10^-5 g /cm ms^2

    Conversion Factor =  10^-5

    Energy Nm = 10*g cm ^2 / ms^2 

    Conversion Factor = 10

    Density: - ρ = 10^-3 g/cm^3

    Conversion Factor = 10^-3

    Young's Modulus = 210 GPa = 210*10^4 g/cm ms^2

    Conversion Factor = 10^4

    Velocity = 56.33 kmph =1.5647 cm/ms

    Conversion Factor =1

    Gravity = 9.8*10^-4 cm / ms^2

    Conversion Factor =10^-4

     

    SI unit to g cm us 

    Force  N = 10^7 g cm /us^2

    Conversion Factor = 10^-7

    Stress: - Pa = 10^-11 g /cm us^2

    Conversion Factor =  10^-11

    Energy Nm = 10^-5 g cm^2 / us^2 

    Conversion Factor = 10^-5

    Density: - ρ =  10^-3 g/cm^3

    Conversion Factor = 10^-3 

    Young's Modulus = 210 GPa = 210*10^-2 g / cm us^2

    Conversion Factor = 10^-2

    Velocity = 56.33 kmph = 1.5647*10^-4 cm/us

    Conversion Factor = 10^-4

    Gravity = 9.8*10^-10 cm /us^2 

    Conversion Factor = 10^-10

     

    SI unit to kg m s 

    Force  N = 1 kg m /s^2

    Conversion Factor = 1 

    Stress: - Pa = 1 kg / s^2 m

    Conversion Factor =  1

    Energy Nm = 1 kg m^2 / s^2

    Conversion Factor = 1

    Density: - ρ = 1 kg / m^3

    Conversion Factor = 1

    Young's Modulus = 210 GPa = 210*10^9 kg/s^2 .m 

    Conversion Factor = 10^9

    Velocity = 56.33 kmph = 15.64 m/s

    Conversion Factor =1

    Gravity = 9.8 m/s^2 

    Conversion Factor = 1

     

    SI unit to kg cm s 

    Force  N = 10^2 kg cm /s^2

    Conversion Factor = 10^2 

    Stress: - Pa = 10^-2 kg / cm s^2

    Conversion Factor =  10^-2

    Energy Nm = 10^4 kg cm^2 /s^2

    Conversion Factor = 10^4

    Density: - ρ = 10^-6 kg / cm^3

    Conversion Factor = 10^-6

    Young's Modulus = 210 GPa = 210*10^7 kg /cm s^2

    Conversion Factor = 10^7

    Velocity = 56.33 kmph = 1564.72 cm / s

    Conversion Factor =  1

    Gravity = 9.8*10^2 cm /s^2

    Conversion Factor = 10^2

     

    SI unit to kg  cm ms

    Force  N = 10^-4 kg cm /ms^2 

    Conversion Factor = 10^-4 

    Stress: - Pa = 10^-8 kg / cm ms^2

    Conversion Factor =  10^-8

    Energy Nm = 10^-2 kg cm^2 / ms^2

    Conversion Factor = 10^-2

    Density: - ρ = 10^-6 kg /cm ^3

    Conversion Factor = 10^-6

    Young's Modulus = 210 GPa = 210*10^1 kg /cm ms^2

    Conversion Factor = 10

    Velocity = 56.33 kmph = 1.5647 cm /ms 

    Conversion Factor =1

    Gravity = 9.8*10^-4 cm / ms^2

    Conversion Factor = 10^-4

     

    SI unit to kg mm s 

    Force  N = 10^3 kg mm / s^2

    Conversion Factor = 10^3 

    Stress: - Pa = 10^-3 kg / mm s^2 

    Conversion Factor =  10^-3

    Energy Nm = 10^6 kg mm^2 /s^2

    Conversion Factor = 10^6

    Density: - ρ = 10^-9 kg / mm^3

    Conversion Factor = 10^-9

    Young's Modulus = 210 GPa = 210*10^6 kg mm^2 /s^2

    Conversion Factor = 10^6 

    Velocity = 56.33 kmph = 15.64*10^3 mm / s

    Conversion Factor = 10^3

    Gravity =  9.8*10^3 mm/s^2

    Conversion Factor = 10^3

     

    SI unit to kg mm ms 

    Force  N = 10^-3 kg mm /ms^2

    Conversion Factor = 10^-3

    Stress: - Pa = 10^-9 kg / ms^2 mm

    Conversion Factor =  10^-9

    Energy Nm = 1 kg mm^2 /ms^2

    Conversion Factor = 1

    Density: - ρ = 10^-9 kg / mm^3

    Conversion Factor = 10^-9

    Young's Modulus = 210 GPa = 210 kg / mm ms^2

    Conversion Factor = 1

    Velocity = 56.33 kmph = 15.64 mm / ms

    Conversion Factor = 1

    Gravity = 9.8*10^-3 mm/ms^2

    Conversion Factor = 10^-3

     

    SI unit to ton mm s 

    Force  N = 1 ton mm /s^2

    Conversion Factor = 1

    Stress: - Pa = 10^-6 ton/mm s^2

    Conversion Factor =   10^-6

    Energy Nm = 10^3 ton mm^2 /s^2

    Conversion Factor = 10^3

    Density: - ρ = 10^-12 ton / mm^3

    Conversion Factor = 10^-12

    Young's Modulus = 210 GPa = 210*10^3 ton / mm s^2

    Conversion Factor = 10^3

    Velocity = 56.33 kmph = 15647 mm / s

    Conversion Factor = 1

    Gravity = 9.8*10^3 mm / s^2

    Conversion Factor = 10^3

     

    SI unit to slug ft s

    Mass: - 

    1 slug = 14.5939 kg

    Length: -

    1 ft = 0.3048 m

    Time: - 

    1 s

    Force  N = 0.2248 slug ft / s^2 

    Conversion Factor = 1

    Stress: - Pa = 0.02088 slug /ft s^2

    Conversion Factor =  1

    Energy Nm = 0.7375 slug ft^2 / s^2

    Conversion Factor = 1

    Density: - ρ = 1.9403*10^-3 slug /ft^3

    Conversion Factor = 10^-3

    Young's Modulus = 210 GPa = 4.3848*10^9 slug / ft s^2

    Conversion Factor = 10^9

    Velocity = 56.33 kmph = 51.33 ft / s

    Conversion Factor = 1

    Gravity = 32.1522 ft /s^2

    Conversion Factor = 1

    Table : - 

    S.I Units Mass  Length  Time  Force (N) Stress (Pa) Energy (Nm) Density (ρ)

    Young's Modulus

    210

    GPa

    Velocity 

    56.33

    kmph

    Gravity 

    9.8
    Kg m s

    1

    kg

    1

    m

    1

    s

    1

    kg m /s^2

    1

    kg / s^2 m

    1

    kg m^2 / s^2

    1

    kg / m^3

    		 210*10^9 kg/s^2 .m 

    15.64

    m/s

    9.8

    m/s^2 
    kg cm s 

    1

    kg 

    100

    cm 

    1

    s

    10^2

    kg cm /s^2

     

    10^-2

    kg / cm s^2

    10^4

    kg cm^2 /s^2

    10^-6

    kg / cm^3

    		 210*10^7 kg/cm s^2

    1564.72

    cm / s

    9.8*10^2

    cm /s^2
    kg cm ms

    1

    kg 

    100

    cm 

    		 1000 ms

    10^-4

    kg cm/ms^2 

    10^-8

    kg / cm ms^2

    10^-2

    kg cm^2 / ms^2

    10^-6

    kg /cm ^3

    210*10^1

    kg /cm ms^2

     

    1.5647

    cm /ms

    9.8*10^-4

    cm / ms^2
    kg mm ms

    1

    kg

    		 1000 mm 1000 ms

    10^-3

    kg mm/ms^2

    10^-9

    kg / mm. ms^2

    1

    kg mm^2/ms^2

    10^-9

    kg / mm^3

    210

    kg / mm. ms^2

    15.64

    mm / ms

    		  9.8*10^-3 mm /ms^2
    kg mm s

    1

    kg

    		  1000 mm 1 s

    10^3

    kg mm / s^2

    10^-3

    kg / mm s^2 

    10^6

    kg mm^2 /s^2

    10^-9

    kg / mm^3

    210*10^6

    kg mm^2 /s^2

    		 15.64*10^3 mm / s 9.8*10^3 mm/s^2
    g  cm s 

    1000

    g

    100

    cm 

    		 1 s

    10^5

    g cm /s^2

    10

    g /cm s^2

    10^7

    g cm^2/s^2

    10^-3

    g /cm^3

    		 210*10^10    g/cm s^2

    1564.72

    cm/s

    		 9.8*10^2 cm/s^2
    g cm us

    1000

    g

    100

    cm 

    10e6

    s

    10^7

    g cm /us^2

    10^-11

    g /cm us^2

    10^-5

    g cm^2 / us^2 

    10^-3

    g/cm^3

    210*10^-2

    g / cm us^2

    		 1.5647*10^-4 cm/us

    9.8*10^-10

    cm /us^2 
    g mm s 

    1000

    g 

    		 1000 mm 

    1

    s

    10^6

    g mm/s^2

    1*

    g/mm s^2

    10^9

    g mm^2/s^2

    10^-6

    g/mm^3 

    210* 10^9

    g/ mm s^2 

    15647

    mm/s

    		 9.8*10^3 mm/s^2
    g mm ms 

    1000

    g

    		 1000 mm  1000 ms

    1

    g mm/ms^2 

    10^-6

    g /mm ms^2 

    10^3

    g mm^2 /ms^2

    10^-6

    g /mm^3

    		 210*10^3 g/mm ms^2 15.60 mm/ms 

    9.8*10^-3

    mm / ms^2
    g cm ms 1000 g 

    100

    cm 

    		 1000 ms

    10^-1

    g cm /ms^2

    10^-5

    g /cm ms^2

    10*

    g cm ^2 / ms^2

    10^-3

    g/cm^3

    210*10^4

    g/cm ms^2

    1.5647

    cm/ms

    9.8*10^-4

    cm / ms^2
    ton mm s 0.001 tonne 1000 mm

    1

    s

    1

    ton mm /s^2

    10^-6

    ton/mm s^2

    10^3

    ton mm^2 /s^2

    10^-12

    ton / mm^3

    210*10^3

    ton / mm s^2

    15647

    mm / s

    9.8*10^3

    mm / s^2
    slug ft s 0.068 slug

    3.28

    ft 

    1

    s

    0.2248

    slug ft / s^2 

    		 0.02088 slug /ft.s^2

    0.7375

    slug ft^2 / s^2

    1.9403*10^-3

    slug /ft^3

    		 4.3848*10^9 slug /ft s^2

    51.33

    ft / s

    32.1522

    ft /s^2

     

    Conclusion: - 

    In this challenge, we convert the S.I. unit to other different units with a conversion factor.

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