Week - 1 - Consistency of Units

OBJECTIVE: -

        Convert given measurements into different system of units and finding their corresponding conversion factors.

Measurements given: -

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

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

Conversions: -

MASS:           1Kg = 1000gm

              Conversion factor: 10³

LENGTH:

                                                 1Meter = 1000mm

                                                 Conversion factor: 10³

TIME:

                                                 1Sec = 1000ms

                                                 Conversion factor: 10³

FORCE:

                                                 1N = 1Kg x 1 m/s²

                                                                      = (1000g x 1000mm)/(1000 ms)²

                                                                      = 10⁶ x 10^-6 (g x mm)/ms²

                                                                      = 1 (g x mm) /ms²

                                                Conversion factor: 1

STRESS:

                                                 1Pa = 1N/m² = {1Kg x (1m/s²)}/m² = 1Kg / (m x s²)

                                                   = 1000g / {1000mm x (1000ms)²}

                                                   = 10^-6 g / (mm x ms²)

                                                 Conversion factor: 10^-6

ENERGY:

                                                 1J = 1Nm = (1kg x 1 m/s²) * m = 1 (kg x m²/s²)

                                                    = {1000g x (1000mm)²}/(1000ms)²

                                                    = (109 g x mm²) / (106 ms²)

                                                    = 103 (g x mm²/ ms²)

                                                 Conversion factor: 10³

DENSITY:

                                                 1Kg/m³ = 1000g/(1000mm)³

                                                              = 10^-6 g/mm³

                                                 Conversion factor: 10^-6 

YOUNGS MODULUS: 

                                                 210GPa = 210e+9 kg/(m x s²)

                                                               = 210e+9 x 10^-6 g/ (mm x ms²)

              = 210e+3 g/ (mm x m s²)

               = 210 x 10³ g/ (mm x ms²)

                                                 Conversion factor: 10³

VELOCITY: 

                                                 56.33 Kmph = 56.33 x {10⁶mm/(3600 x 1000ms)}

                                                                        = 15.647 mm/ms

                                                 Conversion factor: 5/18

GRAVITY: 

                                                 9.8m/s² = 9.8 x 1000mm/(1000ms)²

                                                              = 9.8 x 10^-3 mm/ms²

                                                 Conversion factor: 10^-3

UNITS	MASS	LENGTH	TIME	FORCE	STRESS	ENERGY	DENSITY	YOUNGS MODULUS	VELOCITY	GRAVITY
Kg/cm/ms	1	100	1000	10-4kg×cmms2</math>">10−4kg×cm/ms2	10-8kgcm×ms2</math>">10−8kg/cm×ms2	10-2kg×cm2ms2</math>">10−2kg×cm2/ms2	10-6kgcm3</math>">10−6kg/cm3	2100kgcm×ms2</math>">2100kg/cm×ms2	1.5647cmms</math>">1.5647cm/ms	9.8×10-4cmms2</math>">9.8×10−4cm/ms
Kg/cm/s	1	100	1	100kg×cms2</math>">100kg×cm/s2	10-2kgcm×s2</math>">10−2kg/cm×s2	104kg×cm2s2</math>">104kg×cm2/s2	10-6kgcm3</math>">10−6kg/cm3	210×107kgcm×s2</math>">210×107kg/cm×s2	1564.72cms</math>">1564.72cm/s	9.8×102cms2</math>">9.8×102cm/s2
Gm/mm/ms	103g</math>">103 g	103mm</math>">103mm	103ms</math>">103ms	1g×mmms2</math>">1g×mm/ms2	10-6gmm×ms2</math>">10−6g/mm×ms2	103g×mm2ms2</math>">103g×mm2/ms2	10-6gmm3</math>">10−6g/mm3	210×103gmm×ms2</math>">210×103g/mm×ms2	15.647mmms</math>">15.647mm/ms	9.8×10-3mmms2</math>">9.8×10−3mm/ms2
Kg/m/s	1	1	1	1kg×ms2</math>">1kg×m/s2	1kgm×s2</math>">1kg/m×s2	1kg×m2s2</math>">1kg×m2/s2	1kgm3</math>">1kg/m3	210×109kgm×s2</math>">210×109kg/m×s2	15.647ms</math>">15.647m/s	9.8ms2</math>">9.8m/s2
g/cm/s	103g</math>">103 g	102cm</math>">102cm	1	105g×cms2</math>">105g×cm/s2	10gcm×s2</math>">10g/cm×s2	107g×cm2s2</math>">107g×cm2/s2	10-3gcm3</math>">10−3g/cm3	210×1010gcm×s2</math>">210×1010g/cm×s2	1564.72cms</math>">1564.72cm/s	9.8×102cms2</math>">9.8×102cm/s2
g/ cm/  μ</math>">μ`s	103g</math>">103g	102cm</math>">102cm	106μs</math>">106μs	10-7g×cmμs2</math>">10−7g×cm/μs2	10-11gcm×μs2</math>">10−11g/cm×μs2	10-5g×cm2s2</math>">10−5g×cm2/s2	10-3gcm3</math>">10−3g/cm3	2.10gcm×μs2</math>">2.10g/cm×μs2	15.647×10-4cmμs</math>">15.647×10−4cm/15.647×10-4cmμs</math>">μs	9.8×10-10cmμs2</math>">9.8×10−10cm/μs2
g/mm/ s	103g</math>">103 g	103mm</math>">103mm	1	106g×mms2</math>">106g×mm/s2	1gmm×s2</math>">1g/mm×s2	109g×mm2s2</math>">109g×mm2/s2	10-6gmm3</math>">10−6gm/m3	210×109gmm×s2</math>">210×109g/mm×s2	15647.2mms</math>">15647.2mm/s	9.8×103mms2</math>">9.8×103mm/s2
Ton/mm/s	10-4tonne</math>">10−4tonne	103mm</math>">103mm	1	10-1tonne×mms2</math>">10−1tonne×mm/s2	10-7tonnemm×s2</math>">10-7tonne/mm×s2	102tonne×mm2s2</math>">102tonne×mm2/s2	10-13tonnemm3</math>">10−13tonne/mm3	210×102tonnemm×s2</math>">210×102tonne/mm×s2	15647.2mms</math>">15647.2mm/s	9.8×103mms2</math>">9.8×103mm/s2
Slug/ ft/ s	0.068slug</math>">0.068slug	3.28ft</math>">3.28ft	1	0.223slug×fts2</math>">0.223slug×ft/s2	0.0207slugft×s2</math>">0.0207slug/ft×s2	0.7314slug×ft2s2</math>">0.7314slug×ft2/s2	19×10-4slugft3</math>">19×10−4slug/ft3	4.347×109slugft×s2</math>">4.347×109slug/ft×s2	51.34fts</math>">51.34ft/s	32.14fts2</math>">32.14ft/s2
kg/mm/s	1	103mm</math>">103mm	1	103kg×mms2</math>">103kg×mm/s2	10-3kgmm×s2</math>">10−3kg/mm×s2	106kg×mm2s2</math>">106kg×mm2/s2	10-9kgmm3</math>">10−9kg/mm3	210×106kgmm×s2</math>">210×106kg/mm×s2	15647.2mms</math>">15647.2mm/s	9.8×103mms2</math>">9.8×103mm/s2
g/ cm/ ms	103g</math>">103g	102cm</math>">102cm	103ms</math>">103ms	10-1g×cmms2</math>">10−1g×cmm/s2	10-5gcm×ms2</math>">10−5g/cm×ms2	10g×cm2ms2</math>">10g×cm2/ms2	10-3gcm3</math>">10−3g/cm3	210×104gcm×ms2</math>">210×104g/cm×ms2	1.5647cmms</math>">1.5647cm/ms	9.8×10-4cmms2</math>">9.8×10−4cmm/s2
Kg/ mm/ ms	1	103mm</math>">103mm	103ms</math>">103ms	10-3kg×mmms2</math>">10−3kg×mm/ms2	10-9kgmm×ms2</math>">10−9kg/mm×ms2	1kg×mm2ms2</math>">1kg×mm2/ms2	10-9kgmm3</math>">10−9kg/mm3	210kgmm×ms2</math>">210kg/mm×ms2	15.647mmms</math>">15.647mm/ms	9.8×10-3mmms2</math>">9.8×10−3mm/ms2

RESULT:

The given task of converting the SI unit values to the required conversion units is done and the values are shared in the table format.calculation part is shown for the "gm/mm/ms".