Week - 1 - Consistency of Units

Week - 1 - Consistency of Units:

objective: To convert the given quantity into diffrent unit system and show the conversion factor.

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

conversion from SI unit to gm/mm/ms unit system:

Mass 1 kg = 1000g ---------------------------------- #conversion factor =10³

length 1M = 1000mm--------------------------------#conversion factor =10³

time 1S = 1000millisecond--------------------------#conversion factor=10³

force 1N = 1kg*m/s

= 1000g*1000mm/(10³)²

= 1g*m/ms.------------------------------#conversion factor=1

stress 1 pascal = 1N/m²

= 1kg*m/(s²)*(m²)

= 1000g*1000mm/(1000²)ms²*(1000²)

= 10^-6 g/ms²*mm--------------------------#conversion factor=10^-6

energy1Nm = 1kg*m/s² *m

= 1000g*1000mm/(1000)² ms *(1000)mm

= 10³ g*mm/ms-----------------------------#conversion factor=10³

Density 1kg/m³ = 1000g/(1000)³

⁼ 10^-6 g/mm³ ------------------------------#conversion 10^-6

youngs modulas 210GPA = 210*10⁹*pa

= 210*10⁹*1N/m²

= 210*10⁹*1kg*m/s2*m²

= 210*10⁹*1000g/(1000)² ms² *1000 mm²

= 210*10³ g/mm*ms.------------------------#conversion factor 10³

velocity 56.33kmph = 56.33*10³*1000/3600*1000ms

= 15.64 mm/ms--------------------conversion factor 5/18

Gravity = 9.8m/s2

= 9.8*1000/(1000)² ms²

= 9.8*10^-3 mm/ms² --------------------------#conversion factor=10-³

units	mass 1kg	time 1s	force 1N	stress 1pa	energy 1J	Length 1m
Kg m s	1kg	1s	1kg*m/s2	1kg/m*s2	1kg*m2/s2	1m
Kg cm ms	1kg	1000ms	10-4 kg*cm/ms2	10-8 kg/cm*ms2	10-2 kg cm2 /ms2	100cm
Kg cm s	1kg	1s	102 kg*cm/s2	10-2 kg/cm*s2	104 kg cm2/s2	100cm
g mm ms	1000g	1000ms	1 g*mm/ms2	10-6 g/mm*ms2	103 g*mm/ms2	1000mm
g cm s	1000g	1s	105 g*cm/s2	10g/cm*s2	107 g*cm2 /s2	100cm
g cm us	1000g	106 us	10-7 g*cm/us2	10-11 g/cm*us2	10-5 g cm2/us2	100cm
g mm s	1000g	1 s	g*mm/s2	1g/mm*s2	109 g*mm2/s2	1000mm
ton mm s	0.001ton	1 s	1 ton*mm/s2	10-6 ton/mm*s2	103 ton*mm2/s2	1000mm
Slug ft s	0.068slug	1s	0.2246slug*ft/s2	0.0208 slug/ft*s2	0.7366slug*ft2/s2	3.28ft
Kg mm s	1kg	1s	103 kg*mm/s2	10-3 kg/mm*s-2	106 kg*mm2 /s2	1000mm
g cm ms	1000g	1000ms	10-1 g*cm/ms2	10-5 g/m*ms2	10g*cm2 /ms2	100cm
Kg mm ms	1 kg	1000ms	10-3 kg*mm/ms2	10-9 kg/mm* ms2	1kg*mm2 /ms2	1000mm

result:

• unit conversion has been done to all the given parameters
• conversion factor for all quantities is written

learning outcomes:

• learned how to convert units from one system to another