Week - 1 - Consistency of Units

Consistency of Units

Aim: To write the given measurements in the above different system of units. Also, to 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

Procedure:

The given values are to be converted from SI units to gm/mm/ms unit system.

Mass 1kg = 1000g (Conversion factor is 10^3)
Length 1m = 1000mm (Conversion factor is 10^3)
Time 1s = 1000ms (Conversion factor is 10^3)

Force 1N =`(kg*m)/s^2`

= (1000*1000)/1000^2 `(1g*mm)/(ms)^2` (Conversion factor is 1)

Stress 1Pa = `N/m^2`= {(1g*1mm)/(1ms)^2}/1000^2`

= `10^-6g/(mm*ms)^2`(Conversion factor is 10^-6)

Energy 1Nm = {(1g*mm)/(ms)^2}*1000mm

= 10^3g mm^2/(ms)^2(Conversion factor is 10^3)

Density 1kg/m^3 = 1000gm/1000^3mm^3 = 10^-6 g/mm^3 (Conversion factor is 10^-6)

Young's modulus 210GPa = 210 * 10^9N/m^2

= 210 * 10^9 * 10^-6 g/(mm*ms)^2

= 210 *10^3 g/(mm*ms)^2 (Conversion factor is 10^3)

Velocity 56.33KMPH = (56.33*1000)/ (60 *60) = 15.647m/s

= 15.647 *(1000/1000) = 15.647mm/ms (Conversion factor is 5/18)

Gravity 9.8m/s^2 = (9.8*(1000mm/1000^2ms^2)

= 9.8*10^-3mm/ms^2 (Conversion factor is 10^-3)

System of Units:

Units	Mass	Length	Time	Force	Stress	Energy	Density	Young'sModulus	Velocity	Gravity
kg cm ms	1kg	`10^2cm`	`10^3ms`	`10^-4 kg*(cm)/(ms)^2`	`10^-8(kg)/(cm)*(ms)^2`	`10^-2(kg)*(cm)^2/(ms)^2`	`(10)^-6(kg)/(cm)^3`	2100kg/cm*`ms^2`	1.5647 (cm)/(ms)	`9.8*10^-4 (cm)/(ms)^2`
Kg cm s	1kg	`10^2cm`	1s	`10^2kg*(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)`	1564.72cm/s	`9.8*10^2(cm)/s^2`
gm mm ms	`10^3gm`	`10^3mm`	`10^3ms`	1gm*(mm)/ms	`10^-6(gm)/(mm)*(ms)^2`	`10^3(gm)*(mm)^2/(ms)^2`	`(10)^-6(gm)/(mm)^3`	`210*10^3(gm)/((mm)*(ms)^2`	15.6472mm/ms	9.8*10^-3(mm)/(ms)^2
kg m s	1kg	1m	1s	1kg*m/S2	1kg/m*`s^2`	1(kg)*`m^2/s^2`	1kg/`m^3`	`210*10^9 N/m^2`	15.6472m/s	9.8 m/s^2
gm cm s	`10^3gm`	`10^2cm`	1s	`10^5gm*(cm)/S2`	10gm/cm*ms^2	`10^7(gm)*(cm)^2/(s)^2`	`10^-3(gm)/(cm)^3`	`210*10^10(gm)/((cm)*s^2)`	1564.72cm/s	`9.8*10^2 (cm)/s^2`
gm cm `mu`s	`10^3gm`	`10^2cm`	106`mus`	`10^-7gm*(cm)/(mu*s)^2`	`10^-11(gm)/(cm)*mus^2`	`10^-5(gm)*(cm)^2/(mus)^2`	`10^-3(gm)/(cm)^3`	`2.1(gm)/(cm)*(mus)^2`	`15.64*10^-4 (cm)/(mus)`	9.8*`10^-10 (cm)/(mus)^2`
gm mm s	`10^3gm`	`10^3mm`	1s	`10^6gm*(mm)/s^2`	1gm/mm*`s^2`	`10^9(gm)*(mm)^2/s^2`	`10^-6(gm)/(mm)^3`	`210*10^11(gm)/((mm)*s^2)`	15647mm/s	9.8*`10^3(mm)/s^2`
Ton mm s	`10^-3gm`	`10^3mm`	1s	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`	15647mm/s	9.8*`10^3(mm)/s^2`
Slug ft s	0.068slug3.28ft	3.28ft	1s	0.224slug*ft/s^2	0.0208slug/ft*`s^2`	0.7366slug*`(ft)^2/s^2`	`1.938*10^-3`slug/`ft^3`	4.368 slug/ft*`s^2`	51.32ft/s	32.144 ft/`s^2`
Kg mm s	1kg	`10^3mm`	1s	`10^3kg*(mm)/s2`	`10^-3(kg)/(mm)*s^2`	106kg*`(mm)^2/s^2`	`10^-9(kg)/(mm)^3`	210*`10^6(kg)/((mm)*s^2)`	156472mm/s	`9.8*10^3(mm)/s^2`
gm cm ms	103gm	`10^2cm`	`10^3ms`	`10^-1gm*(cm)/(ms)^2`	`10^-5(gm)/(cm)*(ms)^2`	`10gm*(cm)^2/(ms)^2`	`10^-3(gm)/(cm)^3`	`210*10^4 (gm)/((cm)*(ms)^2)`	1.56472cm/ms	`9.8*10^-4(cm)/(ms)^2`
Kg mm ms	1kg	`10^3mm`	`10^3ms`	`10^-3kg*(mm)/(ms)^2`	`10^-9(kg)/(mm)*(ms)^2`	`1kg*(mm)^2/(ms)^2`	`10^-9(kg)/(mm)^3`	210 (kg)/(mm)*(ms)^2	15.6472mm/ms	9.8*`10^-3`mm/`s^2`

Result: Thus the given values are converted in different unit systems above.