Week - 1 - Consistency of Units

OBJECTIVE:

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

Write the given measurements in the above different system of units. Also, mention the conversion factors.

1.CONVERSION OF SI UNITS INTO gm,mm,ms:

mass=kg =1000g

conversion factor is 10^3

length=m=1000mm

conversion factor is 10^3

time=sec=1000ms

conversion factor is 10^3

force 1N= gxmm/ms^2

 conversion factor is 1

FORCE 1N= Massxacceleration

               = Kg x (m/s^2)

               =10^3 g x (10^3mm/10^6 ms^2)

               =gxmm/ms^2

Stress 1Pa = force/area

                = 1N/m^2

                = (g/ms^2)/10^6 mm

                = 10^-6 (g /(mm x ms^2)

conversion factor is 10^-6

Energy 1Nm= (gxmm/ms^2) x 10^3 mm

                  =  10^3 g x(mm/ms)^2

conversion factor is 10^3

Density Kg/m^3 = 10^3g /10^9 mm^3

                         = 10^-6 g/mm^3

conversion factor is 10^-6

youngs Modulus 210 Gpa= 210 x 10^9 x 10^-6 (g /(mm x ms^2)

                                     = 210 x 10^3 (g /(mm x ms^2)

conversion factor is 10^3

velocity 56.33 kmph = 56.33 x (10^6 mm/3.6 x 10^6 ms)

                              = 56.33/3.6(mm / ms)

                              = 15.64 (mm / ms)

conversion factor is 15.64

gravity = 9.8 m/s^2

           = 9.8 x 10^3mm / 10^6 ms^2

           =9.8 x 10^-3 (mm/ms^2)

conversion factor is 10^-3

Table:

CONCLUSION:

The calculation for conversion from SI unit to gm/mm/ms unit system. For others the answers in the form of a table with the unit systems as rows and measured quantities as columns.