CONSISTENCY OF UNITS

Objective

      The objective of this challenge is to convert the given SI unit values of the given quantities to gm/mm/ms units and also to prepare consistent unit system table for different unit system.

Value of the following measurements are given as follows:

1.MASS 1kg
2.LENGTH 1m
3.TIME 1s
4.FORCE 1N
5.STRESS 1Pa
6.ENERGY 1Nm
7.DENSITY 1Kg/m3
8.YOUNG'S Modulus  210GPa
9.Velocity 56.33KMPH
10.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

EXPLANATION 0F UNITS

• Units are most basic aspects of any measurements.
• they are arbitrarily chosen and internatinally accepted.

categories of units

a.Fundamental units

• Some units are arbitrarily chosen to be fundamental.
• they become foundation for system.
• every other units is derivable from them.

b.Derived units

• units derived from the fundamental units by multiplication and division are called derived units.

example   LENGTH=SPEED*TIME

In this length is a derived unit

At different points of time  different systems of measurement were pervasive

1.CGS SYSTEM

• Centimetre for length
• gram for mass
• second for time

2.FPS SYSTEM

• Foot for length
• pound for mass
• second for time

3.MKS SYSTEM

• Meter for length
• kilogram for mass
• second for time

EXAMPLE FOR CGS,MKS,FPS SYSTEMS

FORCE=MASS*ACCERLATION

SI UNIT-NEWTON

• F=M*a          m=1kg  a=1m/sec^2

           =1kg*1m/s^2

        1N=1kg.m/s^2

CGS

1DYNE=1gm * 1cm/s^2

1Newton=1kg * 1m/s^2

                 =1000gm * 100 cm/s^2

                 =10^5 gmcm/s^2

              1N   =10^5 dyne

MKS

1KGF=1kg * 9.81 kg.m/s^2

1kgf=9.81N

FPS

1LBF=1lb *  32.17 ft/s^2

g=9.81m/s^2

1m=3.28 ft

1N=9.81  *  3.28 ft/s^2

    =32.17 ft/s^2

calculation for conversion from SI unit to gm/mm/ms unit

MASS 1 Kg  =  1000 gm

LENGTH 1 m =  1000 mm

TIME 1 s = 1000 ms

1.FORCE 

• 1N = (1Kg * m)/s^2 

                 = (1000 gm * 1000 mm) / (1000 ms *1000 ms)

                 = (1 gm * mm ) / ms^2

conversion factor=1

2.STRESS

• 1Pa  = N / m^2  =1 kg / m · s².
   
        = 1000gm/1000mm (1000 ms *1000 ms)

                                     =   10^-6 gm /mm*ms^2

conversion factor=10^-6

3.ENERGY

• 1Nm  = { (1Kg * m^2)/s^2 } 

                 =1000gm*1000mm*1000mm/1000ms*1000ms

                      = 10^3 gm*mm^2/ms^2

conversion factor=10^3

4.DENSITY

• 1Kg/m3  = 1000 gm /1000mm*1000mm*1000mm                                      

                            = 10^3 gm/ 10^9 ms^3

                           = 10^-6gm/ms^3

conversion factor=10^-6

5.YOUNG'S Modulus 

•  210GPa = 210 X  [10^9 X (N / m^2)]                          { 1 GPa   = 10^9 X (N / m^2)}

                     = 210 X [10^9 X (10^-6 gm /mm*ms^2)]

                    = 210 X 10^3 gm/mm*ms^2

                   = 210000 gm/mm*ms^2

conversion factor=10^3

6.Velocity

1KMPH = 10^6mm / (3600 *1000 ms)                                                           { 1KM = 10^6mm}

      = 10/36 = 0.277 mm/ms                                                                      { 1hr = 3600 *1000 ms}

                   56.33KMPH  = 56.33 x 0.277

                  56.33KMPH   = 15.64 mm/ms

conversion factor=1

7.GRAVITY 9.8m/s

•  1 m/s2  = 1000 mm/(1000 ms X 1000 ms)

                      = 10^-3 mm/ms^2

                          9.8m/s2  = 9.8 X 10^-3 mm/ms^2

conversion factor=10^-3

 CONCLUSION

• Learnt the values of the parameters in different unit system