Week - 1 - Consistency of Units

 Objective:- Write a detailed report on unit conversion with calculations and there units.

1) Convert Kg cm ms

MASS 1kg = 1000gms.

LENGTH 1m = 100cm.

TIME 1s = 1000ms

FORCE = Force is an external agent capable of changing the state of rest or motion of a particular body. It has a magnitude and a direction.

unit = kg·m/s²

STRESS = It is defined as internal resistance offered by the body or force per unit area.

unit = N/m^2.

Value of the following measurements is 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 systems 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 internationally accepted.

Categories of units

1. Fundamental units

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

1. 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

• Centimeter 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 gm cm/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

Unit system	Mass	Length	Time	Force	Stress	Energy
SI Unit kg m s	1kg	1m	1s	1 N = 1 kg*m/s2	1 Pa = 1 kg/(m* s2)	1 J = 1Nm = 1 kg*m2/s2
kg cm ms	1kg	102cm	103ms	10-4 kg*cm/ms2	10-8 kg/(cm*ms2)	10-2 kg*cm2/ms2
kg cm s	1kg	102cm	1s	102 kg*cm/s2	10-2 kg/(cm*s2)	104 kg*cm2/s2
g mm ms	103g	103mm	103ms	1 g*mm/ms2	10-6 g/(mm*ms2)	103 g*mm2/ms2
g cm s	103g	102cm	1s	105 g*cm/s2	10 g/(cm*s2)	107 g*cm2/s2
g cm μs	103g	102cm	106μs	10-7 g*cm/μs2	10-11 g/(cm*μs2)	10-5 g*cm2/μs2
g mm s	103g	103mm	1s	106 g*mm/ s2	1 g/(mm*s2)	109 g*mm2/s2
Ton mm s	10-3ton	103mm	1s	1 ton*mm/s2	10-6 ton/(mm*s2)	103 ton*mm2/s2
slug ft s	0.068slug	3.28 ft	1s	0.2246 slug*ft/ s2	0.0208 slug/(ft*s2)	0.7366 slug*ft2/s2
kg mm s	1kg	103mm	1s	103 kg*mm/s2	10-3 kg/(mm*s2)	106 kg*mm2/s2
g cm ms	103g	102cm	103ms	10-1 g*cm/ms2	10-5 g/(cm*ms2)	10 g*cm2/ms2
kg mm ms	1kg	103mm	103ms	10-3 kg*mm/ms2	10-9 kg/(mm*ms2)	1 kg*mm2/ms2

Conclusion:

The unit conversion was done for a different systems of units.