Week - 1 - Consistency of Units

AIM:

To convert the given set of quantities to the required set of units as required in the question , mention the conversion factor and prepare a table for establishing the results.

PROCEDURE:

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

CONVERSION FROM SI UNIT TO gm/mm/ms UNIT SYSTEM

1.Mass 1 kg =1000gm

2.Length 1m=1000mm

3.Time 1s=1000ms

4.Force=1N

=m*a=1kg*m/ `s^2`

=(1000g*1000mm)/`(1000ms)^2`

=1gm*mm/ms^2.

Conversion factor=1.

5.Stress=1Pa

1Pa=1N/m^2

=>1(gm*mm/ms^2)/(1000mm^2)

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

Conversion Factor=10^-6

6.Energy=1Nm

=>(1gm*mm/ms^2)(1000mm)

=>1000gm*mm^2/ms^2

=>10^3 (gm*mm^2/ms^2)

Conversion factor=10^3

7.Density=1kg/m^3

=>1000g/1000mm^3

=>1g/(10^6)mm^3

=>10^-6(g/mm^3)

Conversion factor=10^-6

8.Youngs Modulus=210GPa

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

210GPa=210*(10^3)gm/mm*ms^2

Conversion factor=10^3

9.Velocity=56.33 Kmph

1Km=10^6mm

1hr=60min*60sec*1000

=36*10^5 ms

1kmph=10^6/(36*10^5)

=0.278mm/ms

Conversion factor=0.278

56.33 Kmph=15.64 mm/ms.

10.Gravity=9.8m/s^2

=>9.8*(1000mm)/1000ms)^2

=>9.8*(10^-3 mm/ms^2)

Conversion factor=10^-3.

	Mass	Length	Time	Force	Stress	Energy	Density	Youngs Modulus	Velocity	Gravity
kg cm ms	1kg	100cm	1000ms	10^-4 kg*cm/ms^2	10^-8kg/cm.ms^2	10^-2 kg*cm^2/ms^2	10^-6 kg/cm^3	210 kg/cm*ms^2	1.566 cm/ms	9.8(10^-4)cm/ ms^2
kg cm s	1kg	100 cm	1s	10^2 kg*cm/s^2	10^-2kg/cm.s^2	10^4 kg*cm^2/s^2	10^-6 kg/cm^3	210*10^7 (kg/cm*s^2)	1564.8cm/s	9.8*(10^2) cm/s^2
gm mm ms	1000g	1000mm	1000ms	1gm*mm/ms^2	10^-6gm/mm.ms^2	10^3 gm*mm^2/ms^2	10^-6 gm/mm^3	210*10^3(gm/mm*ms^2)	15.64 mm/ms	9.8*(10^-3)mm/ms^2
kg m s	1kg	1m	1s	1kg m /s^2	1kg/m*s^2	1kg m^2 /s^2	1 kg/m^3	210*10^9 (kg/m*s^2)	15.647m/s	9.8 m/s^2
g cm s	1000g	100cm	1s	10^5 g cm /s^2	10 g/cm*s^2	10^7 g cm^2 /s^2	10^-3 g/cm^3	210*10^10 (g/cm s^2)	1564 cm/s	9.8*10^2(cm/s^2)
g cm us	1000g	100cm	10^-6 us	10^-7 g cm/us^2	10^-11 g/cm*us^2	10^-5 g cm^2 /us^2	10^-3 gm/cm^3	210*10^-2(g/ cm*us^2)	1564*10^-6 cm/us	9.8*10^-10(cm/us^2)
g mm s	1000g	1000mm	1s	10^6 g*mm/s^2	1 g/mm*s^2	10^9 g mm^2/s^2	10^-6 g/mm^3	210*10^-9 (g/mm*s^2)	15647 mm/s	9.8*10^3(mm/s^2)
tom mm s	0.001 ton	1000mm	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)	15647 mm/s	9.8*10^3(mm/s^2)
slug ft s	0.068 slug	3.28ft	1s	0.223 slug*ft/s^2	0.02 slug/ft*s^2	0.731 slug*ft^2/s^2	1.92*10^-3 slug/ft^3	4.34*10^9 slug/ft*s^2)	51.32 ft/s	32.14 ft/s^2
kg mm s	1kg	1000mm	1s	1000kg*mm/s^2	10^-3 kg/mm*s^2	10^6 kg*mm^2/s^2	10^-9 kg/mm^3	210*10^6 (kg/mm*s^2)	15647 mm/s	9.8*10^3 mm/s^2
g cm ms	1000g	100cm	1000ms	0.1 g*cm/ms^2	10^-5 g/cm*ms^2	10 g*cm^2/ms^2	10^-6 g/cm^3	210*10^4 (g/cm*ms^2)	1.564 cm/s	9.8*10^-4 cm/ms^2
kg mm ms	1 kg	1000mm	1000ms	10^-3 kg*mm/ms^2	10^-9 kg/mm*ms^2	1 kg * mm^2/ms^2	10^-9 kg/mm^3	210kg/mm*ms^2	15.64 mm/ms	9.8 *10^-3(mm/ms^2)

RESULT:

Thus the given quantities were converted to the required system of units and are tabulated as needed.