Week - 1 - Consistency of Units

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

Value of the following measurements is given as follows:

1. MASS

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.
• 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

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	Density	Young’s Modulus	Velocity	Gravity
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	1kg/m3	210 GPa = 210e+9 kg/(m*s2)	15.647 m/s	9.8 m/s2
kg cm ms	1kg	102cm	103ms	10-4 kg*cm/ms2	10-8 kg/(cm*ms2)	10-2 kg*cm2/ms2	10-6 kg/cm3	2100 kg/(cm*ms2)	1.5647 cm/ms	9.8*10-4 cm/ms2
kg cm s	1kg	102cm	1s	102 kg*cm/s2	10-2 kg/(cm*s2)	104 kg*cm2/s2	10-6 kg/cm3	210e+7 kg/(cm*s2)	1564.7 cm/s	9.8*102 cm/s2
g mm ms	103g	103mm	103ms	1 g*mm/ms2	10-6 g/(mm*ms2)	103 g*mm2/ms2	10-6 g/mm3	210e+3 g/(mm*ms2)	15.647 mm/ms	9.8*10-3 mm/ms2
g cm s	103g	102cm	1s	105 g*cm/s2	10 g/(cm*s2)	107 g*cm2/s2	10-3 g/cm3	210e+10 g/(cm*s2)	1564.7 cm/s	9.8*102 cm/s2
g cm μs	103g	102cm	106μs	10-7 g*cm/μs2	10-11 g/(cm*μs2)	10-5 g*cm2/μs2	10-3 g/cm3	2.10 g/(cm*μs2)	15.647*10-4 cm/ μs	9.8*10-10 cm/μs2
g mm s	103g	103mm	1s	106 g*mm/ s2	1 g/(mm*s2)	109 g*mm2/s2	10-6 g/mm3	2.10 e+11 g/(mm*s2)	15647 mm/s	9.8*103 mm/s2
Ton mm s	10-3ton	103mm	1s	1 ton*mm/s2	10-6 ton/(mm*s2)	103 ton*mm2/s2	10-12 ton/mm3	210e+3 ton/(mm*s2)	15647 mm/s	9.8*103 mm/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	1.93*10-3 slug/ft3	4.368 e+9 slug/(ft*s2)	51.322 ft/s	32.144 ft/s2
kg mm s	1kg	103mm	1s	103 kg*mm/s2	10-3 kg/(mm*s2)	106 kg*mm2/s2	10-9 kg/mm3	210e+6 kg/(mm*s2)	15647 mm/s	9.8*103 mm/s2
g cm ms	103g	102cm	103ms	10-1 g*cm/ms2	10-5 g/(cm*ms2)	10 g*cm2/ms2	10-3 g/cm3	210e+4 g/(cm*ms2)	1.5647 cm/ms	9.8*10-4 cm/ ms2
kg mm ms	1kg	103mm	103ms	10-3 kg*mm/ms2	10-9 kg/(mm*ms2)	1 kg*mm2/ms2	10-9 kg/mm3	210 kg/(mm*ms2)	15.647 mm/ms	9.8*10-3 mm/ms2

Conclusion:

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