Week - 1 - Consistency of Units
CONSISTENCY OF UNITS
AIM:
To convert the given SI unit of given quantities to gm/mm/ms units.
GIVEN:
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
ANSWER:
FUNDAMENTAL QUANTITY:
A Quantity which is independent of any other quantity.(E.g.. Length(m),Mass(kg),Time(s)).
DERIVED QUANTITY:
A Quantity which is dependent of any other quantity.(E.g..Density(kg/m³),Acceleration (m/s²),Velocity (m/s)).
SLUG:
It is a mass that accelerates by 1 ft/s² when a force of one pound-force (lbf) is exerted on it.
One slug is a mass equal to 32.1740 lb (14.59390 kg) based on standard gravity.
CALCULATION OF COVERSION FROM SI UNIT TO g, mm, ms
Force 1N= 1 mass*acceleration
=1kg*1m/s²
=1000g*1000mm/(1000ms²)
=106*10-6(g*mm)/ms²
=1(g*mm)/ms²
Conversion Factor = 1
Stress 1pa= 1N/m² =[1kg*(1m/s²)]/m² =1 kg/(m*s²)
=1000g/[1000mm*(1000ms)²]
=10-6 g/(mm*ms²)
Conversion Factor = 10-6
Energy 1Nm: 1J= 1Nm=(1kg*1m/s²) *m=1(kg*m²/s²) = [1000g*(1000mm)²]/(1000ms)²
= (109 g*mm²) / (106 ms²)
=10³ (g*mm²/ ms²)
Conversion Factor = 10³
Density 1kg/m³ = 10-6 g/mm³
Conversion Factor = 10-6
Young’s modulus 210Gpa = 210e+9 kg/(m*s²)
1 kg/(m*s²) =1000g/[1000mm*(1000ms)²] =10-6 g/mm*ms²
= 210e+9*10-6 g/mm*ms² note(e+9=109)
= 210*10³ g/mm*ms²
Conversion Factor = 10³
Velocity 56.33 kmph =56.33*[106mm/(3600*1000ms)]
=15.647 mm/ms
Conversion Factor = 1
Gravity 9.8 m/s² = 9.8*1000mm/(1000ms)²
=9.8*10-3 mm/ms²
Conversion Factor = 10-3
Mass 1kg = 1000g
Length 1M = 1000mm
Time 1s = 1000 ms
Table will all the parameters with respect to unit system:
Conversion Factor:
It is a number used to convert one unit set to another unit by multiplying or dividing.
|
Unit system (SI unit) |
Mass (1kg) |
Length (1m) |
Time (1s) |
Force (1N) |
Stress (1pa) |
Energy (1Nm) |
Density (1Kg/m³) |
Young’s modulus (210Gpa) |
Velocity (56.33 kmph) |
Gravity (9.8m/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*10-4cm/ms² |
|
Conversion Factor |
1 |
10² |
10³ |
10-4 |
10-8 |
10-8 |
10-6 |
10 |
1 |
10-4 |
|
Kg cm s |
1kg |
10²cm |
1s |
10² kg*cm/s² |
10-2 kg/cm*s |
104 kg*cm²/s² |
10-6 kg/cm³ |
210e+7 kg/cm*s² |
1564.7 cm/s |
9.8*10² cm/s² |
|
Conversion Factor |
1 |
10² |
1 |
10² |
10-2 |
104 |
10-6 |
107 |
1 |
10² |
|
gm mm ms |
10³g |
10³mm |
10³ms |
1 g*mm/ms² |
10-6 g/mm*ms² |
10³ g*mm²/ms² |
10-6g/mm³ |
210e+3 g/mm*ms² |
15.647mm/ms |
9.8*10-3 mm/ms² |
|
Conversion Factor |
10³ |
10³ |
10³ |
1 |
10-6 |
10³ |
10-6 |
10³ |
1 |
10-3 |
|
Kg m s |
1kg |
1m |
1s |
Kg m/s² |
Kg/ms² |
Kgm²/s² |
1kg/m³ |
210e+9 Kg/ms² |
15.647 m/s |
9.8 m/s² |
|
Conversion Factor |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
109 |
1 |
1 |
|
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 |
|
Conversion Factor |
10³ |
10² |
1 |
105 |
10 |
107 |
10-3 |
1010 |
1 |
10² |
|
g cm us |
10³g |
10²cm |
106us |
10-7 g*cm/us² |
10-11 g/cm*us² |
10-5 g*cm²/us² |
10-3 g/cm³ |
2.10 g/cm*us² |
15.647*10-4 cm/us |
9.8*10-10cm/us² |
|
Conversion Factor |
10³ |
10² |
106 |
10-7 |
10-11 |
10-5 |
10-3 |
10--2 |
10-4 |
10-10 |
|
g mm s |
10³g |
10³mm |
1s |
106 g*mm/s² |
1 g/mm*s² |
109 g*mm²/s² |
10-6 g/mm³ |
210 e+9 g/mm*s² |
15647 mm/s |
9.8*10³ mm/s² |
|
Conversion Factor |
10³ |
10³ |
1 |
106 |
1 |
109 |
10-6 |
109 |
1 |
10³ |
|
Ton mm s |
0.001Ton |
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 |
|
Conversion Factor |
1 |
10³ |
1 |
1 |
10-6 |
10³ |
10-12 |
10³ |
1 |
10³ |
|
Slug ft s |
0.068 Slug |
3.28ft |
1s |
0.2246 slug*ft/s² |
0.0208slug/ft*s² |
0.7366 slug*ft²/s² |
1.93*10-3 slug/ft³ |
4.369 e9 slug/ft*s² |
51.322 ft/s |
32.144 ft/s² |
|
Conversion Factor |
1 |
1 |
1 |
1 |
1 |
1 |
10-3 |
109 |
1 |
1 |
|
Kg mm s |
1kg |
10³mm |
1s |
10³ kg*mm/s² |
10-3kg/mm*s² |
106 kg*mm²/s² |
10-9 kg/mm³ |
210e+6 kg/mm*s² |
15647 mm/s |
9.8*10³ mm/s² |
|
Conversion Factor |
1 |
10³ |
1 |
10³ |
10-3 |
106 |
10-9 |
106 |
1 |
10³ |
|
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 |
|
Conversion Factor |
10³ |
10² |
10³ |
10-1 |
10-5 |
10 |
10-3 |
104 |
1 |
10-4 |
|
Kg mm ms |
1kg |
10³mm |
10³ms |
10-3kg*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 |
|
Conversion Factor |
1 |
10³ |
10³ |
10-3 |
10-9 |
1 |
10-9 |
1 |
1 |
10-3 |
CONCLUSION:
I had learnt about unit system and its conversion of all parameters while working on this challenge.