Week - 1 - Consistency of Units
|
Mass (1Kg) |
Length (1 m) |
Time (1 s) |
Force (1 N) |
Stress (1 Pa = [N/m^2]) |
Energy (1 Nm) |
Density (1 kg/m^3) |
YOUNG'S Modulus (210GPa) [210E+9 N/m^2] |
Velocity (56.33KMPH) |
GRAVITY (9.8m/s2) |
|
| Kg cm ms | 1 | 100 | 1000 | 1 | 1E-4 N/cm^2 | 1E+2 N-cm | 1E-6 Kg/cm^3 | 210E+5 N/cm^2 | 1.5647 cm/ms | 9.8E-4 cm/ms^2 |
| Kg cm s | 1 | 100 | 1 | 1 | 1E-4 N/cm^2 | 1E+2 N-cm | 1E-6 Kg/cm^3 | 210E+5 N/cm^2 | 15.6472E+2 cm/s | 9.8E+2 cm/s^2 |
| gm mm ms | 1000 | 1000 | 1000 | 1 | 1E-6 N/mm^2 | 1E+3 N-mm | 1E-6 g/mm^3 | 210E+3 N/mm^2 | 15.6472 mm/ms | 9.8E-3 mm/ms^2 |
| kg m s | 1 | 1 | 1 | 1 | 1 (N/m^2) | 1 N-m | 1 Kg/m^3 | 210E+9 N/m^2 | 15.6472 m/s | 9.8 m/s^2 |
| g cm s | 1000 | 100 | 1 | 1 | 1E-4 N/cm^2 | 1E+2 N-cm | 1E-3 g/cm^3 | 210E+5 N/cm^2 | 15.6472E+2 cm/s | 9.8E+2 cm/s^2 |
| g cm us | 1000 | 100 | 1 | 1 | 1E-4 N/cm^2 | 1E+2 N-cm | 1E-3 g/cm^3 | 210E+5 N/cm^2 | 15.6472E+2 cm/s | 9.8E+2 cm/s^2 |
| g mm s | 1000 | 1000 | 1 | 1 | 1E-6 N/mm^2 | 1E+3 N-mm | 1E-6 g/mm^3 | 210E+3 N/mm^2 | 15.6472E+3 mm/s | 9.8E+3 mm/s^2 |
| ton mm s | 0.001 | 1000 | 1 | 1 | 1E-6 N/mm^2 | 1E+3 N-mm | 1E-12 ton/mm^3 | 210E+3 N/mm^2 | 15.6472E+3 mm/s | 9.8E+3 mm/s^2 |
| slug ft s | 0.06852 | 3.28084 | 1 | 1 | 0.0929 N/ft^2 | 3.28084 N-ft | 1.94027E-3 slug/ft^3 | 19.51E+9 N/ft^2 | 51.3360 ft/s | 32.185 ft/s^2 |
| kg mm s | 1 | 1000 | 1 | 1 | 1E-6 N/mm^2 | 1E+3 N-mm | 1E-9 Kg/mm^3 | 210E+3 N/mm^2 | 15.6472E+3 mm/s | 9.8E+3 mm/s^2 |
| g cm ms | 1000 | 100 | 1000 | 1 | 1E-4 N/cm^2 | 1E+2 N-cm | 1E-3 g/cm^3 | 210E+5 N/cm^2 | 1.5647 cm/ms | 9.8E-4 cm/ms^2 |
| kg mm ms | 1 | 1000 | 1000 | 1 | 1E-6 N/mm^2 | 1E+3 N-mm | 1E-9 Kg/mm^3 | 210E+3 N/mm^2 | 15.6472 mm/ms | 9.8E-3 mm/ms^2 |
Note: In the given conversation table 1N is considered as the standard unit and not derived further eg. (1N = Kg-m/s^2 to 1E-04 Kg-cm/ms^2). As it is not mentioned in the challenge that force unit N should be considered as 1 mass unit * 1 acceleration unit.
Unit Conversation Factors :
1N/m2 = 1E-4 N/cm2
1N/m2 = 1E-6 N/mm2
1N/m2 = 0.092905 N/ft2
(1 Gpa = 1E+9 N/m2)
For Velocity
1 Km/hr = 1/36 cm/ms = 1000/36 cm/s = 1E4/36 mm/s = 1/3.6 mm/ms = 1/3.6 m/s = 0.91134 ft/s
Gravity
1 m/s2 = 1E-2 cm/ms2 = 100 cm/s2 = 1E-3 mm/ms = 3.28084 ft/s2
**Detailed calculation for conversion from SI unit to gm/mm/ms unit system**
Mass 1 kg = 1000 gm
Length 1 m = 1000 mm
Time 1 s = 1000 ms
Force 1 N = 1 N
Stress 1 Pa = 1 N/m2 = 1 N / (1E3)^2 mm^2 = 1E-6 N / mm^2
Energy 1 N-m = 1 * 1E+3 N-mm = 1E+3 N-mm
Density 1 Kg / m^3 = 1E+3 / (1E+3)^3 g/mm^3 = 1E-6 g/mm^3
Young's Modulus 210 Gpa = 210E+09 N/m^2 = 210E+09 / 1E+06 N/mm^2 = 210E+03 N/mm^2
Velocity 56.33 Km/hr = 56.33 * 1E+06 / 3.6E+06 mm/ms = 15.6472 mm/ms
Gravity 9.8 m/s^2 = 9.8 * 1E+03 / (1E+03)^2 mm/ms^2 = 9.81E-03 mm/ms^2