Week - 1 - Consistency of Units
OBJECTIVE:-
the objective of this challenge is to convert the given unit system (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) into the required unit system (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) and detailed convertion for gm mm ms unit system.
PROCEDURE:-
Unit Convertion Table:
| unit system | MASS 1kg |
LENGTH 1m |
TIME 1s | FORCE 1N | STRESS 1Pa | ENERGY 1Nm | DENSITY 1Kg/m^3 | YOUNG'S Modulus 210GPa | Velocity 56.33KMPH | GRAVITY 9.8m/s2 |
| Kg cm ms | 1 kg | 100 cm | 1000 ms |
10^4 kg*cm/ms^2 |
10^-8 kg/cm*ms^2 | 10^-2 kg*cm^2/ms^2 | 10^-6 kg/cm^3 | 210 kg/cm*ms^2 | 1.565 cm/ms | 9.8x10^-4 cm/ms^2 |
| Kg cm s | 1 kg | 100 cm | 1 s |
10^2 kg*cm/s^2 |
10^-2 kg/cm*s^2 | 10^4 kg*cm^2/s^2 | 10^-6 kg/cm^3 | 2.1x10^9 kg/cm*s^2 | 1.565x10^3 cm/s | 9.8x10^2 cm/s^2 |
| gm mm ms | 1000 g | 1000 mm | 1000 ms | 1 g*mm/ms^2 | 10^-6 g/mm*ms^2 | 10^3 g*mm^2/ms^2 | 10^-6 g/mm^3 | 2.1x10^5 g/mm*ms^2 | 15.65 mm/ms | 9.8x10^-3 mm/ms^2 |
| kg m s | 1 kg | 1 m | 1 s | 1 kg m/s^2 | 1 kg/m*s^2 | 1 kg*m^2/s^2 | 1 kg/m^3 | 210x10^9 kg/m*s^2 | 15.65 m/s | 9.8 m/s^2 |
| g cm s | 1000 g | 100 cm | 1 s | 10^5 g*cm/s^2 |
10 g/cm*s^2 |
10^7 g*cm^2/s^2 | 10^-3 g/cm^3 | 2.1x10^12 g/cm*s^2 | 1.565x10^3 cm/s | 9.8x10^2 cm/s^2 |
| g cm us | 1000 g | 100 cm | 1000000 us | 10^-7 g*cm/s^2 | 10^-11 g/cm*us^2 | 10^-5 g*cm^2/us^2 | 10^-3 g/cm^3 | 2.1 g/cm*us^2 | 1.565x10^-3 cm/us | 9.8x10^-10 cm/us^2 |
| g mm s | 1000 g | 1000 mm | 1 s | 10^6 g*mm/s^2 | 1 g/mm*s^2 | 10^9 g*mm^2/s^2 | 10^-6 g/mm^3 | 2.1x10^11 g/mm*s^2 | 1.565x10^4 mm/s | 9.8x10^3 mm/s^2 |
| ton mm s | 0.001 ton | 1000 mm | 1 s | 1 ton*mm/s^2 | 10^-6 ton/mm*s^2 | 10^3 ton*mm^2/s^2 | 10^-12 ton/mm^3 | 2.1x10^5 ton/mm*s^2 | 1.565x10^4 mm/s | 9.8x10^3 mm/s^2 |
| slug ft s | 0.0685 slug | 3.28 ft | 1 s | 0.225 slug*ft/s^2 | 0.021 slug/ft*s^2 | 0.737 slug*ft^2/s^2 | 0.002 slug/ft^3 | 4.386x10^9 slug/ft*s^2 | 51.332 ft/s | 32.144 ft/s^2 |
| kg mm s | 1 kg | 1000 mm | 1 s | 10^3 kg*mm/s^2 | 10^-3 kg/mm*s^2 | 10^6 kg*mm^2/s^2 | 10^-9 kg/mm^3 | 2.1x10^8 kg/mm*s^2 | 1.565x10^4 mm/s | 9.8x10^3 mm/s^2 |
| g cm ms | 1000 g | 100 cm | 1000 ms | 10^-1 g*cm/ms^2 | 10^-5 g/cm*ms^2 | 10 g*cm^2/ms^2 | 10^-3 g/cm^3 | 2.1x10^6 g/cm*ms^2 | 1.565 cm/ms | 9.8x10^-4 cm/ms^2 |
| kg mm ms | 1 kg | 1000 mm | 1000 ms | 10^-3kg*mm/ms^2 | 10^-9 kg/mm*ms^2 | 1 kg*mm^2/ms^2 | 10^-9 kg/mm^3 | 2.1x10^2 kg/mm*ms^2 | 15.65 mm/ms | 9.8x10^-3 mm/ms^2 |
Detailed convertion of gm mm ms Unit System:
- Mass 1 Kg = 1x10^3 g = 1000 gm.
- Length 1m = 1x10^3 mm = 1000 mm.
- Time 1min = 1x10^3 = 1000 ms.
- Force 1N = 1x((10^3x10^3)/(10^3)^2) = 1x((10^6)/(10^6)) = 1 gm*mm/ms^2.
- Stress 1Pa = 1x((10^3)/((10^3)(10^3)^2) = 1x10^-6 gm/mm*ms^2.
- Energy 1 Nm = 1x((10^3x(10^3)^2)/(10^3)^2) = 1x((10^9)/(10^6)) = 10^3 gm*mm^2/ms^2.
- Density kg/m^3 = 1x((10^3)/((10^3)^3) = 1x(10^3/10^9) = 1x10^-6 g/mm^3.
- Young's Modulus 210 GPa = 210x10^9x((10^3)/((10^3)(10^3)^2) = 210x10^3 gm/mm*ms^2.
- Velocity 56.33 KMPH = (56.33x(10^6)/(3600x10^3)) = 15.65 mm/ms.
- Gravity 9.8 m/s^2 = 9.8x(10^3/(10^3^2)) = 9.8x10^-3 mm/ms.
RESULT:-
the given unit system is converted into the required unit system and the knowledge of conversion of the unit system is gained through this challenge.