Week - 1 - Consistency of Units
Objective: To write the given measurements in the above different system of units.
Value of the following measurements are given as follows:
MASS 1kg
LENGTH 1m
TIME 1s
FORCE 1N
STRESS 1Pa
ENERGY 1Nm
DENSITY 1 `frac{kg}{m^3}`
YOUNG'S Modulus 210GPa
Velocity 56.33KMPH
GRAVITY 9.8`frac{m}{s^2}`
Conversion from SI unit to gm-mm-ms unit system
Mass, 1 kg = 1000g
Length, 1m = 1000mm
Time, 1s = 1000ms
Force, 1N = 1 `frac{kg m}{s^2}`=1 `frac{(1000g).( 1000mm)}{1000^2ms^2}`= 1 `frac{gmm}{ms^2}` = 1N
Stress, 1Pa = 1 `frac{kg m}{s^2}/m^2` = 1 `frac{(1000g).( 1000mm)}{1000^2ms^2}/(1000^2mm^2)` =`10^-6 frac{gmm}{ms^2}/{mm^2}` = `10^-6`MPa
Energy, 1 Nm = 1 `frac{kg.m}{s^2}.m` = 1`frac{(1000g).(1000mm)}(1000^2ms^2) 1000mm` = 1000 `frac{gmm}{ms^2}.mm`
Density, 1 `frac{kg}{m^3}` = 1 x `frac{1000g}{1000^3mm^3}` = `10^-6 frac{g}{mm^3}`
Young's Modulus , 210GPa = 210 x `10^9 kgfrac{m}{s^2}`=210 x `10^9 frac{(1000g).(1000mm)}{1000^2ms^2}/(1000^2mm^2)` = 2.1 x `10^5 frac{gmm}{ms^2}/(mm^2)`
Velocity, 56.33km/h = 56.33 x `frac{5}{18} = 15.647frac{m}{s} = 15.647 frac{1000mm}{1000ms} = 15.647frac{mm}{ms}`
Gravity, 9.8`frac{m}{s^2}` = 9.8 x `frac{1000mm}{1000^2ms^2}` = 9.8 x `10^-3frac{mm}{ms^2}`
| Measurements/ Unit System |
Mass (1kg) |
Length (1 m) |
Time (1 s) |
Force (1 N) |
Stress (1Pa) |
Energy (1N.m) |
Density (1 `frac{kg}{m^3}`) |
Young's Modulus (210GPa) |
Velocity (56.33km/h) (15.647m/s) |
Gravity (9.8`frac{m}{s^2}`) |
| kg cm ms | 1 | 100 | 1000 | `10^-4` | `10^-8` | 0.01 | `10^-6` | 2.1 x 1000 | 15.647 x 0.1 | 9.8 x `10^-4` |
| Kg cm s | 1 | 100 | 1 | 100 | 0.01 | `10^4` | `10^-6` | 2.1 x `10^9` | 15.647 x 100 | 9.8 x 100 |
| gm mm ms | 1000 | 1000 | 1000 | 1 | `10^-6` | 1000 | `10^-6` | 2.1 x `10^5` | 15.647 | 9.8 x `10^-3` |
| kg m s | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2.1 x `10^11` | 15.647 | 9.8 |
| g cm s | 1000 | 100 | 1 | `10^5` | 10 | `10^7` | `10^-3` | 2.1 x 10^12 | 15.647 x 100 | 9.8 x 100 |
| g cm us | 1000 | 100 | `10^-6` | `10^-7` | `10^-11` | `10^-5` | `10^-3` | 2.1 | 15.647 x `10^-4` | 9.8 x `10^-10` |
| g mm s | 1000 | 1000 | 1 | `10^6` | 1 | `10^9` | `10^-6` | 2.1 x `10^11` | 15.647 x `10^3` | 9.8 x `10^3` |
| ton mm s | 0.001 | 1000 | 1 | 1 | `10^-6` | 1000 | `10^-12` | 2.1 x `10^5` | 15.647 x 1000 | 9.8 x 1000 |
| slug ft s | 0.06852 | 3.2808 | 1 |
0.2248 (1 N =0.2248lbf) |
0.02088 (1 Pa = 0.0208854 lbf/ft^2) |
0.7375 (1 J =0.7375 lbs ft ) |
0.00194 | 4.38 x `10^9` | 51.3346 | 32.1518 |
| kg mm s | 1 | 1000 | 1 | 1000 | 0.001 | `10^6` | `10^-9` | 2.1 x `10^8` | 15.647 x `10^3` | 9.8 x `10^3` |
| g cm ms | 1000 | 100 | 1000 | 0.1 | `10^-5` | 10 | 0.001 | 2.1 x `10^6` | 15.647 x 0.1 | 9.8 x `10^-4` |
| kg mm ms | 1 | 1000 | 1000 | `10^-3` | `10^-9` | 1 | `10^-9` | 210 | 15.647 | 9.8 x `10^-3` |