Week - 1 - Consistency of Units
Reort on Consistency of Units
First we have to convert all Fundamental quantity i.e mass, length, time into their respective unit system.
After that rest of all the other quantities are derived quantity , which are derived from fundamental quantity.
So we can derive any physical quantity with the help of fundamental quantity only we need to know the formulas.
for example :-
1 force unit = 1 mass unit * 1 acceleration unit
1 acceleration unit = 1 length unit / (1 time unit)^2 {for gravity the calculation of acceleration is same only we need to multiply with 9.81}
1 density unit = 1 mass unit / (1 length unit)^3
1 stress unit = 1 force unit /(1 length unit)^2 {the unit of young's modulus is same as stress but according to question it given in GPa=10^9Pa}
1 Energy unit = 1 force unit*1 length unit
1 Velocity unit= 1 length unit/1 time unit
1KMPH=1000/3600=5/18 m/s or 1m/s=18/5 KMPH = 3.6 KMPH
Note:- We represent the converted unit in terms of SI unit
| Unit system | MASS 1kg | LENGTH 1m | TIME 1s | FORCE 1N | STRESS 1Pa or (N/(m)^2) | ENERGY 1Nm | DENSITY 1Kg/m3 | YOUNG'S Modulus 210GPa | Velocity 56.33KMPH=15.647m/s | GRAVITY 9.8m/s2 |
| Kg cm ms | 1 kg | 1e-2 m | 1e-3 s | 1e+4N | 1 Pa | 100Nm | 1e+6 Kg/m3 | 1*210=210GPa | 156.47 m/s | 1e+4*9.8 m/s2 |
| Kg cm s | 1 kg | 1e-2 m | 1 s | 1e-2N | 1e+2 Pa | 1e-4 Nm | 1e+6 Kg/m3 | 1e+2*210=21000GPa | 0.15647 m/s | 1e-2*9.8 m/s2 |
| gm mm ms | 1e-3 kg | 1e-3 m | 1e-3 s | 1N | 1e+6 Pa | 1e-3 Nm | 1e+6 Kg/m3 | 1e+6*210=21e+7GPa | 15.647 m/s | 1e+3*9.8 m/s2 |
| kg m s | 1 kg | 1 m | 1 s | 1N | 1 Pa | 1 Nm | 1 Kg/m3 | 1*210=210GPa | 15.647 m/s | 9.8 m/s2 |
| g cm s | 1e-3 kg | 1e-2 m | 1 s | 1e-5N |
1e-1 Pa |
1e-7 Nm | 1e+3 Kg/m3 | 1e-1*210=21GPa | 0.15647 m/s | 1e-2*9.8 m/s2 |
|
g cm us |
1e-3 kg | 1e-2 m | 1e-6 s | 1e+7N | 1e+3 Pa | 1e+5 Nm | 1e+3 Kg/m3 | 1e+3*210=210,000GPa | 15.647e+4 m/s | 1e+10*9.8 m/s2 |
| g mm s | 1e-3 kg | 1e-3 m | 1 s | 1e-6N | 1 Pa | 1e-9 Nm | 1e+6 Kg/m3 | 1*210=210GPa | 0.015647 m/s | 1e-3*9.8 m/s2 |
| ton mm s | 1000 kg | 1e-3 m | 1 s | N | 1e+6 Pa | 1e-3 Nm | 1e+12 Kg/m3 | 1e+6*210=GPa | 0.015647 m/s | 1e-3*9.8 m/s2 |
| slug ft s | 14.5939 kg | 0.3048 m | 1 s | 4.4482N=1lbf | 47.88 Pa | 1.3558 Nm | 515.3787 Kg/m3 | 47.88*210=10054.8GPa | 4.7692 m/s | 0.3048*9.8 m/s2 |
| kg mm s | 1 kg | 1e-3 m | 1 s | 1N | 1e+6 Pa | 1e-3 Nm | 1e+9 Kg/m3 | 1e+6*210=21e+7GPa | 0.015647 m/s | 1e-3*9.8 m/s2 |
| g cm ms | 1e-3 kg | 1e-2 m | 1e-3 s | 1e+1N | 1e+5 Pa | 1e-1 Nm | 1e+3 Kg/m3 | 1e+5*210=21e+6GPa | 156.47 m/s | 1e+4*9.8 m/s2 |
| kg mm ms | 1 kg | 1e-3 m | 1e-3 s | 1e+6N | 1e+12 Pa | 1e+3 Nm | 1e+9 Kg/m3 | 1e+12*210=21e+13GPa | 15.647 m/s | 1e+3*9.8 m/s2 |