Week - 1 - Consistency of Units
Objective:
To calculate the conversiton factor for different unit system with respect to the SI system of units.
Given Inputs:
The value of SI units 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
Calculation.
Let us see how the values will get modified in kgmms unit system.
| SI unit value | Calculation | kg mm s value | Conversion factor | |
| Mass | 1kg | 1kg | 1 | |
| Length | 1m | 1m = 1000mm | 1000mm | 1000 |
| Time | 1s | 1s | 1 | |
| Force | 1N |
1N = 1kgm/s2 = 1000kgmm/s2 (since 1m = 1000mm) |
1000kgmm/s2 | 1000 |
| Stress | 1Pa |
1Pa = 1N/m2 =1kgm/s2m2 =1e-3kgs2/m (since 1m = 1000mm) |
1e-3N/mm2 | 1e-3 |
| Work | 1Nm |
1Nm = 1kgm2/s2 = 1e6 kgmm2/s2 (since 1m = 1000mm) |
1e6 kgmm2/s2 | 1e6 |
| Density | 1Kg/m3 | 1Kg/m3 = 1e-9 kg/mm3 | 1e-9 kg/mm3 | 1e-9 |
| Youngs modulus | 210GPa |
210GPa = 210e9 N/m2 = 210e9 kgm/s2m2 = 210e9 kg/s2m = 210e6 kg/s2mm (since 1m = 1000mm) |
210e6 kg/s2mm | 1e-3 |
| Velocity | 56.33KMPH |
56.33KM/H = 56.33e6mm/h =(56.33e6/3600)mm/s =15.64e3mm/3 |
15.64e3mm/3 | 277.78 |
| accelaration | 9.8m/s2 | 9.8m/s2 = 9800mm/s2 | 9800mm/s2 | 1e3 |
Conclusion:
Hence the values of each input is converted to kgmms unit system.