Week - 1 - Consistency of units
Aim :
Understand the unit conversion practices and calculate the conversion factor for the different unit systems.
Theory :
To avoid misinterpretations of the measuring quantities, a universal and more consistent sytem i.e. SI unit system came into practise. Before the SI system, many unit systems has been practised around the world based on the convienience and comfort. Now a days many industries are practising the different unit systems based on the scale of the measuring quantities being used. Unit convesrion is important to know the relation between the measuring quantities.
Explanation :
Conversion of given measurements from SI unit to gm/mm/ms.
1. Mass: 1 Kg
`1" Kg" = 1000" grams"`
To convert mass, from Kilogram to gram, quantity has to be multiplied by 1000. Convesion factor is 1000.
2. Length: 1m
`1" m" = 1000" mm"`
To convert length, from metre to millimetre, quantity has to be multiplied by 1000. Conversion factor is 1000.
3. Time: 1s
`1" s" = 1000" ms"`
To convert time, from seconds to milliseconds, quantity has to be multiplied by 1000. Conversion factor is 1000.
4.Force: 1N
`1 N = 1" Kg.m"//"s"^2 = (1000" g")xx(1000" mm")//(1000" ms")^2`
`= (1000.1000)/(1000^2)" g.mm"//"ms"^2 = 1" g.mm"//"ms"^2`
To convert force, from Newtons to gm/mm/ms system, quantity has to be multiplied by 1, i.e. newtons can be used without conversion. Conversion factor is 1.
5. Stress :1Pa
`1" Pa" = 1" N"//"m"^2 =(1" N")/(1000" mm")^2`
`= 1/1000^2" N"//"mm"^2 = 1xx10^-6" N"//"mm"^2 =1xx10^-6" MPa"`
To convert stress, from pascals to MPa (`"N"//"mm"^2`), quantity has to be multiplied by `1xx10^-6`. Conversion factor is `1xx10^-6``
6. Energy :1Nm
`1" Nm" = 1" J"= 1" N"xx(1000" mm")`
`= 1000" N.mm" =1000" mJ"`
To convert energy, from joules to millijoules, quantity has to be multiplied by 1000. Conversion factor is 1000.
7.Density :1Kg/m3 (1 m Kg/L)
`1" Kg"//"m"^3 = (1000" g").//(1000" mm")^3 = 1xx10^-6" g"//"mm"^3`
`= 1xx10^-6" g"//"mm"^3 = 1xx10^-6 " K Kg"//"l"`
To convert density, from Kg/m3 (m Kg/L) to K Kg/L, quantity has to be multiplied by `1xx10^-6`. Conversion factor is `1xx10^-6`.
8. Young's modulus : 210 GPa
`1" GPa" = 1xx10^9" Pa" = 1xx10^9 *(1xx10^-6" MPa")`
`=1xx10^3" MPa" = 1xx10^3" N"//"mm"^2`
To convert young's modulus, from GPa to MPa(`"N"//"mm"^2`), quantity has to be multiplied by `1xx10^3`. Conversion factor is `1xx10^3`
Therefore, `210" GPa" =210xx10^3" MPa" = 210xx10^3" N"//"mm"^2`
9. Velocity :56.33KMPH
`1" KMPH" = (1000" m")/(1" hour") = (1000" m")/(60.60" sec"`
`(1000" m")/(3600" sec") = (10cancel(00).cancel(1000)" mm")/(36cancel(00).cancel(1000)" ms" )=(5/18)" mm"//"ms" = 0.278" mm"//"ms"`
To convert velocity, from KMPH to mm/ms (m/s), quantity has to be multiplied by 0.278. Conversion factor is 0.278.
Therefore, `56.33" KMPH" = 56.33xx(0.278)" mm"//"ms" = 15.647" mm"//"ms"`
10. Gravity : 9.8m/s2
`1" m"//"s"^2 = (1000" mm")/(1000" ms")^2 =(1" mm")/(1000" ms"^2 ) = 1xx10^-3" mm"//"ms"^2`
To convert gravity, from m/s2 to mm/ms2, quantity has to be multiplied by `1xx10^-3`. Conversion factor is `1xx10^-3``
Therefore, `9.8" m"//"s"^2 = 9.8xx10^-3" mm"//"ms"^2`
To convert value from one unit syatem to another unit system, multiply the given quantity with the suitable conversion factor. Conversion factors for given quantities in various unit sytems is tabulated below.
| Given Quantity | 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 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Mass (1Kg) | `1` | `1` | `1000` | `1` | `1000` | `1000` | `1000` | `0.001102` | `0.068521` | `1` | `1000` | `1` |
| Length (1m) | `100` | `100` | `1000` | `1` | `100` | `100` | `1000` | `1000` | `3.281` | `1000` | `100` | `1000` |
| Time (1s) | `1000` | `1` | `1000` | `1` | `1` | `1xx10^6` | `1` | `1` | `1` | `1` | `1000` | `1000` |
| Force (1N) | `1xx10^-4` | 100 | `1` | `1` | `1xx10^5` | `1xx10^-7` | `1xx10^6` | `1.102` | `0.224` | `1000` | `0.1` | `1xx10^-3` |
| Stress (1Pa) | `1xx10^-8` | `0.01` | `1xx10^-6` | `1` | `10` | `1xx10^-11` | `1` | `1.102xx10^-6` | `0.020004` | `1xx10^-3` | `1xx10^-5` | `1xx10^-9` |
| Energy (1Nm) | `0.01` | `1xx10^4` | `1000` | `1` | `1xx10^7` | `1xx10^-5` | `1xx10^9` | `1102` | `0.73495` | `1xx10^6` | `10` | `1` |
| Density (1Kg/m3) | `1xx10^-6` | `1xx10^-6` | `1xx10^-6` | `1` | `1xx10^-3` | `1xx10^-3` | `1xx10^-6` | `1.102xx10^-12` | `1.94xx10^-3` | `1xx10^-9` | `1xx10^-3` | `1xx10^-9` |
| Young's Modulus (210GPa) | `10` | `1xx10^7` | `1xx10^3` | `1xx10^9` | `1xx10^10` | `0.01` | `1xx10^9` | `1102` | `2.0004xx10^7` | `1xx10^6` | `1xx10^4` | `1` |
| Velocity (56.33KMPH) | `0.0278` | `27.8` | `0.278` | `0.278` | `27.8` | `2.78xx10^-5` | `278` | `278` | `0.911389` | `278` | `0.0278` | `0.278` |
| Gravity (9.8m/s2) | `1xx10^-4` | `100` | `1 xx10^-3` | `1` | `100` | `1xx10^-10` | `1000` | `1000` | `3.281` | `1000` | `1xx10^-4` | `1xx10^-3` |
Conclusion :
The conversation factors for each quantity in different unit systems is calculated and the values for the given quantities are converted into gm/mm/ms unit system.