Consistency of Units
Aim:
To convert the given measurements to different units given below.
Measurements:
Mass 1 kg
Length 1 m
Time 1 s
Force 1 N
Stress 1 Pa
Energy 1 Nm
Density 1 Kg/m3
Young's Modulus 210 GPa
Velocity 56.33 KMPH
Gravity 9.8 m/s2
Unit Systems:
1. Kg cm ms
2. Kg cm s
3. g mm ms
4. kg m s
5. g cm s
6. g cm us
7. g mm s
8. ton mm s
9. slug ft s
10. kg mm s
11. g cm ms
12. kg mm ms
Calculations:
Conversion from SI Units Kg/m/s to g/mm/ms
. Mass = 1 Kg
Kg to g = 1000 g or `10^3 g`
Conversion Factor = `10^3`
. Length = 1 m
m to mm = 1000 mm or `10^3 mm`
Conversion Factor = `10^3`
. Time = 1 Sec
Sec to ms = 1000 ms or `10^3 ms`
Conversion Factor = `10^3`
. Force = 1 N
Force = Mass x Accleration
= Kg `(m/s^2)`
= 1000 x `(1000/1000^2)` (`g((mm)/(ms^2))`)
= 1 `g((mm)/(ms^2))`
Conversion Factor = 1
. Stress = 1 Pa
= Force/Area = N/`m^2`
= 1 `(Kg (m/s^2))/m^2`
= 1 `g((mm)/(ms^2))/(mm^2)`
= `1/(1000^2)` `g((mm)/(ms^2))/(mm^2)`
= `10^-6` `g((mm)/(ms^2))/(mm^2)`
= `10^-6` `g/((mm)(ms^2))`
Conversion Factor = `10^-6`
. Energy = 1 J = 1 Nm = Force x Distance
= 1 `g((mm)/(ms^2)) mm`
= `10^3` `g((mm)/(ms))^2`
Conversion Factor = `10^3`
. Density = 1 `(Kg)/m^3` = Mass/Volume
= 1 x `1000/(1000)^3` `g/(mm^3)`
= 1 x `10^-6` `g/(mm^3)`
Conversion Factor = `10^-6`
. Young's Modulus = 210 GPa = Stress/Strain
= 210 x `10^9` `N/m^2`
= 210 x `10^9` x `(1/(1000^2))` `g((mm)/(ms^2))/(mm^2)`
= 2.1 x `10^5` `g/((ms^2)(mm))`
Conversion Factor = `10^3`
. Velocity = 56.33 `(Km)/(Hr)` Distance/Time
= 56.33 `(1000 m)/(3600 s)`
= 15.64 `m/s`
= 15.64 x `(1000/1000) ((mm)/(ms))`
= 15.64 `(mm)/(ms)`
Conversion Factor = 1
. Accleration Due to Gravity = 9.81 `(m)/(s^2)` = Distance/Time^2
= 9.81 x `((1000)/(1000^2))` `(mm)/(ms^2)`
= 9.81 x `10^-3` `(mm)/(ms^2)`
Conversion Factor = `10^-3`
| Sl.No | Measurements | Mass | Length | Time | Force | Stress | Energy | Density | Young's Modulus | Velocity | Accleration Due to Gravity |
|
1 |
kg m s | 1 Kg | 1 m | 1 s | 1 N | 1 Pa | 1 J | 1 `(Kg)/(m^3)` | 210 x `10^9` `(kg)/(m(s^2))` | 15.64 `m/s` | 9.81 `m/s^2` |
| 2 | Kg cm s | 1 Kg | `10^2 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)` | 210 x `10^7` `(Kg)/(cm(s^2))` | 15.64 x`10^2``(cm)/(s)` | 9.81 x`10^2``(cm)/(s^2)` |
| 3 | Kg mm s | 1 Kg | `10^3 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)` | 210 x `10^6` `(Kg)/(mm(s^2)` | 15.64 x `10^3``(mm)/s` | 9.81 x `10^3``(mm)/s^2` |
| 4 | Kg cm ms | 1 Kg | `10^2`cm | `10^3 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)` | 2100 `(Kg)/(cm(ms^2))` | 15.64 x `10^-1``(cm)/(ms)` | 9.81 x `10^-4``(cm)/(ms^2)` |
| 5 | g mm ms | `10^3g` | `10^3mm` | `10^3ms` | 1 `g((mm)/(ms^2))` | `10^-6` `g/(mm(ms^2))` | `10^3` `g((mm^2)/(ms^2))` | `10^-6` `g/(mm^3)` | 210 x`10^3` `g/(mm(ms^2))` | 15.64`(mm)/(ms)` | 9.81 x`10^-3``(mm)/(ms^2)` |
| 6 | g cm s | `10^3g` | `10^2cm` | 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)` | 210 x`10^10` `g/(cm(s^2))` | 15.64 x`10^2``(cm)/s` | 9.81 x`10^2``(cm)/s^2` |
| 7 | g cm `mu`s | `10^3g` | `10^2cm` | `10^6mus` | `10^-7` `g((cm)/(mus^2))` | `10^-11` `g/(cm(mus^2))` | `10^-5` `g((cm^2)/(mus^2))` | `10^-3` `g/(cm^3)` | 210 x `10^-11` `g/(cm(mus^2))` | 15.64 x`10^-4``(cm)/(mus)` | 9.81 x`10^-10``(cm)/(mus^2)` |
| 8 | g mm s | `10^3g` | `10^3mm` | 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)` | 210 x`10^9` `g/(mm(s^2))` | 15.64 x`10^3``(mm)/s` | 9.81 x`10^3``(mm)/s^2` |
| 9 | ton mm s | `10^-3`Ton | `10^3mm` | 1 s | 1 Tonne`((mm)/s^2)` | `10^-6` `Tonne/`mm(s^2)` | `10^3` `Tonne`((mm^2)/s^2)` | `10^-12` `(Ton)/(mm^3)` | 210 x`10^3` `(Ton)/(mm(s^2))` | 15.64 x`10^3``(mm)/s` | 9.81 x`10^3``(mm)/s^2` |
| 10 | slug ft s | 0.0685 Slug | `3.28ft` | 1 s | 0.224 `slug((ft)/(s^2))` | 0.021 `(slug)/(ft(s^2))` | 0.735 `slug((ft^2)/(s^2))` | 0.002 `(slug)/(ft^3)` | 4.41 x`10^9` `(slug)/(ft(s^2))` | 51.29`(ft)/s` | 32.2`(ft)/s^2` |
| 11 | g cm ms | `10^3g` | `10^2cm` | `10^3ms` | `10^-1` `g((cm)/(ms^2))` | `10^-5` `g/(cm(ms^2))` | 10 `g((cm^2)/(ms^2))` | `10^-3` `g/(cm^3)` | 210 x`10^4` `g/(cm(ms^2))` | 15.64 x`10^-1``(cm)/(ms)` | 9.81 x`10^-4``(cm)/(ms^2)` |
| 12 | kg mm ms | 1 Kg | `10^3mm` | `10^3ms` | `10^-3` `Kg((mm)/(ms^2))` | `10^-9` `(Kg)/(mm(ms^2))` | 1 `Kg((mm^2)/(ms^2))` | `10^-9` `(Kg)/(mm^3)` | 210 `(Kg)/(mm(ms^2))` | 15.64`(mm)/(ms)` | 9.81 x`10^-3``(mm)/(ms^2)` |
Conversion Factor:
| Sl.No | Unit System | Mass | Length | Time | Force | Stress | Energy | Density | Young's Modulus | Velocity | Accleration Due to Gravity |
| 1 | kg m s | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | Kg cm s | 1 | `10^2` | 1 | `10^2` | `10^-2` | `10^4` | `10^-6` | `10^7` | `10^2` | `10^2` |
| 3 | Kg mm s | 1 | `10^3` | 1 | `10^3` | `10^-3` | `10^6` | `10^-9` | `10^6` | `10^3` | `10^3` |
| 4 | Kg cm ms | 1 | `10^2` | `10^3` | `10^-4` | `10^-8` | `10^-2` | `10^-6` | `10^1` | `10^-1` | `10^-4` |
| 5 | g mm ms | `10^3` | `10^3` | `10^3` | 1 | `10^-6` | `10^3` | `10^-6` | `10^3` | 1 | `10^-3` |
| 6 | g cm s | `10^3` | `10^2` | 1 | `10^5` | 10 | `10^7` | `10^-3` | `10^10` | `10^2` | `10^2` |
| 7 | g cm `mu`s | `10^3` | `10^2` | `10^6` | `10^-7` | `10^-11` | `10^-5` | `10^-3` | `10^-11` | `10^-4` | `10^-10` |
| 8 | g mm s | `10^3` | `10^3` | 1 | `10^6` | 1 | `10^9` | `10^-6` | `10^9` | `10^3` | `10^3` |
| 9 | ton mm s | `10^-3` | `10^3` | 1 | 1 | `10^-6` | `10^3` | `10^-12` | `10^3` | `10^3` | `10^3` |
| 10 | slug ft s | 0.0685 | 3.28 | 1 | 0.224 | 0.021 | 0.735 | 0.002 | `10^9` | 51.29 | 32.2 |
| 11 | g cm ms | `10^3` | `10^2` | `10^3` | `10^-1` | `10^-5` | 10 | `10^-3` | `10^4` | `10^-1` | `10^-4` |
| 12 | kg mm ms | 1 | `10^3` | `10^3` | `10^-3` | `10^-9` | 1 | `10^-9` | 1 | 1 | `10^-3` |