Week - 1 - Consistency of units
OBJECTIVE :
To Convert the given measurements to the provided different system of units and to mention the conversion factors for the same.
Measurements: 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
Unit System to convert to :
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
Also, a detailed calculation must be provided for conversion from provided SI unit to gm/mm/ms unit system and for the other unit systems, answers should be in the form of a table with the unit systems as rows and measured quantities as columns
CONVERSION TO g/mm/ms UNIT SYSTEM :
Conversion Factors :
Weight : kg to g - Value * `10^3`
Length : m to mm - Value * `10^3`
Time : s to ms - Value * `10^3`
| S.No. | Measured Quantity | Value in provided SI Unit System (kg/m/s) | Value in g/mm/ms unit System |
|---|---|---|---|
| 1 | Mass | 1 kg | = 1 *`10^3` g = 1000 g |
| 2 | Length | 1 m | = 1*`10^3` mm = 1000 mm |
| 3 | Time | 1 s | = 1 *`10^3` ms = 1000 ms |
| 4 | Force | 1 N = 1 `(kg.m)/s^2` | = 1 * `(10^3 * 10^3)/(10^3 * 10^3) (g.mm)/(ms^2)` = 1 `(g.mm)/(ms^2)` |
| 5 | Stress | 1 Pa = 1 `N/m^2` = 1 `(kg.m)/(m^2.s^2)` = `(kg)/(m.s^2)` | = 1 * `10^3/(10^3*10^6) g/(mm*ms^2)` = 1*`10^-6 g/(mm.ms^2)` |
| 6 | Energy | 1 Nm = 1 `(kg.m^2)/s^2` | = 1 * `(10^3 * 10^6)/10^6 (g*mm^2)/(ms^2)` = 1*`10^3` `(g*mm^2)/(ms^2)` |
| 7 | Density | 1 `(kg)/m^3` | = 1 * `10^3/10^9 g/(mm^3)` = 1* `10^-6 g/(mm^3)` |
| 8 | Young's Modulus | 210 GPa = 210 x `10^9` Pa = 210 x `10^9` `(kg.m)/(m^2.s^2)` | = 210 * `(10^9 * 10^3)/(10^3 * 10^6) g/(mm*ms^2)` = 210* `10^3 g/(mm.ms^2)` |
| 9 | Velocity | 56.33 `(km)/(hr)` = `((56.33)* 10^3)/(60*60) m/s` = 15.647 `m/s` | = 15.647 * `10^3/10^3 (mm)/(ms)` =15.647 `(mm)/(ms)` |
| 10 | Gravity | 9.8 `m/s^2` | = 9.8 * `10^3/10^6 (mm)/(ms^2)` = 9.8 * `10^-3 (mm)/(ms^2)` |
CONVERSION TO OTHER UNIT SYSTEMS :
| S.No | Unit Systems | Mass | Length | Time | Force | Stress | Energy | Density | Young's Modulus | Velocity | Acc. Due to Gravity |
| 1 | kg-m-s | 1 kg | 1 m | 1 s | 1 `(kg.m)/s^2` | 1 `(kg)/(m.s^2)` | 1 `(kg.m^2)/s^2` | 1 `(kg)/m^3` |
210 x `10^9` `(kg)/(m.s^2)` |
15.64 `m/s` | 9.8 `m/s^2` |
| 2 | kg-cm-s | 1 kg | 100 cm | 1 s |
100 `(kg.cm)/s^2` |
`10^-2` `(kg)/(m.s^2)` |
`10^4 (kg.cm^2)/s^2` | `10^-6 (kg)/(cm^3)` |
210 x `10^7` `(kg)/(cm.s^2)` |
1564 `(cm)/s` | 980`(cm)/s^2` |
| 3 | g-mm-ms | `10^3`g | `10^3`mm | `10^3`ms |
1 `(g.mm)/(ms^2)` |
1* `10^-6` `g/(mm.ms^2)` |
1*`10^3` `(g*mm^2)/(ms^2)` |
1* `10^-6 g/(mm^3)` | 210* `10^3 g/(mm.ms^2)` | 15.647 `(mm)/(ms)` | 9.8 * `10^-3 (mm)/(ms^2)` |
| 4 | kg-cm-ms | 1 kg | 100 cm | `10^3`ms | `10^-4``(kg.cm)/(ms^2)` | 1* `10^-8` `kg/(cm.ms^2)` |
1*`10^-1` `(kg*cm^2)/(ms^2)` |
1* `10^-6 g/(mm^3)` | 2100 `(kg)/(cm.ms^2)` | 1.5647 `(cm)/(ms)` | 9.8 * `10^-4 (cm)/(ms^2)` |
| 5 | g-cm-s | `10^3`g | 100 cm | 1 s | `10^5``(g.cm)/(s^2)` | 10 `g/(cm.s^2)` | `10^7` | `10^-3` | 210 * `10^10` | 15.64 * `10^2` | 9.8 * `10^2` |
| 6 | g-cm-`mu`s | `10^3`g | 100 cm | `10^6`ms | `10^-7``(g.cm)/(`mu`s^2)` | 1* `10^-11` `g/(cm.`mu`s^2)` | `10^-5` | `10^-3` | 210 * `10^-11` | 15.64 * `10^-4` | 9.8 * `10^-10` |
| 7 | g-mm-s | `10^3`g | `10^3`mm | 1 s | `10^6``(g.mm)/(s^2)` | 1 `g/(mm.s^2)` | `10^9` | `10^-6` | 210 * `10^9` | 15.64 * `10^3` | 9.8 * `10^3` |
| 8 | Ton-mm-s | `10^-3` Ton | `10^3`mm | 1 s | 1`(Ton.mm)/(s^2)` | 1* `10^-6` `kg/(cm.s^2)` | `10^3` | `10^-12` | 210 * `10^3` | 15.64 * `10^3` | 9.8 * `10^3` |
| 9 | Slug-ft-s | 0.0685 Slug | 3.28 ft | 1 s | 0.224 `(Slug.ft)/(s)` | 0.021 | 0.735 | 0.002 | 4.41 * `10^9 | 51.29 ft/s | 32.2 |
| 10 | kg-mm-s | 1 | `10^3`mm | 1 s | `10^3``(kg.mm)/(s^2)` | `10^-3` | `10^6` | `10^-9` | 210 * `10^6` | 15.64 * `10^3` | 9.8 * `10^3` |
| 11 | g-cm-ms | `10^3`g | 100 cm | `10^3`ms | `10^-1``(g.cm)/(ms^2)` | `10^-5` | 10 | `10^-3` | 210 * `10^4` | 1.564 | 9.8 * `10^-4` |
| 12 | kg-mm-ms | 1 | `10^3`mm | `10^3`ms | `10^-3``(kg.mm)/(ms^2)` | `10^-9` | 1 | `10^-9` | 210 | 15.64 | 9.8 * `10^-3` |
CONVERSION FACTORS :
| S.No | Unit Systems | Mass | Length | Time | Force | Stress | Energy | Density | Young's Modulus | Velocity | Acc. 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^-2` |
`10^2` | `10^2` |
| 3 | g-mm-ms | `10^3` | `10^3` | `10^3` |
1 |
`10^-6` |
`10^3` |
`10^-6` | `10^-6` | 1 | `10^-3` |
| 4 | kg-cm-ms | 1 | `10^2` | `10^3` | `10^-4` | `10^-8` | `10^-2` | `10^-6` | `10^-8` | `10^-1` | `10^-4` |
| 5 | g-cm-s | `10^3` | `10^2` | 1 | `10^5` | 10 | `10^7` | `10^-3` | 10 | `10^2` | `10^2` |
| 6 | g-cm-`mu`s | `10^3` | `10^2` | `10^6` | `10^-7` | `10^-5` | `10^-11` | `10^-3` | `10^-11` | `10^-4` | `10^-10` |
| 7 | g-mm-s | `10^3` | `10^3` | 1 | `10^6` | 1 | `10^9` | `10^-6` | 1 | `10^3` | `10^3` |
| 8 | Ton-mm-s | `10^-3` | `10^3` | 1 | 1 | `10^-6` | `10^3` | `10^-12` | `10^-6` | `10^3` | `10^3` |
| 9 | Slug-ft-s | 0.0685 | 3.28 | 1 | 0.224 | 0.021 | 0.735 | 0.002 | 0.21 | 51.29 | 3.282 |
| 10 | kg-mm-s | 1 | `10^3` | 1 | `10^3` | `10^-3` | `10^6` | `10^-9` | `10^-3` | `10^3` | `10^3` |
| 11 | g-cm-ms | `10^3` | `10^2` | `10^3` | 0.1 | `10^-5` | 10 | `10^-3` | `10^-5` | `10^-1` | `10^-4` |
| 12 | kg-mm-ms | 1 | `10^3` | `10^3` | `10^-3` | `10^-9` | 1 | `10^-9` | `10^-9` | 1 | `10^-3` |
CONCLUSION :
Thus, the given measurements were converted to the provided different system of units and the conversion factors for the same was also provided with respect to the guidelines.