Week - 1 - Consistency of Units
OBJECTIVE: calculate the conversion factors for given units and convert the given measurements to the specified units.
EXPLANATION:
UNIT SYSTEM : gm mm ms
How to calculate conversiobn factor :
Let us take the first given unit system which is kg, cm, ms.
we know that 1) 1kg = 1000gm, (conversion factor = 1000)
2) 1m = 1000mm, (conversion factor = 1000)
3) 1 s = 1000ms. (conversion factor = 1000)
4) 1N = 1kg*1m*s^-2 = 1000gm*1000mm*(1000ms)^-2.
= 1000gm*1000mm*10^-6 (ms)^-2.
= 1 gm mm/ms^2
1N = 1 gm mm/ms^2 ( conversion factor = 1)
5)1pa = N/m2
= 1000gm*1000mm*(1000ms)^-2 * 1000mm^-2.
= 1000gm*1000mm* 10^-6 (ms)^-2 * 1000^-2 (mm)^-2.
= 100*100^-6 * 10^-4 gm*mm*(,m)^-2 (ms)^-2.
= 10^-6 gm mm^-1 ms^-2. (conversion factor= 10^-6)
6)1Nm = 1kg*1m*1s^-2*1m.
= 1000gm*1000mm* (1000)^-2* ms^-2 * 1000mm.
= 1000gm*1000*1000*mm^2 * 10^-6 ms^-2.
= 1*10^9* 10^-6 * gm mm^2 ms^-2.
= 10^3 gm mm^2 ms^-2. (conversion factor = 1000)
7)1kg/m^3 = 1kg* m^-3.
= 1000gm* (1000)^-3 mm^-3.
= 1*10^-6 gm/mm^3 (conversion factor = 10^-6.)
8)1Gpa = 10^6pa = 10^6 N/m2 = 10^6 * 1000gm*1000mm*(1000ms)^-2* (1000mm)^-2.
= 10^6*1 gm *1000mm*(1000ms)^-2 * (1000mm)^-2
= 10^6* 1* 100*10^-6* 10^-4 kg cm^-1 ms^-2.
1Gpa = 1 gm/mm/ms^2 (conversion factor =1)
9)1KMPH = 10^6mm*(3600*10^3 ms)^-1.
= 1000* 1000mm*(3600*1000 ms)^-1.
= 1000* 1000* 1000^-1 * 3600^-1 cm/ms.
= 1000/3600 * mm/ms
= 0.27778 mm/ms. (conversion factor = 0.27778).
10)1m/s^2 = 1000mm* (1000ms)^-2
= 1000* 10^-6 *cm* ms^-2
= 10^-3 mm/ms^2. (conversion factor = 10^-3.)
TABLE FOR gm mm ms UNIT SYSTEM.
| S.No | Measurements | Conversion factor | original value | converted value |
| 1 | MASS | 1000 | 1 | 1000gm |
| 2 |
LENGTH |
1000 | 1 | 1000mm |
| 3 | TIME | 1000 | 1 | 1000ms |
| 4 | FORCE | 1 | 1 | 1 gm mm/ms^2 |
| 5 | STRESS | 10^-6 | 1 | 10^-6 gm/ mm/ ms^2 |
| 6 | ENERGY | 1000 | 1 | 1000 gm mm^2 ms^-2 |
| 7 | DENSITY | 10^-6 | 1 | 10^-6 gm/mm^3 |
| 8 | YOUNGS MODULUS | 1 | 210 | 210 gm/mm/ms^2 |
| 9 | VELOCITY | 0.27778 | 56.33 | 15.647 mm/ms |
| 10 | GRAVITY | 0.001 | 9.8 | 0.0098 mm/ms^2 |
UNIT SYSTEM : Kg cm ms
| S.No | Measurements | Conversion factor | original value | converted value |
| 1 | MASS | 1 | 1 | 1 kg |
| 2 |
LENGTH |
100 | 1 | 100 cm |
| 3 | TIME | 1000 | 1 | 1000 ms |
| 4 | FORCE | 10^-4 | 1 | 10^-4 kg cm/ms^2 |
| 5 | STRESS | 10^-8 | 1 | 10^-8 kg/cm/ms^2 |
| 6 | ENERGY | 10^-2 | 1 | 10^-2 kg cm^2/ms^2 |
| 7 | DENSITY | 10^-6 | 1 | 10^-6 kg/cm^3 |
| 8 | YOUNGS MODULUS | 10^-2 | 210 | 2.1 kg/cm/ms^2 |
| 9 | VELOCITY | 0.027778 | 56.33 | 1.567 cm/ms |
| 10 | GRAVITY | 10^-4 | 9.8 | 9.8*10^-4 cm/ms^2 |
UNIT SYSTEM : kg m s
| S.No | Measurements | Conversion factor | original value | converted value |
| 1 | MASS | 1 | 1 | 1 kg |
| 2 |
LENGTH |
1 | 1 | 1 m |
| 3 | TIME | 1 | 1 | 1 s |
| 4 | FORCE | 1 | 1 | 1 kg m/s^2 |
| 5 | STRESS | 1 | 1 | 1 kg/m/s^2 |
| 6 | ENERGY | 1 | 1 | 1 kg m^2/s^2 |
| 7 | DENSITY | 1 | 1 | 1 kg/m^3 |
| 8 | YOUNGS MODULUS | 10^6 | 210 | 210*10^6 kg/m/s^2 |
| 9 | VELOCITY | 0.27778 | 56.33 | 15.647 m/s |
| 10 | GRAVITY | 1 | 9.8 | 9.8 m/s^2 |
UNIT SYSTEM : Kg cm s
| S.No | Measurements | Conversion factor | original value | converted value |
| 1 | MASS | 1 | 1 | 1 kg |
| 2 |
LENGTH |
100 | 1 | 100cm |
| 3 | TIME | 1 | 1 | 1 s |
| 4 | FORCE | 100 | 1 | 100 kg cm/s^2 |
| 5 | STRESS | 0.01 | 1 | 0.01 kg/cm/s^2 |
| 6 | ENERGY | 10000 | 1 | 10000 kg cm^2/s^2 |
| 7 | DENSITY | 10^-6 | 1 | 10^-6 kg/cm^3 |
| 8 | YOUNGS MODULUS | 10^4 | 210 | 0.21 kg/cm/s^2 |
| 9 | VELOCITY | 27.778 | 56.33 | 1564. 73 cm/s |
| 10 | GRAVITY | 100 | 9.8 | 980 cm/s^2 |
UNIT SYSTEM : g cm s
| S.No | Measurements | Conversion factor | original value | converted value |
| 1 | MASS | 1000 | 1 | 1000 g |
| 2 |
LENGTH |
100 | 1 | 100 cm |
| 3 | TIME | 1 | 1 | 1s |
| 4 | FORCE | 10^5 | 1 | 10^5 g cm/s^2 |
| 5 | STRESS | 10 | 1 | 10 g/cm/s^2 |
| 6 | ENERGY | 10^7 | 1 | 10^7 g cm^2/s^2 |
| 7 | DENSITY | 10^-3 | 1 | 0.001 g/cm^3 |
| 8 | YOUNGS MODULUS | 10^7 | 210 | 21*10^8 g/cm/s^2 |
| 9 | VELOCITY | 27.778 | 56.33 | 156.47 cm/s |
| 10 | GRAVITY | 100 | 9.8 | 980 cm/s^2 |
UNIT SYSTEM : g cm us
| S.No | Measurements | Conversion factor | original value | converted value |
| 1 | MASS | 1000 | 1 | 1000g |
| 2 |
LENGTH |
100 | 1 | 100 cm |
| 3 | TIME | 10^-6 | 1 | 10^-6 us |
| 4 | FORCE | 10^17 | 1 | 10^17 g cm/us^2 |
| 5 | STRESS | 10^13 | 1 | 10^13 g/cm/us^2 |
| 6 | ENERGY | 10^19 | 1 | 10^19 g cm^2/us^2 |
| 7 | DENSITY | 10^-3 | 1 | 0.001 g/cm^3 |
| 8 | YOUNGS MODULUS | 10^19 | 210 | 210*10^19 g/cm/us^2 |
| 9 | VELOCITY | 2.7778*10^6 | 56.33 | 156.47*10^6 cm/us |
| 10 | GRAVITY | 10^14 | 9.8 | 9.8*10^14 cm/us^2 |
UNIT SYSTEM : g mm s
| S.No | Measurements | Conversion factor | original value | converted value |
| 1 | MASS | 1000 | 1 | 1000 g |
| 2 |
LENGTH |
1000 | 1 | 1000 mm |
| 3 | TIME | 1 | 1 | 1 s |
| 4 | FORCE | 10^6 | 1 | 10^6 g mm/s^2 |
| 5 | STRESS | 1 | 1 | 1 g/mm/s^2 |
| 6 | ENERGY | 10^9 | 1 | 10^9 g mm^2/s^2 |
| 7 | DENSITY | 10^-6 | 1 | 10^-6 g/mm^3 |
| 8 | YOUNGS MODULUS | 10^6 | 210 | 21*10^7 g/mm/s^2 |
| 9 | VELOCITY | 277.78 | 56.33 | 15647.23 mm/s |
| 10 | GRAVITY | 1000 | 9.8 | 9800 mm/s^2 |
UNIT SYSTEM : ton mm s
| S.No | Measurements | Conversion factor | original value | converted value |
| 1 | MASS | 1.1*10^-3 | 1 | 1.1*10^-3 ton |
| 2 |
LENGTH |
1000 | 1 | 1000mm |
| 3 | TIME | 1 | 1 | 1 s |
| 4 | FORCE | 1.1 | 1 | 1.1 tom mm/s^2 |
| 5 | STRESS | 1.1*10^-6 | 1 | 1.1*10^-6 ton/mm/s^2 |
| 6 | ENERGY | 1.1*10^3 | 1 | 1100 ton mm^2/s^2 |
| 7 | DENSITY | 1.1*10^-12 | 1 | 1.1*10^-12 ton/mm^3 |
| 8 | YOUNGS MODULUS | 1.1 | 210 | 231 ton/mm/s^2 |
| 9 | VELOCITY | 277.78 | 56.33 | 15647.23 mm/s |
| 10 | GRAVITY | 1000 | 9.8 | 9800 mm/s^2 |
UNIT SYSTEM : slug ft s
| S.No | Measurements | Conversion factor | original value | converted value |
| 1 | MASS | 0.0685 | 1 | 0.0685kg |
| 2 |
LENGTH |
3.28 | 1 | 3.28ft |
| 3 | TIME | 1 | 1 | 1s |
| 4 | FORCE | 0.225 | 1 | 0.225 slug ft/s^2 |
| 5 | STRESS | 0.021 | 1 | 0.021 slug/ft/s^2 |
| 6 | ENERGY | 0.225 | 1 | 0.225 slug ft^2/s^2 |
| 7 | DENSITY | 0.002 | 1 | 0.002 slug/ft^3 |
| 8 | YOUNGS MODULUS | 21*10^3 | 210 | 441*10^4 slug/ft/s^2 |
| 9 | VELOCITY | 0.9111 | 56.33 | 51.32 ft/s |
| 10 | GRAVITY | 3.28 | 9.8 | 32.144 ft/s^2 |
UNIT SYSTEM : kg mm s
| S.No | Measurements | Conversion factor | original value | converted value |
| 1 | MASS | 1 | 1 | 1 kg |
| 2 |
LENGTH |
1000 | 1 | 1000 m |
| 3 | TIME | 1 | 1 | 1s |
| 4 | FORCE | 1000 | 1 | 1000 kg mm/s^2 |
| 5 | STRESS | 10^-3 | 1 | 0.001 kg/m/s^2 |
| 6 | ENERGY | 10^6 | 1 | 10^6 kg m^2/s^2 |
| 7 | DENSITY | 10^-9 | 1 | 10^-9 kg/mm^2 |
| 8 | YOUNGS MODULUS | 10^3 | 210 | 21*10^4 kg/mm/s^2 |
| 9 | VELOCITY | 277.78 | 56.33 | 15647.23 mm/s |
| 10 | GRAVITY | 1000 | 9.8 | 9800 mm/s^2 |
UNIT SYSTEM : g cm ms
| S.No | Measurements | Conversion factor | original value | converted value |
| 1 | MASS | 1000 | 1 | 1000g |
| 2 |
LENGTH |
100 | 1 | 100 cm |
| 3 | TIME | 1000 | 1 | 1000 ms |
| 4 | FORCE | 0.1 | 1 | 0.1 g cm/ms^2 |
| 5 | STRESS | 10^-5 | 1 | 10^-5 g/cm/ms^-2 |
| 6 | ENERGY | 10 | 1 |
10 g cm^2 |
| 7 | DENSITY | 10^-3 | 1 | 0.001 g/cm^2 |
| 8 | YOUNGS MODULUS | 10 | 210 | 2100 g/cm/ms^2 |
| 9 | VELOCITY | 0.027778 | 56.33 | 1.56 cm/ms |
| 10 | GRAVITY | 100 | 9.8 | 980 cm/ms^2 |
UNIT SYSTEM : kg mm ms
| S.No | Measurements | Conversion factor | original value | converted value |
| 1 | MASS | 1 | 1 | 1 kg |
| 2 |
LENGTH |
1000 | 1 | 1000 mm |
| 3 | TIME | 1000 | 1 | 1000 ms |
| 4 | FORCE | 10^-3 | 1 | 10^-3 kg mm/ms^2 |
| 5 | STRESS | 10^-9 | 1 | 10^-9 kg /mm/ms^2 |
| 6 | ENERGY | 1 | 1 | 1 kg mm^2/ |
| 7 | DENSITY | 10^-9 | 1 | 10^-9 kg/mm^3 |
| 8 | YOUNGS MODULUS | 10^-3 | 210 | 0.21 kg/mm/ms^2 |
| 9 | VELOCITY | 0.27778 | 56.33 | 15.634 mm/ms |
| 10 | GRAVITY | 10^-3 | 9.8 | 0.0098 mm/ms^2 |