Week - 1 - Consistency of Units
AIM: Convert the given values in the required conversion factor units with detailed calculation.
OBJECTIVE :
- Note down the given data values.
- Detailed calculation for conversion from SI unit to gm/mm/ms unit system.
- Table content of the remaining values of conversion from SI to different unit values as per requirement.
PROCEDURE :
Given data :
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
1) conversion from SI unit to gm/mm/ms unit system :
MASS : 1kg = 1000gm = 10^3 g
LENGTH : 1m = 100 cm = 10000 mm = 10^3 mm
TIME : 1s = 1000 ms = 10^3 ms
Force : 1N = 1×kg×(ms2)1×kg×(ms2)
= 1×(103g)×103mm106ms21×(103g)×103mm106ms2
- Force : 1N = 1 gm*mm/ms^2
STRESS : 1Pa = 1×(Nm2)1×(Nm2)
= 1×1gm×mmms2106mm1×1gm×mmms2106mm
- STRESS : 1Pa = 10−6gmmm×ms210-6gmmm×ms2 = 10^-6 gm / mm*ms^2
ENERGY : 1Nm = 1×1gm×mmms2×103mm1×1gm×mmms2×103mm
- ENERGY : 1Nm = 103gm×mm2ms2103gm×mm2ms2 = 10^3 gm * mm^2 * / ms^2
DENSITY : 1KG/m^3 = 1×KGm31×KGm3
= 1×103g109mm31×103g109mm3
- DENSITY : 1KG/m^3 = 10−6gmm310-6gmm3 = 10^-6 g/mm^3
YOUNGS MODULUS : 210GPa = 210×109×Pa210×109×Pa
=210×109×Nm2210×109×Nm2
= 210×109×(1gm×mm106mm2×ms2)210×109×(1gm×mm106mm2×ms2)
- YOUNGS MODULUS = 210GPa = 210×103gmmm×ms2210×103gmmm×ms2 = 210 x 10^3 gm/mm*ms^2
VELOCITY : 56.33 KMPH = 56.33×(KMhr)56.33×(KMhr)
= 56.33×106mm3600×(103ms)56.33×106mm3600×(103ms)
- VELOCITY : 56.33 KMPH = 15.647mmms15.647mmms = 15.647 mm/ms
GRAVITY : 9.8 m/s^2 = 9.8×ms29.8×ms2
= 9.8×103mm106ms9.8×103mm106ms
- GRAVITY : 9.8 m/s^2 = 9.8×10−3mmms29.8×10-3mmms2 = 9.8*10^-3 mm/ms^2
NOTE: By following a similar calculation method we took out the values for the other convergence units from SI unit and the values are shown in the table below.
TABLE: content values of conversion units from SI units
| UNITS | MASS | LENGTH | TIME | FORCE | STRESS | ENERGY | DENSITY | YOUNGS MODULUS | VELOCITY | GRAVITY |
| KG/ CM/ MS | 1 | 100 | 1000 |
10^−4kg×cm/ms^2 |
10^−8kg/cm×ms^2 |
10^−2kg×cm2/ms^2 |
10^−6kg/cm^3 |
2100kg/cm×ms^2 | 1.5647cm/ms |
9.8×10^−4cm/ms |
| KG/ CM/ S | 1 | 100 | 1 | 100kg×cm/s^2 |
10^−2kg/cm×s^2 |
10^4kg×cm^2/s^2 |
10^−6kg/cm^3 |
210×10^7kg/cm×s^2 | 1564.72cm/s | 9.8×10^2cm/s^2 |
| GM/MM/ MS | 10^3g | 10^3mm | 10^3ms | 1g×mm/ms^2 |
10^−6g/mm×ms^2 |
10^3g×mm2/ms^2 |
10^−6g/mm^3 |
210×10^3g/mm×ms^2 | 15.647mm/ms |
9.8×10^−3mm/ms^2 |
| KG/ M/ S | 1 | 1 | 1 | 1kg×m/s^2 | 1kg/m×s^2 | 1kg×m^2/s^2 | 1kg/m^3 | 210×10^9kg/m×s^2 | 15.647m/s | 9.8m/s^2 |
| G/ CM/ S | 10^3g | 10^2cm | 1 | 10^5g×cm/s^2 | 10g/cm×s^2 | 10^7g×cm^2/s^2 | 10^−3g/cm^3 | 210×10^10g/cm×s^2 | 1564.72cm/s | 9.8×10^2cm/s^2 |
| G/ CM/ μμ`s | 10^3g | 10^2cm | 10^6μs |
10^−7g×cm/μs^2 |
10^−11g/cm×μs^2 |
10^−5g×cm^2/s^2 | 10^−3g/cm^3 | 2.10g/cm×μs^2 |
15.647×10^−4cm/μs |
9.8×10^−10cm/μs^2 |
| G/ MM/ S | 10^3g | 10^3mm | 1 | 10^6g×mm/s^2 | 1g/mm×s^2 | 10^9g×mm^2/s^2 |
10^−6gm/m^3 |
210×10^9g/mm×s^2 | 15647.2mm/s | 9.8×10^3mm/s^2 |
| TONNE/ MM/ S |
10^−4tonne |
10^3mm | 1 |
10^−1tonne×mm/s^2 |
10^−7tonne/mm×s^2 |
10^2tonne×mm^2/s^2 |
10^−13tonne/mm^3 |
210×10^2tonne/mm×s^2 | 15647.2mm/s | 9.8×10^3mm/s^2 |
| SLUG/ FT/ S | 0.068slug | 3.28ft | 1 | 0.223slug×ft/s^2 | 0.0207slug/ft×s^2 | 0.7314slug×ft^2/s^2 |
19×10^−4slug/ft^3 |
4.347×109slug/ft×s^2 | 51.34ft/s | 32.14ft/s^2 |
| KG/ MM/ S | 1 | 10^3mm | 1 | 10^3kg×mm/s^2 | 10^−3kg/mm×s^2 | 10^6kg×mm^2/s^2 |
10^−9kg/mm^3 |
210×10^6kg/mm×s^2 | 15647.2mm/s | 9.8×10^3mm/s^2 |
| G/ CM/ MS | 10^3g | 10^2cm | 10^3ms |
10^−1g×cmm/s^2 |
10^−5g/cm×ms^2 | 10g×cm^2/ms^2 | 10^−3g/cm^3 | 210×10^4g/cm×ms^2 | 1.5647cm/ms |
9.8×10^−4cmm/s^2 |
| KG/ MM/ MS | 1 | 10^3mm | 10^3ms | 10−3kg×mm/ms^2 |
10^−9kg/mm×ms^2 |
1kg×mm^2/ms^21 |
10^−9kg/mm^3 |
210kg/mm×ms^2 | 15.647mm/ms | 9.8×10^−3mm/ms^2 |
RESULT: The given task of converting the SI unit values to the required conversion units is done and the values are shared in the table format.calculation part is shown for the "gm/mm/ms".