Week - 1 - Consistency of Units
AIM :- Convert the given measurements into different system of units .
MESURMENTS :-
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
System of Units to which we shall convert :-
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
ANSWERS:-
Detailed calculation for conversion from SI unit to gm/mm/ms unit system.
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
TABLE WITH ALL THE CONVERSIONS:-
| 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 |