Week - 1 - Consistency of Units
OBJECTIVE :- Convert given measurements into different system of units and finding their corresponding conversion factors.
measurements given
1.MASS 1kg
2.LENGTH 1m
3.TIME 1s
4.FORCE 1N
5.STRESS 1Pa
6.ENERGY 1Nm
7.DENSITY 1Kg/m3
8.YOUNG'S Modulus 210GPa
9.Velocity 56.33KMPH
10.GRAVITY 9.8m/s2
system of units
kg m s
Kg cm ms
Kg cm s
gm mm ms
g cm s
g cm us
g mm s
ton mm s
slug ft s
kg mm s
g cm ms
kg mm ms
PROCEDURE
Conversions of given measuremnts From SI unit to gm/mm/ms unit system
1.MASS : 1kg = 1000gm
Conversion factor : 10^3
2.LENGTH : 1m = 1000mm
Conversion factor : 10^3
3.TIME : 1s = 1000ms
Conversion factor : 10^3
4.FORCE (F) = 1N =ma
m= mass = kg = 10^3gm
a= acceleration = m/s^2 = 10^3mm/(10^3)^2 = 10^3/10^6
ma = 10^3 * 10 ^3
10^6
ma = 10^6/10^6 = 1
Conversion factor : 1
5.STRESS : force per unit area ,1Pa = 1N/m^2 = {1kg*(1 m/s^2)}/m^2 = 1 kg/ (m* s^2)
= 1000g/{1000mm*(1000ms)^2}
= 10-6 g/ (mm*ms^2)
Conversion factor : 10^-6
6.ENERGY : 1J = 1Nm = (1kg*1 m/s^2) * m = 1 (kg*m^2/s^2)
= {1000g * (1000mm)^2}/(1000ms)^2
= (109 g*mm2) / (106 ms2)
= 10^3 (g*mm2/ ms2)
Conversion factor : 10^3
7.DENSITY : mass per volume = 1Kg/m^3 = 1000g/(1000mm)^3
= 10^-6 g/mm^3
Conversion factor : 10^-6
8.YOUNGS MODULUS : ratio of stress to strain = 210GPa = 210*10^9 pa
1pa=1N/m^2
1N= 1 kg*m/s^2
1N= 1000gm*1000mm/{10^3}^2ms
1N= 1gm*mm/ms
1pa= 1/10^6
210GPa=210*10^9pa = 210*10^9*10^-6
210 GPa = 210*10^3 g/ (mm*ms2)
= 210e+3 g/ (mm*m s2) = 210*103 g/ (mm*m s2)
Conversion factor : 10^3
9.VELOCITY : 56.33 Kmph = 56.33 * {10^6mm/(3600*1000ms)}
= 15.647 mm/ms
Conversion factor : 5/18
10.GRAVITY : 9.8m/s2 = 9.8 * 1000mm/(1000ms)^2
= 9.8* 10-3 mm/ms2
Conversion factor : 10-3
Convertion factors of given measurements
| unit systems | Mass | Length | Time | Force | Stress | Energy | Density | Young's modulus | Velocity | Gravity |
| kg m s | 1 kg | 1m | 1s | 1N = 1Kg*m/s2 | 1pa=1kg/(m*s^2) |
1J=1Nm =1kg*m^2/s^2 |
1kg/m^3 | 210GPA = 210*10^9 kg/m*s2 | 15.647 m/s | 9.8m/s2 |
| Kg cm ms | 1kg | 10^2cm | 10^3ms | 10^-4 kg*cm/ms^2 | 10^-8 kg/(cm*ms^2) | 10^-2 kg*cm^2/ms^2 | 10^-6kg/cm^3 | 2100kg/cm*ms2 | 1.5467cm/ms | 9.8*10^-4cm/ms2 |
| Kg cm s | 1kg | 10^2cm | 1s | 10^2 kg*cm/s2 | 10^-2 kg/(cm*s^2) | 10^4kg*cm^2/s^2 | 10^-6kg/cm^3 | 210*10^7kg/cm*s2 | 1564.7 cm/s | 9.8*10^2cm/s2 |
| g mm ms | 10^3g | 10^3mm | 10^3ms | 1g*mm/ms2 | 10^-6g/(mm*ms^2) | 10^3g*mm^2/ms^2 | 10^-6g/mm^3 | 210*10^3 g/mm*ms2 | 15.647 mm/ms | 9.8*10^-3mm/ms2 |
| g cm s | 10^3g | 10^2cm | 1s | 10^5g*cm/s2 | 10 g/(cm*s^2) | 10^7g*cm^2/s^2 | 10^-3g/cm^3 | 210*10^10g/cm*s2 | 1564.7 cm/s | 9.8*10^2cm/s2 |
| g cm us | 10^3g | 10^2cm | 10^6us | 10^-7g*cm/us2 | 10^-11g/(cm*us^2) | 10^-5g*cm^2/us^2 | 10^-3g/cm^3 | 2.10 g/cm*us2 | 15.647*10^-4 cm/us | 9.8*10^-10cm/us2 |
| g mm s | 10^3g | 10^3mm | 1s | 10^6g*mm/s2 | 1g/(mm*s^2) | 10^9g*mm^2/s^2 | 10^-6g/mm^3 | 210*10^11g/mm*s2 | 15647 mm/s | 9.8*10^3mm/s2 |
| ton mm s | 10^-3ton | 10^3mm | 1s | 1 ton*mm/s2 | 10^-6ton/(mm*s^2) | 10^3ton*mm^2/s^2 | 10^-12ton/mm^3 | 210*10^3ton/mm*s2 | 15647 mm/s | 9.8*10^3mm/s2 |
| slug ft s | 0.068slug | 3.28ft | 1s | 0.2246slug*ft/s2 | 0.0208slug/(ft*s^2) | 0.7366slug*ft^2/s^2 | 1.93*10^-3slug/ft^3 | 4.368*10^9slug/ft*s2 | 51.322 ft/s | 32.144 ft/s2 |
| kg mm s | 1 kg | 10^3mm | 1s | 10^3kg*mm/s2 | 10^-3 kg/(mm*s^2) | 10^6kg*mm^2/s^2 | 10^-9kg/mm^3 | 210*10^6kg/mm*s2 | 15647 mm/s | 9.8*10^3mm/s2 |
| g cm ms | 10^3g | 10^2cm | 10^3ms | 10^-1 g*cm/ms^2 | 10^-5g/(cm*ms^2) | 10g*cm^2/ms^2 | 10^-3g/cm^3 | 210*10^4g/cm*ms2 | 1.5467cm/ms | 9.8*10^-4cm/ms2 |
| kg mm ms | 1 kg | 10^3mm | 10^3ms | 10^-3 kg*mm/ms^2 | 10^-9kg/(mm*ms^2) | 1kg*mm^2/ms^2 | 10^-9kg/mm^3 | 210kg/mm*ms2 | 15.647mm/ms | 9.8*10^-3mm/ms2 |
conclusion :-
Different industries use different system of units as per their convenience.For example, automotive industries use kg,mm,ms as their standard unit system. Construction industries are likely to use tonne,m,s as their unit system. Similarly, PCB simulation in electronic industry uses gm, micrometer,ms as their system of units.
LS-DYNA doesn't have a default system of units. User needs to input material properties and physical dimensions according to a consistent system of units as per their choice. This warrants that to use LS-DYNA in different circumstances, users has to be conversant with converting quantities from one system of units to another.
In this challenge we converted all the given measurements in different system of units and calculated their corresponding conversion factors.