Challenge

Consistency of Units - Calculation of Data for LS DYNA

OBJECTIVE :

Value of the following measurements are given as follows:

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

Converted Measurements :

MASS 1kg = 1000g
LENGTH 1m = 1000mm
TIME 1s = 1000ms
FORCE 1N = 1kg*1m/s^2 = 1000*1000/(1000^2) = 1g(mm/ms^2)
STRESS 1Pa 1Pa=1N/m^2 = (1kg*1m/s^2)/m^2= (1000*1000/(1000^2))/1000^2 = 1*10^-6(mm*ms^2)
ENERGY 1Nm 1Nm=(1kg*1m/s^2)*m =(1000*1000/(1000^2))/1000 = 1*10^3(g*mm^2/ms)*mm
DENSITY 1Kg/m3 1Nm=(1kg*1m/s^2)*m^3 =(1000*1000/(1000^2))/1000^3 = 1*10^-6(g*mm^2/ms)*mm
YOUNG'S Modulus 210GPa = (1kg*1m/s^2)/m^2*10^9= ((1000*1000/(1000^2))/1000^2)*10^9 = 1*10^3g/(mm*ms^2)
Velocity 56.33KMPH = 56.33*1000*36*10^5mm*ms =15.64mm/ms
GRAVITY 9.8m/s2=9.80*1000/1000*1000= 9.8*10^-3 mm/(ms^2)

Now, here are a few system of units:


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

CONVERTED MEASUREMENTS:

Mass Length Time Force Stress Energy Density Youngs Modulus Velocity Gravity
Kg cm ms 1kg 10^2 cm 10^3 ms 10^-4 (kg*cm)/ms^2 1*10^-8 kg/(ms^2cm) 1(10^-2kg*cm^2)/(ms^2) 1*10^-6 kg/(cm^3) 210*10^1 (kg)/(cm*ms^2) 15.6472*10^-1 cm/ms 9.8*10^-4 cm/ms^2
Kg cm s 1kg 10^2 cm 1 s 10^2 (kg*mm)/s^2 1(10^2kg)/(s^2cm) 1(10^-2kg*cm^2)/(s^2) 1*10^-6 kg/(cm^3) 210*10^7 (kg)/(cm*s^2) 15.6472*10^2 cm/s 9.8*10^2 cm/s^2
gm mm ms 10^3 g 10^3 mm 10^3 ms 10^3 (gm*mm)/ms^2 1(10^-6gm)/(ms^2mm) 1(10^3gm*mm^2)/(ms^2) 1*10^-6 gm/(mm^3) 210*10^3 (gm)/(mm*ms^2) 15.6472 mm/ms 9.8*10^-3 mm/ms^2
kg m s 1kg 1 m 1s 1 (kg*m)/s^2 1(kg)/(s^2*m) 1(kg*m^2)/(s^2) 1(kg)/(m^3) 210*10^9 (kg)/(m*s^2) 15.64 m/s^2 9.8 m/s^2
g cm s 10^3 g 10^2 cm 1s 10^5 (g*cm)/s^2 1(10gm)/(s^2cm) 1(10^7gm*cm^2)/(s^2) 1(10^-3gm)/(cm^3) 210*10^10 gm/(cm*s^2) 15.6472*10^2 cm/s 9.8*10^2 cm/s^2
g cm us 10^3 g 10^2 cm 10^6 us 10^-7 (g*cm)/us^2 1*10^-11 gm/(us^2cm) 1(10^-5gm*cm^2)/(us^2) 1(10^-3gm)/(cm^3) 210*10^-2 gm/(cm*us^2) 15.6472*10^-4 cm/us 9.8*10^-10 cm/us^2
g mm s 10^3 g 10^3 mm 1s 10^6 (g*mm)/s 1 (gm)/(s^2mm) 1(10^9gm*mm^2)/(s^2) 1*10^-6 gm/(mm^3) 210*10^9 gm/(mm*s^2) 15.6472*10^3 mm/(s) 9.8*10^3 mm/s^2
ton mm s 0.001t 10^3 mm 1s 1 (t*mm)/s^2 1*10^-6 Ton/(s^2mm) 1(10^3Ton*mm^2)/(s^2) 1*10^-12 Ton/(mm^3) 210*10^3 Ton/(mm*s^2) 15.6472*10^3 mm/s 9.8*10^3 mm/s^2
slug ft s 0.0685 s 3.28ft 1s 0.2246 (slug*ft)/s^2 2.0606*10^-2 slug/(s^2*ft) 74.052*10^-2 slug*ft^2/(s^2) 0.1892*10^-2 slug/(ft^3) 432.726*10^7 Slug/(s^2*ft) 51.612 ft/s 32.373/s^2
kg mm s 10^3 g 10^3 mm 1s 10^3 (g*mm)/s^2 10^-3 kg/(s*mm) 1(10^6kg*mm^2)/(s) 1*10^-9 kg/(mm^3) 210*10^6 kg/(mm*s) 15.6472*10^3 mm/s 9.8*10^3 mm/s^2
g cm ms 10^3 g 10^2 cm 1000ms 10^-1 (g*cm)/ms^2 1*10^-5 gm/(ms^2cm) 1(10gm*cm^2)/(ms^2) 1*10^-3 gm/(cm^3) 210*10^4 gm/(cm*ms^2) 15.6472*10^-1 cm/ms 9.8*10^-4cm/ms^2
kg mm ms 1kg 10^3 mm 1000ms 10^-3 (kg*mm)/ms^2 1*10^-9 kg/(ms^2mm) 1(10^-9kg*mm^2)/(ms^2) 1*10^-9 kg/(mm^3) 210 kg/(mm*ms^2) 15.6472 mm/ms 9.88 10^-3 mm/ms^2
g mm ms 10^3 g 10^3 mm 1000ms 1g(mm/ms^2) 10^-6(mm*ms^2) 10^3(g*mm^2/ms)*mm 10^-6 (g*mm^2/ms)*mm 10^3 g/(mm*ms^2) 15.64mm/ms 9.8*10^-3
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