Week - 1 - Consistency of Units
AIM: To convert the a given unit system to different unit system
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
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
PROCEDURE
MASS= 1 kg
1kg = 0.0001=1000gm= 10^3gm= 0.0685218 slug
LENGTH= 1m
1m= 100cm=1000mm=3.28 ft
TIME= 1 s
1s=1000ms=1e+6 us
Now we will use conversion of g mm ms
FORCE= 1 N
Force (1N) = mass (m) x acceleration (a) = kg . `m/s^2`
Force = 103 g . `(10^3 mm)/(10^6ms^2)`
Force (1N) = g .`(mm)/(ms^2)`
STRESS= 1Pa
Stress (1Pa) = `N/(m^2)`
Stress = `(g*(mm)/(ms^2))/(10^6 mm^2)`
Stress (1Pa) = `(10^-6 *g)/(mm*ms^2)`
ENERGY 1Nm
Energy(1Nm)= Force(N) . Distance(m)
Energy= `(g*(mm)/(ms^2))*(10^3 mm)`
Energy= `10^3*(g* mm^2)/(ms^2)`
DENSITY= 1Kg/m3
Density (1kg/m3) = `(Mass)/(Volume)`
Density= `(10^3 g)/(10^9 mm^3)`
Density =`(10^-6 *g)/(mm^3)`
YOUNG'S Modulus = 210GPa
`bb "E"` =`210*10^9`.Pa=`210*10^9``(STRESS)/(STRAIN)`=`210*10^9`.`sigma/epsilon`
Strain has no unit. So...
`bb "E"=210*10^9.(10^-6*g/(mm*ms^2))`
`bb "E"=210*10^3*g/(mm*ms^2)`
Velocity 56.33KMPH
Velocit(v) = `(distance)/(time)`=`(km)/h`
v= 53.33 `(km)/h`=`(53.33)*10^6*(mm)/(3.6*10^6 ms)`
v=15.64 `(mm)/(ms)`
``
GRAVITY 9.8m/s2
Gravity(g)= `9.8 * m/(s^2)`
g=`9.8 * 10^3*(mm)/(10^6*ms^2)`
g=`9.8* 10^-3 *(mm)/(ms^2)`
| UNITS | MASS | LENGTH | TIME | FORCE | STRESS | ENERGY | DENSITY | YOUNGE MODULUS | VELOCITY | GRAVITY |
| Kg cm ms | 1kg | 100cm | 1000ms | .0001`(kg*cm)/(ms^2)` | `10^-8` | .01 | `10^-6` | 2100 | 1.564 | .00098 |
| kg cm s | kg | 100cm | 1 s | 100`(kg.cm)/(s^2)` | .01 | `10^4` | `10^-6` | `210*10^7` | 1564.7 | 980 |
| g mm ms | `10^3`g | `10^3`mm | 1000ms | 1`(g*mm)/(ms^2)` | `10^-6` | `10^3` | `10^-6` | `210*10^3` | 15.64 | 0.0098 |
| kg m s | 1 kg | 1 m | 1 s | 1`(kg*m)/(s^2)` | 1 | 1 | 1 | `210*10^9` | 15.64 | 9.8 |
| g cm s | `10^3`g | 100 cm | 1 s | `10^5``(g*cm)/(s^2)` | 10 | `10^7` | `10^-3` | `210*10^10` | 1564.72 | 980 |
| g cm us | `10^3`g | 100 cm | `10^-6`us | `10^-7``(g*cm)/(us^2)` | `10^-11` | `10^-5` | `10^-3` | 2.1 | `15.64*10^-4` | `9.8*10^-10` |
| g mm s | 100g | `10^3`mm | 1 s | `10^6``(g*mm)/(s^2)` | 1 | `10^9` | `10^-6` | `210*10^9` | 15647.2 | 9800 |
| tonn mm s | .001 tonn | `10^3`mm | 1 s | `10^-1``(tonn*mm)/(s^2)` | `10^-7` | 100 | `10^-13` | `210*10^3` | 15647.2 | 9800 |
| slug ft s | .068slug | 3.28 ft | 1 s | 0.223`(slug*ft)/(s^2)` | 0.0207 | .731 | `19*10^`-4 | `435*10^7` | 51.34 | 32.144 |
| kg mm s | 1kg | `10^3`mm | 1 s | `10^3``(kg*mm)/(s^2)` | `10^-3` | `10^6` | `10^-9` | `210*10^6` | 15647.2 | 9800 |
| g cm ms | `10^3g | 100 cm | `10^3`ms | `10^-1``(g*cm)/(ms^2)` | `10^-5` | 10 | `10^*3` | `210*10^4` | 1.5647 | `9.8*10^-4` |
| kg mm ms | 1kg | `10^3`mm | `10^3`ms | `10^-3``(kg*mm)/(ms^2)` | `10^-9` | 1 | `10^-9` | 210 | 15.67 | 0.0098 |
CONLUSION
The given data is converted into required unit system.