Week - 1 - Consistency of Units
Aim: To understand and create a Consistent Unit system to follow the measurement system.
Objective: The Uniform measurement system is used to maintain consistent unit system so that the output will be having right results.
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
Procedure:
The detail for SI unit to gm/mm/ms is
Mass: 1 kg = 1000gm
Length: 1m = 1000mm
Time: 1ms = 1000s
Force=1N = Mass*acceleration= `1kg*m/s^2`=`1000g*(1000mm)/(10^6ms^2)` =`(1gmm)/(ms^2)`
Stress=1 Pa=`N/m^2` =`(1gmm)/(ms^2)/(10^6mm^2)`=`10^-6*g/(mm*ms^2)`
Energy=1 Nm = `(1gmm)/(ms^2)`*1000mm=`10^3 g* (mm^2)/(ms^2 )`
Density= 1`(kg)/m^3`=`1000*(gm)/(10^9 mm^3 )`=`10^(-6) (gm)/(mm^3)`
Young’s modulus= 210 GPa = 210*109 Pa =210* 109 *`10^(-6) g/(mm*ms^2 )`= 210*`10^3g/(mm*ms^2 )`
Velocity= 56.33 Km/h=`(56.33*10^6 mm)/(3.6*10^6 ms) =15.6472`(mm)/(ms)`
Gravity= 9.8`m/s^2`=`9.8 *1000(mm)/(10^6 ms^2 )`=`9.8*10^(-3) (mm)/(ms)^2`
For Kg cm ms is
Mass: 1Kg
Length 1m= 100cm
Time 1s= 1000 ms
Force= 1N= Mass*acceleration=`1kg*m/s^2`= 1kg*`100(cm)/(10^6 ms^2 )`=`10^(-4) (Kg cm)/(ms)^2`
Stress=1 Pa= `N/m^2`=`(10^(-4) (Kg cm)/(ms)^2 )/(10^4 cm^2 )`=`(Kg)/(cm*ms^2 )`
Energy=1 Nm = `10^(-4) (kg cm)/(ms^2 )`*100cm=`10^(-2) (Kg cm^2)/(ms^2 )`
Density= 1`(kg)/m^3`=`(kg)/(10^6 cm^3 )`=`10^(-6) (kg)/(cm^3)`
Young’s modulus= 210 GPa = 210*109 Pa= 210*109 *`(Kg)/(cm*ms^2 )`
Velocity= 56.33 Km/h= `(56.33*10^5 cm)/(3.6*10^6 ms)`=1.56472`(cm)/(ms)`
Gravity= 9.8`m/s^2`=`9.8 *100(cm)/(10^6 ms^2 )`=`9.8*10^(-4) (cm)/(ms^2)`
|
|
Kg cm s |
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 |
|
Mass=1Kg |
1 |
1 |
1000 |
1000 |
1000 |
0.001 |
0.0685 |
1 |
1000 |
1 |
|
Length=1m |
100 |
1 |
100 |
100 |
1000 |
1000 |
3.28084 |
1000 |
100 |
1000 |
|
Time=1S |
1 |
1 |
1 |
106 |
1 |
1 |
1 |
1 |
1000 |
1000 |
|
Force= |
100 |
1 |
105 |
10-7 |
106 |
1 |
10-1 |
103 |
10-1 |
10-3 |
|
Stress= |
100 |
1 |
10 |
10-3 |
1 |
10-6 |
10-2 |
10-3 |
10-5 |
10-9 |
|
Energy= |
104 |
1 |
107 |
10-5 |
109 |
103 |
10-1 |
106 |
10 |
1 |
|
Density= |
10-6 |
1 |
10-3 |
10-3 |
10-6 |
10-12 |
10-3 |
10-9 |
10-3 |
10-9 |
|
Young’s modulus= |
1011 |
1 |
1010 |
10-6 |
1 |
103 |
109 |
106 |
104 |
1 |
|
Velocity= |
103 |
1 |
103 |
10-3 |
106 |
106 |
102 |
106 |
103 |
10 |
|
Gravity= |
102 |
1 |
102 |
10-10 |
103 |
103 |
102 |
103 |
10-3 |
10-3 |