Week - 1 - Consistency of Units
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
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
Write the given measurements in the above different system of units. Also, mention the conversion factors.
1.CONVERSION OF SI UNITS INTO gm,mm,ms:
mass=kg =1000g
conversion factor is 10^3
length=m=1000mm
conversion factor is 10^3
time=sec=1000ms
conversion factor is 10^3
force 1N= gxmm/ms^2
conversion factor is 1
FORCE 1N= Massxacceleration
= Kg x (m/s^2)
=10^3 g x (10^3mm/10^6 ms^2)
=gxmm/ms^2
Stress 1Pa = force/area
= 1N/m^2
= (g/ms^2)/10^6 mm
= 10^-6 (g /(mm x ms^2)
conversion factor is 10^-6
Energy 1Nm= (gxmm/ms^2) x 10^3 mm
= 10^3 g x(mm/ms)^2
conversion factor is 10^3
Density Kg/m^3 = 10^3g /10^9 mm^3
= 10^-6 g/mm^3
conversion factor is 10^-6
youngs Modulus 210 Gpa= 210 x 10^9 x 10^-6 (g /(mm x ms^2)
= 210 x 10^3 (g /(mm x ms^2)
conversion factor is 10^3
velocity 56.33 kmph = 56.33 x (10^6 mm/3.6 x 10^6 ms)
= 56.33/3.6(mm / ms)
= 15.64 (mm / ms)
conversion factor is 15.64
gravity = 9.8 m/s^2
= 9.8 x 10^3mm / 10^6 ms^2
=9.8 x 10^-3 (mm/ms^2)
conversion factor is 10^-3
Table:
| input | Mass | Length | Time | Force | Stress | Energy | Density | youngs modulus | velocity | Gravity |
| Kg cm ms | 1 | 100 | 1000 | 0.0001 | 0.00000001 | 0.01 | 0.000001 | 2100 | 0.277778 |
0.00098 |
| Kg cm s | 1 | 100 | 1 | 100 | 0.01 | 10000 | 0.000001 | 2100000000 | 27.7778 | 980 |
| gm mm ms | 1000 | 1000 | 1000 | 1 | 0.000001 | 1000 | 0.000001 | 210000 | 0.277778 | 0.0098 |
| kg m s | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 2.10E+11 | 0.277778 | 9.8 |
| g cm s | 1000 | 100 | 1 | 100000 | 10 | 10000000 | 0.001 | 2.10E+12 | 27.7778 | 980 |
| g cm us | 1000 | 100 | 1000000 | 0.0000001 | 1.00E-11 | 0.00001 | 0.001 | 2.1 | 0.0000277778 | 9.80E-10 |
| g mm s | 1000 | 1000 | 1 | 1000000 | 1 | 1000000000 | 0.000001 | 2100000000 | 277.778 | 9800 |
| ton mm s | 0.001 | 1000 | 1 | 1 | 0.000001 | 1000 | 1.00E-12 | 210000 | 277.778 | 9800 |
| slug ft s | 0.068 | 3.28 | 1 | 0.2230 | 0.0207 | 0.7315712 | 0.001927025145 | 4353658537 | 0.91111184 | 32.144 |
| kg mm s | 1 | 1000 | 1 | 1000 | 0.001 | 1000000 | 0.000000001 | 210000000 | 277.778 | 9800 |
| g cm ms | 1000 | 100 | 1000 | 0.1 | 0.00001 | 10 | 0.001 | 2100000 | 0.0277778 | 0.00098 |
| kg mm ms | 1 | 1000 | 1000 | 0.001 | 0.000000001 | 1 | 0.000000001 | 210 | 0.277778 | 0.0098 |
CONCLUSION:
The calculation for conversion from SI unit to gm/mm/ms unit system. For others the answers in the form of a table with the unit systems as rows and measured quantities as columns.