Week - 1 - Consistency of Units
Write the given measurements in the below different system of units. Also, mention the conversion factors.
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
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
calculation for conversion of units
Mass(Killo gram)=1kg of mass=1000grams of mass =10^3gm
Length(meter)=1 meter of length=1000mm
Time(second)=1s=1000ms
the conversion factor of mass length and time =10^3
Force (Newton)
1Newton=1kg*1m/1s^2
from the above conversion factor of mass ,length and time we can convert the force units
therefore 1Newton=(1*10^3g)*(1*10^3mm)/(1*10^6ms^2)
1 Newton =[(1g*mm)/ms^2]
conversion factor=1
STRESS
STRESS 1Pascal=1N/m^2=[(1g*mm)/ms^2]/10^6mm^2
=10^-6[g/1(mm*ms)]
conversion factor=10^-6
ENERGY (1joule=1Nm)
ENERGY 1Nm=[(1g*mm)/ms^2]*m
=[1gmm^2/ms^2]*10^3mm
=g*mm^2/ms^2
conversion factor=10^3
DENSITY 1Kg/m3
= 10^3g/(10^3mm)^3
= g/mm^3*10^-6
conversion factor=10^-6
YOUNG'S Modulus 210GPa
=210*10^9*1N/m^2
=210*10^9*10^-6[g/1(mm*ms)]
=210*10^3(g/mm*ms)
conversion factor=10^3
Velocity 56.33Kmph
=(56.33)10^6mm/3600*10^3millisec
=(56.33)10^3mm/3600ms
=56.33*(5/18)mm/ms
=15.64mm/ms
conversion factor =5/18
GRAVITY 9.8m/s2
=9.8m/s^2
=9.8*10^3mm/10^6ms^2
=9.8*10^-3mm/ms^2
conversion factor=10^-3
| unit system | Mass(kg) | Length (m) | Time(s) | force(N)(kgm/s2) | Stress(N/m2) | Energy(Nm) |
| 1Kg cm ms | kg | 10^2cm | 10^3ms |
1N=Kg*10^2cm/10^6ms =[kg*cm/ms^2]*10^-4 |
1pa=1N/m^2 =[kg*cm/ms^2*10^4cm^2]*10^-4 =[kg/cm*ms^2]*10^8 |
1Nm=[kg*cm/ms^2]*10^-4*10^2cm [kg*cm^2/ms^2]*10^-2 |
| 1Kg cm s | kg | 10^2cm | 1s | 1N=[Kg*cm/s^2]*10^2 |
=[Kg*cm/s]*10^2/10^4*cm^2 =kg/cm*s^2*10^-2 |
[Kg*cm/s]*10^2*10^2cm [kg*cm^2/s]10^3 |
|
1gm mm ms |
10^3 | 10^3mm | 10^3ms | [1gm*mm/ms^2]*10^5 | [gm/mm*ms2]*10 | [g*mm^2/ms^2]10^7 |
| 1kg m s | 1kg | 1m | 1s | kg*m/s*1 | kg/m*s | kg*m^2/s |
| 1g cm s | 10^3g | 10^2cm | 1s | [g*cm/s^2]*10^5 | [ g/cm*s^2]*10 | [g*cm^2/s^2]*10^7 |
|
1g cm us |
10^3g | 10^2cm | 10^6us | [g*cm/us^2]*10^-7 | [g/us^2*cm]*10^-11 | [g*cm^2/us^2]*10-5 |
| 1g mm s | 10^3g | 10^3mm | 1s | [g.mm/s^2]*10^6 | [g/mm.s^2] | 10^9[g.mm^2/s^2] |
| 1ton mm s | 10^-3 | 10^3mm | 1s | 1ton.mm/s^2 | [ ton/mm.s^2]*10^-4 | [ton.mm^2/s^2]10^3 |
| 1slug ft s | 0.68slug | 3.28ft | 1s | 2.23[slug.ft/s^2] | 0.207[slug/ft.s^2] | 7.5[slug.ft^2/s^2] |
The conversion of given units has been done succesfully