Week - 1 - Consistency of Units
AIM: The primary aim of this challenge is to convert the given unit system to other unit system.
OBJECTIVE: Each and every measurement given in the input parameters are converted into respective system of units.
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.
PROCEDURE: In calculation part the conversion of values with respect to the units are very important inorder to get the accurate results. Mass(Kg), time(s) and Length(m) are the three important factors in unit system these systems are converted into the above mentioned system of units.
Conversion:
1 Kg = 1000 g =0.001 tonne = 0.0685218 slug
1 m = 100 cm =1000 mm = 3.28084 ft
1 s = 1000 ms = 1000000 us
Force unit conversion:
Force(N) = mass(m)*accelertion(a)
F = ma
`Force(N) = Kg.m/s^2`
it will become
`Force = g.(mm)/(ms)^2`
Stress unit conversion:
Stress = Force/area
`sigma = ( Kg.m/s^2)/(m^2)`
it will become
`sigma = (g/(mm.(ms^2)))`
Energy unit conversion:
Energy = length*force
`J = (m) (Kg m/s^2)`
it will become
`J= (g . mm^2)/(ms^2)`
Density unit conversion:
Density = Mass/Volume
`rho = (Kg)/m^3`
it will become
`rho = g/(mm^3)`
Youngs's modulus unit conversion :
In the problem the Young's modulus (E) is given as 210Gpa.
Young's Modulus(E) = stress/strain
`E = sigma/(epsilon)`
there is no unit for strain,
`E= (210*10^9)(N/m^2)`
it will become
`E =210000(g/(mm.ms^2))`
Unit Conversion for Velocity:
In the problem the velocity value is given as 56.33kmph and this value is converted into m/s and then to mm/ms.
velocity = displacement/time
For converting km/h to m/s, multiply by 5/18
velocity = 56.33*(5/18)
velocity = distance/time
`v=m/s`
it will become
`v=0.27778 (mm)/(ms)`
Unit conversion of Gravity:
Given `9.81 m/s^2`
it will become
`g = 0.00981 (mm)/(ms)^2`
Figure1
CONCLUSION:
Thus the given input measurements are converted into respective unit system.