Week - 1 - Consistency of units
Aim : to show the detailed calculation for conversion of SI units to different unit systems according to the given 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 systems 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
To write the given measurements in the above different system of units. Also, mention the conversion factors and show detailed calculation for conversion from SI unit to gm/mm/ms unit system. For others only the answers in the form of a table is sufficient with the unit systems as rows and measured quantities as columns.
Procedure :
The fundamental quantities of unit system are mass, length and time and expressed as Kg, m and s respectively
|
Measurements |
Normal units |
Converted units |
|
Mass |
1Kg |
103 gm |
|
Length |
1m |
103 mm |
|
time |
1s |
103 ms |
Where,
Kg = kilograms
m = Meter
s = seconds
gm = grams
mm = millimetre
ms = millisecond
example:
some of the measurements given are converting to gm/mm/ms
mass = 1kg = 1*103 gm
length = 1m = 1*103 mm
Time = 1s = 1*103 ms
Force = mass*acceleration = 1N = kg*(m/s2) = 103 * (103 /( 103)2) = 1 gm *(mm/ms2)
Stress = force/ area = (mass*acceleration)/area = (kg*(m/s2 )/ m2) = kg/(m*s2 ) = 103/(103 * (103)2) = 1* 10-6 gm/(mm*ms2)
Energy = force*distance = (mass*acceleration) *length = (kg*(m/s2) *m) = kg*(m2/s2) = 103* ((103)2/(103)2) = 1*103 gm*(mm2*ms2)
Density = mass/volume = kg/m3 = 103 / (103 )3 = 1* 10-6 gm/mm3
Youngs modulus = stress/strain = 210*109 N/m2 = 210*109(kg*(m/s2))/m2 = 210*109 kg/(m*s2) = 210*109 *103/(103*(103)2 = 210*103 gm/(mm*ms2)
Velocity = 56.33 kmph = 56.33 * 103/(60*60*103) = 15.64 mm/ms
Gravity = 9.8 m/s2 = 9.8*103/(103)2 = 9.8*10-3 mm/ms2
|
measurements |
Mass 1kg |
Length 1m |
Time 1s |
Force =1N =Kg*(m/s2) |
Stress =pa =kg/(m*s2) |
Energy =Nm =kg*(m/s2) |
Density =kg/m3 |
Young’s modulus =210 GPA = 210*109 kg/(m*s2) |
Velocity 56.33 KMPH |
Gravity =m/s2 |
|
kg cm ms |
1 |
102 |
103 |
10-4 |
10-8 |
10-2 |
10-6 |
210*101 |
1.564 |
9.8*10-4 |
|
kg cm s |
1 |
102 |
1 |
102 |
10-2 |
104 |
10-6 |
210*107 |
15.64*102 |
9.8*102 |
|
gm mm ms |
103 |
103 |
103 |
1 |
10-6 |
103 |
10-6 |
210*103 |
15.64 |
9.8*10-3 |
|
kg m s |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
210*109 |
15.64 |
9.8 |
|
gm cm s |
103 |
102 |
1 |
105 |
101 |
107 |
10-3 |
210*1010 |
15.64*102 |
9.8*102 |
|
gm cm µs |
103 |
102 |
106 |
10-7 |
10-11 |
10-5 |
10-3 |
210*10-2 |
0.0015 |
9.8*10-10 |
|
gm mm s |
103 |
103 |
1 |
106 |
101 |
109 |
10-6 |
210*109 |
15.64*103 |
9.8*103 |
|
ton mm s |
10-3 |
103 |
1 |
1 |
10-6 |
103 |
10-6 |
210*109 |
15.64*102 |
9.8*103 |
|
slug ft s |
0.068 |
3.28 |
1 |
0.223 |
0.0208 |
0.7366 |
0.00192 |
4.347*109 |
50.512 |
32.14 |
|
kg mm s |
1 |
103 |
1 |
103 |
10-3 |
106 |
10-9 |
210*106 |
15.64*102 |
9.8*103 |
|
gm cm ms |
103 |
102 |
103 |
10-1 |
10-5 |
10-1 |
10-3 |
210*104 |
1.56 |
9.8*10-4 |
|
kg mm ms |
1 |
103 |
103 |
10-3 |
10-9 |
1 |
10-9 |
210 |
15.64 |
9.8*10-3 |