Week - 1 - Consistency of units
OBJECTIVE:
To obtain given measurements in different unit systems listed as below
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
|
Quantity |
Value (given unit) |
|
|
|
|
Mass |
1 kg |
|
Length |
1m |
|
Time |
1 s |
|
Force |
1 N |
|
Stress |
1 Pa |
|
Energy |
1 Nm |
|
Density |
1 kg/m3 |
|
Youngs Modulus |
210 GPa |
|
Velocity |
56.33 kmph |
|
Gravity |
9.8 m/s2 |
PROCEDURE:
Step 1 – convert the given measurements in standard SI Units.
|
Quantity |
Value (given unit) |
SI Unit |
Conversion factor |
Value (SI Unit) |
|
|
|
|||
|
Mass |
1 kg |
Kg |
1 |
1 |
|
Length |
1m |
M |
1 |
1 |
|
Time |
1 s |
S |
1 |
1 |
|
Force |
1 N |
Kg m/s2 |
1 |
1 |
|
Stress |
1 Pa |
Kg/m s2 |
1 |
1 |
|
Energy |
1 Nm |
Kg m2/s2 |
1 |
1 |
|
Density |
1 kg/m3 |
Kg/m3 |
1 |
1 |
|
Youngs Modulus |
210 GPa |
Kg/m s2 |
10 ^ 9 |
210 * 10^9 |
|
Velocity |
56.33 kmph |
m/s |
5/18 |
15.64 |
|
Gravity |
9.8 m/s2 |
m/s2 |
1 |
9.8 |
Step 2 - Basic Unit Conversion:
Mass
1 kg = 1000 g
1 kg = 0.001 ton
1 kg = 0.0685 slug
Time
1s = 1000 ms
1 s = 10^6 micro second
Length
1 m = 100 cm
1 m = 1000 mm
1 m = 3.28 ft
Step – 3 – Detailed Measurement Conversion SI units to gm/mm/ms
- Mass (kg)
1 kg = 1000 g
CF: 1000
- Length (m)
1 m = 1000 mm
CF: 1000
- Time (s)
1 s = 1000 ms
CF: 1000
- Force (N of kg m/s2)
1 N = 1 kg m/s2
so, 1 N = 1000 * 1000 / (1000)^2 = 1 g mm/ms2
CF: 1
- Stress (Pa or N/m2 or kg/m s2)
1 Pa = 1 kg/m s2
So, 1 Pa = 1000 / 1000 * (1000)^2 = 10^-6 g/mm ms2
CF: 10^-6
- Energy (Nm or kg m2/s2)
1 Nm = 1 kg m2/s2
So, 1 Nm = 1000 * (1000)^2 / (1000)^2 = 1000 g mm2/ms2
CF: 1000
- Density (kg/m3)
1 kg/m3 = 1000 / (1000)^3 = 10^-6 g/mm3
CF: 10^-6 - Young’s Modulus (GPa or N/m2 or kg/m s2)
1 GPa = 10^9 N/m2 = 10^9 kg/m s2
So 210 GPa = 210 * 10^9 * 1000 / 1000 * (1000)^2 = 210000 g/mm ms2
CF: 1000 - Velocity (kmph or m/s)
1 kmph = 0.2778 m/s
33 kmph = 56.33 * 0.2778 * 1000 / 1000 = 15.64 mm/ms
CF: 0.2778 - Gravity (m/s2)
9.8m/s2 = 9.8 * 1000/ (1000)^2 = 0.0098 mm/ms2
CF: 0.001
Step – 4 – Measurement Conversion to different unit systems
|
Unit System |
Mass |
Length |
Time |
Force |
Stress |
Energy |
Density |
Young’s Modulus |
Velocity |
Gravity |
|
|
||||||||||
|
Given |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
210 |
56.33 |
9.8 |
|
SI (mks) |
1 |
1 |
1 |
1 |
1 Kg/m s2 |
1 |
1 |
210*10^9 |
15.64 |
9.8 |
|
Kg-cm-ms |
1 |
100 |
1000 |
0.0001 |
10^-8 |
10^-2 |
10^-6 |
2100 |
1.564 |
0.00098 |
|
Kg-cm-s |
1 |
100 |
1 |
100 |
0.01 |
10^4 |
10^-6 |
210*10^7 |
1564 |
980 |
|
Gm-mm-ms |
1000 |
1000 |
1000 |
1 |
10^-6 |
1000 |
10^-6 |
210000 |
15.64 |
0.0098 |
|
Kg-m-s |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
210*10^9 |
15.64 |
9.8 |
|
g-cm-s |
1000 |
100 |
1 |
10^5 |
10 |
10^7 |
0.001 g/cm3 |
210*10^10 |
1564 |
980 |
|
g-cm-us |
1000 |
100 |
10^6 |
10^-7 |
10^-11 |
10^-5 |
0.001 |
2.1 |
15.64*10^-4 |
9.8*10^-10 Cm/us2 |
|
g-mm-s |
1000 |
1000 |
1 |
10^6 |
1 |
1000 |
10^-6 |
210*10^9 |
15640 |
9800 |
|
Ton-mm-s |
0.001 |
1000 |
1 |
1 |
10^-6 |
1000 |
10^-12 |
210000 |
15640 |
9800 |
|
Slug-ft-s |
0.0685 |
3.28 |
1 |
0.224 |
0.020 |
0.73 |
1.94*10^-3 |
4.38*10^9 |
51.3 |
32.144 |
|
Kg-mm-s |
1 |
1000 |
1 |
1000 |
0.001 |
10^6 |
10^-9 |
210*10^6 |
15640 |
9800 |
|
g-cm-ms |
1000 |
100 |
1000 |
0.1 |
10^-5 |
10 |
0.001 |
210*10^4 |
1.564 |
0.00098 |
|
Kg-mm-ms |
1 |
100 |
1000 |
0.001 |
10^-9 |
1 |
10^-9 |
210 |
15.64 |
0.0098 |
CONCLUSION:
The above activity shows few different unit systems that can be used in engineering activities. It helps us understand the conversion of few important quantities in different unit system.