Week - 1 - Consistency of Units
Aim:- To convert the given system of measurment in the respective 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
Detailed calculation for conversion from SI unit to gm/mm/ms unit system:
Mass: 1Kg=1000gm, Conversation Factor = 1*1000 = 10^3;
Length: 1m=1000mm, Conversation Factor = 1*1000 = 10^3;
Time: 1s=1000ms, Conversation Factor = 1*1000 = 10^3;
Force: 1N = 1(kg*m)/S2
= 1(1000gm*1000mm)/ (1000ms)2
= 1(gm*mm)/ms2, Conversation Factor = 1
Stress: 1Pa = 1 N/m2 = ((1Kg*m)/S2))/ m2
= ((1000gm*1000mm)/1000000 ms2)/1000000mm2
= ((1gm*mm)/ms2)/106 mm2
= 10-6 gm/mm*ms2, Conversation Factor = 10-6
Energy: 1Nm = (1 Kg*m/S2)*m
= ((1000gm*1000mm)/1000000 ms2) * 1000mm
= 103 (gm*mm2) / ms2, Conversation Factor = 10^3
Density: 1Kg/m3 = 1000gm / 109 mm3
= 10-6 gm/mm3, Conversation Factor = 10-6
Young’s Modulus: 210GPa = 210 * 109 N/m2
= 210*109 ((Kg*m)/S2) / m2
= 210*109 ((1000gm*1000mm)/1000000 ms2)/1000000mm2
= 210*109 ((gm*mm)/ms2)/106 mm2
= 210*10^3 gm/mm*ms2, Conversation Factor = 10^3
Velocity: 56.33KMPH = (56.33 * 1000m) / H
= (56.33 * 106mm) / 3600 * 1000 ms
= (56.33 * 106mm) / 36 * 105 ms
= 15.6472 mm/ms, Conversation Factor = 5/18
Gravity: 9.8 m/S2 = 9.8 (1000mm)/ (1000000ms)
= 9.8 (10^3mm) / 10^6ms2
= 9.8 * 10-3 mm/ms2, Conversation Factor = 10-3
Systems of Units:
|
Units |
Mass |
Length |
Time |
Force |
Stress |
Energy |
|
Kg cm ms |
1kg |
102cm |
103ms |
10-4kg*cm/ms2 |
10-8kg/cm*ms2 |
10-2kg*cm2/ms2 |
|
Kg cm s |
1kg |
102cm |
1s |
102kg*cm/s2 |
10-2kg/cm*s2 |
104kg*cm2/s2 |
|
gm mm ms |
103gm |
103mm |
103ms |
1gm*mm/ms2 |
10-6gm/mm*ms2 |
103gm*mm2/ms2 |
|
Kg m s |
1kg |
1m |
1s |
1 kg*m/S2 |
1 kg/m*s2 |
1 kg*m2/s2 |
|
gm cm s |
103gm |
102cm |
1s |
105gm*cm/S2 |
10 gm/cm*ms2 |
107gm*cm2/s2 |
|
gm cm µs |
103gm |
102cm |
106µs |
10-7gm*cm/µs2 |
10-11gm/cm*µs2 |
10-5gm*cm2/µs2 |
|
gm mm s |
103gm |
103mm |
1s |
106gm*mm/s2 |
1 gm/mm*s2 |
109gm*mm2/s2 |
|
Ton mm s |
10-3gm |
103mm |
1s |
1 ton*mm/s2 |
10-6 ton/mm*s2 |
103 ton*mm2/s2 |
|
Slug ft s |
0.068slug |
3.28 ft |
1s |
0.224 slug*ft/s2 |
0.0208slug/ft*s2 |
0.7366slug*ft2/s2 |
|
Kg mm s |
1kg |
103mm |
1s |
103kg*mm/s2 |
10-3kg/mm*s2 |
106 kg*mm2/s2 |
|
gm cm ms |
103gm |
102cm |
103ms |
10-1gm*cm/ms2 |
10-5gm/cm*ms2 |
10 gm*cm2/ms2 |
|
Kg mm ms |
1kg |
103mm |
103ms |
10-3kg*mm/ms2 |
10-9kg/mm*ms2 |
1 kg*mm2/ms2 |
|
Units |
Density |
Young’s Modulus |
Velocity |
Gravity |
|
Kg cm ms |
10-6kg/cm3 |
2100kg/cm*ms2 |
1.56472 cm/ms |
9.8*10-4 cm/ms2 |
|
Kg cm s |
10-6kg/cm3 |
210*107kg/cm*s2 |
1564.72 cm/s |
9.8*102 cm/s2 |
|
gm mm ms |
10-6gm/mm3 |
210*103gm/mm*ms2 |
15.6472 mm/ms |
9.8*10-3 mm/ms2 |
|
Kg m s |
1 kg/m3 |
210*109 N/m2 |
15.6472 m/s |
9.8 m/s2 |
|
gm cm s |
10-3gm/cm3 |
210*1010gm/cm*s2 |
1564.72 cm/s |
9.8*102 cm/s2 |
|
gm cm µs |
10-3gm/cm3 |
2.1gm/cm*µs2 |
15.64*10-4 cm/µs |
9.8*10-10 cm/µs2 |
|
gm mm s |
10-6gm/mm3 |
210*1011gm/mm*s2 |
156472 mm/s |
9.8*10^3 mm/s2 |
|
Ton mm s |
10-12 ton/mm3 |
210*103 ton/mm*s2 |
156472 mm/s |
9.8*10^3 mm/s2 |
|
Slug ft s |
1.93*10-3slug/ft3 |
4.368 slug/ft*s2 |
51.322 ft/s |
32.144 ft/s2 |
|
Kg mm s |
10-9 kg/mm3 |
210*106kg/mm*s2 |
156472 mm/s |
9.8*10^3 mm/s2 |
|
gm cm ms |
10-3gm/cm3 |
210*104gm/cm*ms2 |
1.56472 cm/ms |
9.8*10-4 cm/ms2 |
|
Kg mm ms |
10-9kg/mm3 |
210 kg/mm*ms2 |
15.6472 mm/ms |
9.8*10-3 mm/s2 |
RESULT:- The given system of unit conversion is done with respective system of units.