Week - 1 - Consistency of Units
Aim : To convert given measurements into different system of units and finding their corresponding conversion factors.
Measurements given :
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
Conversions: (From SI unit to gm/mm/ms unit system)
MASS : 1kg = 1000gm Conversion factor : 103
LENGTH : 1m = 1000mm Conversion factor : 103
TIME : 1s = 1000ms Conversion factor : 103
FORCE : 1N = 1kg*1 m/s2
= (1000g*1000mm)/(1000ms)2
= 106*10-6 (g*mm)/ms2
= 1 (g*mm)/ms2
Conversion factor : 1
STRESS : 1Pa = 1N/m2 = {1kg*(1 m/s2)}/m2 = 1 kg/ (m* s2)
= 1000g/{1000mm*(1000ms)2}
= 10-6 g/ (mm*ms2)
Conversion factor : 10-6
ENERGY : 1J = 1Nm = (1kg*1 m/s2) * m = 1 (kg*m2/s2)
= {1000g * (1000mm)2}/(1000ms)2
= (109 g*mm2) / (106 ms2)
= 103 (g*mm2/ ms2)
Conversion factor : 103
DENSITY : 1Kg/m3 = 1000g/(1000mm)3
= 10-6 g/mm3
Conversion factor : 10-6
YOUNGS MODULUS : 210GPa = 210e+9 kg/(m*s2) = 210e+9 * 10-6 g/ (mm*m s2)
= 210e+3 g/ (mm*m s2) = 210*103 g/ (mm*m s2)
Conversion factor : 103
VELOCITY : 56.33 Kmph = 56.33 * {106mm/(3600*1000ms)}
= 15.647 mm/ms
Conversion factor : 5/18
GRAVITY : 9.8m/s2 = 9.8 * 1000mm/(1000ms)2
= 9.8* 10-3 mm/ms2
Conversion factor : 10-3
Table unit systems as rows and measured quantities as columns :
|
Unit system |
Mass |
Length |
Time |
Force |
Stress |
Energy |
|
SI Unit kg m s |
1kg |
1m |
1s |
1 N = 1 kg*m/s2 |
1 Pa = 1 kg/(m* s2) |
1 J = 1Nm = 1 kg*m2/s2 |
|
kg cm ms |
1kg |
102cm |
103ms |
10-4 kg*cm/ms2 |
10-8 kg/(cm*ms2) |
10-2 kg*cm2/ms2 |
|
kg cm s |
1kg |
102cm |
1s |
102 kg*cm/s2 |
10-2 kg/(cm*s2) |
104 kg*cm2/s2 |
|
g mm ms |
103g |
103mm |
103ms |
1 g*mm/ms2 |
10-6 g/(mm*ms2) |
103 g*mm2/ms2 |
|
g cm s |
103g |
102cm |
1s |
105 g*cm/s2 |
10 g/(cm*s2) |
107 g*cm2/s2 |
|
g cm μs |
103g |
102cm |
106μs |
10-7 g*cm/μs2 |
10-11 g/(cm*μs2) |
10-5 g*cm2/μs2 |
|
g mm s |
103g |
103mm |
1s |
106 g*mm/ s2 |
1 g/(mm*s2) |
109 g*mm2/s2 |
|
Ton mm s |
10-3ton |
103mm |
1s |
1 ton*mm/s2 |
10-6 ton/(mm*s2) |
103 ton*mm2/s2 |
|
slug ft s |
0.068slug |
3.28 ft |
1s |
0.2246 slug*ft/ s2 |
0.0208 slug/(ft*s2) |
0.7366 slug*ft2/s2 |
|
kg mm s |
1kg |
103mm |
1s |
103 kg*mm/s2 |
10-3 kg/(mm*s2) |
106 kg*mm2/s2 |
|
g cm ms |
103g |
102cm |
103ms |
10-1 g*cm/ms2 |
10-5 g/(cm*ms2) |
10 g*cm2/ms2 |
|
kg mm ms |
1kg |
103mm |
103ms |
10-3 kg*mm/ms2 |
10-9 kg/(mm*ms2) |
1 kg*mm2/ms2 |