Week - 1 - Consistency of Units
Aim : To obtain the conversion factor for different system of units .
Task :
The assignment should 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
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
SI unit conversion for gm-mm-ms :
Mass 1kg : 1000gm
Lenght 1m : 1000mm
Time 1s : 1000ms
Force 1N : 1kg*m/s^2
(1000gm*1000mm)/(1000ms)^2
( `10^3`gm * `10^3`mm`)/`10^6``ms^2`
( 1gm*1mm)/`ms^2`
Stress 1Pa : 1 {(kg*m)/`s^2`}/`m^2` = kg/`m*s^2`
1000mg/(1000mm*`(1000ms)^2`)
`10^3mg`/`{10^3mm*10^6ms^2}`
`10^-6`gm/mm*`ms^2`
Energy 1Nm :1 {(kg*m)/`s^2`}*m
1{(1000gm*1000mm)/`(1000ms)^2`}*1000mm
`10^3 gm*mm^2`/`ms^2`
Density 1Kg/`m^3`: 1000gm/`(1000mm)^3`
`10^3gm`/`10^9``mm^3`
`10^-6`gm/`mm^3`
Young's Modulus 210 Gpa
210Gpa =210*`10^9`N/`m^2`
=210*`10^9`{(kg*m)/`s^2`}/`m^2` = 210*`10^9`kg/`m*s^2`
=210*`10^9`(1000mg)/(1000mm*`(1000ms)^2`)
=210*`10^9`*`10^3`/`(10^3mm*10^6ms^2)`
=210*`10^3`gm/mm*`ms^2`
Velocity 56.33KMPH
56.33KMPH = 56.33*`10^6mm`/(3600*1000ms)
= 56.33*`10^6`/(36*`10^5`ms)
= 56.33* 10/36 mm/ms
= 15.64 mm/ms
Gravity 9.8 m/`s^2` =9.8*1000mm/`(1000ms)^2`
=9.8*`10^3`mm/`10^6ms^2`
=9.8*`10^-3`mm/`ms^2`
Unit System Table
|
|
Mass |
Length |
Time |
Force |
Stress |
Energy |
Density |
Young's Modulus |
Velocity |
Gravity |
|
Kg cm ms |
1Kg |
100cm |
1000ms |
`10^-4 kg*cm`/`ms^2` |
`10^-8 kg`/`cm*ms^2` |
`10^-2`kg*`cm^2` /`ms^2` |
`10^-6 kg`/`cm^3` |
210 kg/cm*`ms^2` |
156.4*`10^-2` cm/ms |
9.8*`10^-4` cm/`ms^2` |
|
Kg cm s |
1Kg |
100cm |
1s |
`10^2` kg*cm/`s^2` |
`10^-2`kg/`c,*s^2` |
`10^4`kg*`cm^2`/`s^2` |
`10^-6`kg/`cm^3` |
210*`10^7` kg/cm*`s^2` |
15647 cm/s |
9.80*`10^2` cm/`s^2` |
|
gm mm ms |
1000gm |
1000mm |
1000ms |
1 gm*mm/`ms^2` |
`10^-6`gm/`mm*ms^2` |
`10^3`gm*`mm^2`/`ms^2` |
`10^-6`gm/`mm^3` |
210*`10^3` gm/mm*`ms^2` |
15.64 mm/ms |
9.8*`10^-3` mm/`ms^2` |
|
kg m s |
1kg |
1m |
1s |
1 kg*m/`s^2` |
1 kg/`m*s^2` |
1 kg*`m^2`/`s^2` |
1kg/`mm^3` |
210*`10^9` kg/m*`s^2` |
15.64 m/s |
9.8 m/`s^2` |
|
g cm s |
1000gm |
100cm |
1s |
`10^5`g*cm/`s^2` |
10g/`cm*s^2` |
10^7 gm*`cm^2`/`s^2` |
`10^-3`gm/`cm^3` |
210*`10^10` g/cm*`s^2` |
1564 cm/s |
9.80*`10^2` cm/`s^2` |
|
g cm us |
1000gm |
100cm |
`10^-6`us |
`10^-7`g*cm/`us^2` |
`10^-11`gm/`cm*us^2` |
10-5 gm*`cm^2`/`us^2` |
10gm/`cm^3` |
210*`10^-2` gm/cm*`us^2` |
1564*`10^-6` cm/us |
9.8*`10^-10` cm/`us^2` |
|
g mm s |
1000gm |
1000mm |
1s |
`10^6`g*mm/`s^2` |
1g/`mm*s^2` |
10^9 gm*`mm^2`/`s^2` |
`10^-6`gm/`mm^3` |
210*`10^-9` g/mm*`s^2` |
15647 mm/s |
9.8*`10^3` mm/`s^2` |
|
ton mm s |
0.001ton |
1000mm |
1s |
1ton*mm/`s^2` |
`10^-6`ton/`mm*s^2` |
`10^3`ton*`mm^2`/`s^2` |
`10^-12`ton/`mm^3` |
210*`10^3` ton/mm*`s^2` |
15647 mm/s |
9.8*`10^3` mm/`s^2` |
|
slug ft s |
0.068 slug |
3.28ft |
1s |
0.223 slug*ft/`s^2` |
0.02slug/`ft*s^2` |
0.731 slug*`ft^2`/`s^2` |
1.92*`10^-3` slug/`ft^3` |
4.20*`10^9` slug/ft*`s^2` |
51.33 ft/s |
32.14 ft/`s^2` |
|
kg mm s |
1 kg |
1000mm |
1s |
1000 kg*mm/`s^2` |
`10^-3`kg/`mm*s^2` |
`10^6`kg*`mm^2`/`s^2` |
`10^-9`kg/`mm^3` |
210*`10^6` kg/mm*`s^2` |
15647 mm/s |
9.8*`10^3` mm/`s^2` |
|
g cm ms |
1000gm |
100cm |
1000ms |
0.1 g*cm/`ms^2` |
`10^-5`g/`cm*ms^2` |
10g*`cm^2`/`ms^2` |
`10^-6`gm/`cm^2` |
210*`10^4` g/cm*`ms^2` |
1564*`10^-3` cm/s |
9.8*`10^-4` cm/`ms^2` |
|
kg mm ms |
1kg |
1000mm |
1000ms |
`10^-3` kg*mm/`ms^2` |
`10^-9`kg/`mm*ms^2` |
1kg*`mm^2`/`ms^2` |
`10^-9`kg/`mm^3` |
210 kg/mm*`ms^2` |
15647*`10^-3` mm/ms |
9.8*`10^-3` mm/`ms^2` |