Week - 1 - Consistency of Units
Consistency of Units
Aim: To write the given measurements in the different system of units. Also, mention the conversion factors.
Objective: To mention the conversion factors fot the following unit system Kg cm ms
Kg cm s
Kg cm ms
gm mm ms
kg m s
g cm s
g cm μs
g mm s
ton mm s
slug ft s
kg mm s
g cm ms
kg mm ms
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
1. Kg cm s:
a. Mass = 1kg
b. length = 1cm
c. Time = 1 s
d. Force = ma = kg*`m/s^2` = N
here length = 1cm = 10^-2 m
Force = kg* 0.01 `m /s^2` = `1 X 10^-2` N
e. Stress Pa (`N/m^2`)
= `1 X 10^-2` N /`(10^-4)` `m^2`
Stress = `10^2`Pa
f. Energy = J = Nm
= `1 X 10^-2` N* `10^-2 m`
= `10^-4` Nm
g. Density ` (Kg)/m^3`
= 1 Kg `(10^-6)`/`(10^-6)` `m^3`
= `(10^-6)` Kg / `cm^3`
h.YOUNG'S Modulus 210GPa
= 210 * `10^9` kg/m `s^2` = 210 * `10^7` kg/cm `s^2`
i. Velocity = 56.33KMPH = 1564.7222 cm/s
j. Gravity 9.8m/s2 = 9.8 * `10^2` cm/s2
2.Kg cm ms
a. Mass = 1kg
b. length = 1cm
c. Time = 1 ms
d. Force = ma = kg*`m/s^2` = N
here length = 1cm = 10^-2 m
time = 1ms = `10^-3` ms
Force = kg* `10^-2`/`10^-6` `m /s^2` = `10^4`N
e. Stress Pa (`N/m^2`)
= `1 X 10^-2` N /`(10^-4)` `m^2`
Stress = `10^2`Pa
f. Energy = J = Nm
= `1 X 10^-2` N* `10^-2 m`
= `10^-4` Nm
g. Density ` (Kg)/m^3`
= 1 Kg `(10^-6)`/`(10^-6)` `m^3`
= `(10^-6)` Kg / `cm^3`
h.YOUNG'S Modulus 210GPa
= 210 * `10^9` kg/m `s^2` = 210 * `10^1` kg/cm `ms^2`
i. Velocity = 56.33KMPH = 1.5647222 cm/ms
j. Gravity 9.8m/s2 = 9.8 * `10^-4` cm/ms2
3.g mm ms
a. Mass = 1g
b. length = 1mm
c. Time = 1 ms
d. Force = ma = kg*`m/s^2` = N
here length = 1mm = 10^-3 m
time = 1ms = `10^-3` s
mass = g = `10^-3` kg
Force = `10^-3` kg* `10^-3`/`10^-6` `m /s^2` = 1 N
e. Stress Pa (`N/m^2`)
= `1 N /`(10^-6)` `m^2`
Stress = `10^6`Pa = Mpa
f. Energy = J = Nm
= 1 N* `10^-3 m`
= `10^-3` Nm = mJ
g. Density ` (Kg)/m^3` to g / `mm^3`
= `10^3` g `(10^-9)`/`(10^-9)` `m^3`
= `(10^-6)` g / `mm^3`
h.YOUNG'S Modulus 210GPa
= 210 * `10^9` kg/m `s^2` = 210 * `10^3` g/mm `ms^2`
i. Velocity = 56.33KMPH = 15.647222 mm/ms
j. Gravity 9.8m/s2 = 9.8 * `10^-3` mm/ms2
4. g cm s
a. Mass = g
b. length = 1cm
c. Time = 1 s
d. Force = ma = kg*`m/s^2` = N
here length = 1cm = 10^-2 m
mass = g = `10^-3` kg
Force = `10^-3` kg* `10^-2` `m /s^2` = 1* `10^-5` N =dyne
e. Stress Pa (`N/m^2`)
= `1 X 10^-5` N / `cm^2`
Stress = dyne / `cm^2`
f. Energy = J = Nm
= `1 X `10^-5` N* `10^-2 m`
= `10^-7` Nm = `10^-7`J = erg
g. Density ` (Kg)/m^3` to ` (g)/(cm^3)`
= `10^3`g `(10^-6)`/`(10^-6)` `m^3`
= `(10^-3)` g / `cm^3`
h.YOUNG'S Modulus 210GPa
= 210 * `10^9` kg/m `s^2` = 210 * `10^10` g/cm `s^2`
i. Velocity = 56.33KMPH = 1564.7222 cm/s
j. Gravity 9.8m/s2 = 9.8 * `10^2` cm/s2
5.g cm μs
a. Mass = g
b. length = 1cm
c. Time = 1 μs
d. Force = ma = kg*`m/s^2` = N
here length = 1cm = 10^-2 m
Time = 1 μs = 10^-6 s
mass = g = `10^-3` kg
Force = `10^-3` kg* `10^-2` `m /`10^-12` s^2` = `10^7` N
e. Stress Pa (`N/m^2`)
= `1 X 10^7` N / 10^-4`m^2`
Stress = `1 X 10^11` N / `m^2` = 100GPa
f. Energy = J = Nm
= `1 X `10^7` N* `10^-2 m`
= `10^5` Nm
g. Density ` (Kg)/m^3` to ` (g)/(cm^3)`
= `10^3`g `(10^-6)`/`(10^-6)` `m^3`
= `(10^-3)` g / `cm^3`
h.YOUNG'S Modulus 210GPa
= 210 * `10^9` kg/m `s^2` = 210 * `10^-2` g/cm `μs^2`
i. Velocity = 56.33KMPH = 1564.7222 *`10^-6` cm/μs
j. Gravity 9.8m/s2 = 9.8 * `10^-10` cm/μs2
6. g mm s
a. Mass = g
b. length = 1mm
c. Time = 1 s
d. Force = ma = kg*`m/s^2` = N
here length = 1mm = 10^-3 m
mass = g = `10^-3` kg
Force = `10^-3` kg* `10^-3` `m /s^2` =`10^-6` N
e. Stress Pa (`N/m^2`)
= `1 X 10^-6` N / `10^-6``m^2`
Stress = Pa (`N/m^2`)
f. Energy = J = Nm
= `1 X `10^-6` N* `10^-3 m`
= `10^-9` Nm = `10^-9`J
g. Density ` (Kg)/m^3` to ` (g)/(mm^3)`
= `10^3`g `(10^-9)`/`(10^-9)` `m^3`
= `(10^-6)` g / `mm^3`
h.YOUNG'S Modulus 210GPa
= 210 * `10^9` kg/m `s^2` = 210 * `10^9` g/mm `s^2`
i. Velocity = 56.33KMPH = 15647.222 mm/s
j. Gravity 9.8m/s2 = 9.8 * `10^3` mm/s2
7. ton mm s
a. Mass = ton
b. length = 1mm
c. Time = 1 s
d. Force = ma = kg*`m/s^2` = N
here length = 1mm = 10^-3 m
mass = ton = `10^3` kg
Force = `10^3` kg* `10^-3` `m /s^2` = N
e. Stress Pa (`N/m^2`)
= N / `10^-6``m^2`
Stress = MPa
f. Energy = J = Nm
= N* `10^-3 m`
= `10^-3` Nm = `10^-3`J
g. Density ` (Kg)/m^3` to ` (ton)/(mm^3)`
= `10^-3`ton `(10^-9)`/`(10^-9)` `m^3`
= `(10^-12)` ton / `mm^3`
h.YOUNG'S Modulus 210GPa
= 210 * `10^9` kg/m `s^2` = 210 * `10^3 `ton/mm `s^2`
i. Velocity = 56.33KMPH = 15647.222 mm/s
j. Gravity 9.8m/s2 = 9.8 * `10^3` mm/s2
8.slug ft s
a. Mass = slug
b. length = ft
c. Time = 1 s
d. Force = ma = kg*`m/s^2` = N
here length = ft = 0.3048 m
mass = slug = `14.5939` kg
Force = 14.5939 kg* 0.3048 `m /s^2` = 4.448 N
e. Stress Pa (`N/m^2`)
= 4.448 N / 0.3048^2`m^2`
Stress = 47.877 Pa
f. Energy = J = Nm
= 4.448 N* ` 0.3048m`
= 1.355 Nm = 1.355 J
g. Density ` (Kg)/m^3` to ` (slug)/(ft^3)`
= 0.0685218 slug /`3.28084^3` `ft^3`
= 0.00194 slug/ft3
h.YOUNG'S Modulus 210GPa
= 210 * `10^9` kg/m `s^2` = 210 * `10^9 `* 0.0685218 slug/ 3.28084 ft `s^2`
= 4.3859 * `10^9 ` slug/ ft `s^2`
i. Velocity = 56.33KMPH = 15.64 *3.28084 ft/s = 51.3123 ft/s
j. Gravity 9.8m/s2 = 9.8 * 3.28084 ft/s2 = 32.185 ft/s2
9. kg mm s
a. Mass = kg
b. length = 1mm
c. Time = 1 s
d. Force = ma = kg*`m/s^2` = N
here length = 1mm = 10^-3 m
Force = kg* `10^-3` `m /s^2` =`10^-3` N
e. Stress Pa (`N/m^2`)
= `1 X 10^-3` N / `10^-6``m^2`
Stress = ` 10^3` Pa (`N/m^2`)
f. Energy = J = Nm
= `1 X `10^-3` N* `10^-3 m`
= `10^-6` Nm = `10^-6`J
g. Density ` (Kg)/m^3` to ` (kg)/(mm^3)`
= kg `(10^-9)`/`(10^-9)` `m^3`
= `(10^-9)` kg / `mm^3`
h.YOUNG'S Modulus 210GPa
= 210 * `10^9` kg/m `s^2` = 210 * `10^6` g/mm `s^2`
i. Velocity = 56.33KMPH = 15647.222 mm/s
j. Gravity 9.8m/s2 = 9.8 * `10^3` mm/s2
10. g cm ms
a. Mass = g
b. length = 1cm
c. Time = 1 ms
d. Force = ma = kg*`m/s^2` = N
here length = 1cm = 10^-2 m
mass = g = `10^-3` kg
Time = 1 ms = `10^-3`s
Force = `10^-3` kg* `10^-2` `m /`10^-6`s^2` = 10` N
e. Stress Pa (`N/m^2`)
= `10` N / `10^-4``m^2` = `10^5`Pa
f. Energy = J = Nm
= `10` N* `10^-2 m`
= `10^-1` Nm = `10^-1`J
g. Density ` (Kg)/m^3` to ` (g)/(cm^3)`
= `10^3`g `(10^-6)`/`(10^-6)` `m^3`
= `(10^-3)` g / `cm^3`
h.YOUNG'S Modulus 210GPa
= 210 * `10^9` kg/m `s^2` = 210 * `10^4` g/cm `ms^2`
i. Velocity = 56.33KMPH = 1.5647 cm/ms
j. Gravity 9.8m/s2 = 9.8 * `10^-4` cm/ms2
11.kg mm ms
= kg
b. length = 1mm
c. Time = 1 ms
d. Force = ma = kg*`m/s^2` = N
here length = 1mm = 10^-3 m
Time = 1 ms = `10^-3`s
Force = kg* `10^-3` `m / `10^-6`s^2` =`10^3` N
e. Stress Pa (`N/m^2`)
= `1 X 10^3` N / `10^-6``m^2`
Stress = ` 10^9` Pa (`N/m^2`)
f. Energy = J = Nm
= `1 X `10^3` N* `10^-3 m`
= 1 Nm = J
g. Density ` (Kg)/m^3` to ` (kg)/(mm^3)`
= kg `(10^-9)`/`(10^-9)` `m^3`
= `(10^-9)` kg / `mm^3`
h.YOUNG'S Modulus 210GPa
= 210 * `10^9` kg/m `s^2` = 210 * `10^9` kg/`10^3`mm `10^6``ms^2`
= 210 kg/mm *`ms^2`
i. Velocity = 56.33KMPH = 15.64 mm/ms
j. Gravity 9.8m/s2 = 9.8 * `10^-3` mm/ms2
Find the below tabel for all unit system.
