Consistency Of Units

Objective: Show detailed calculation for conversion from SI units to different unit systems used in different industries and mention the conversion factors.

Question:

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

Write the given measurements in the above different system of units. Also, mention the conversion factors.

**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.**

Write your report here calculations written down on a piece of paper and uploaded as an Image will no be accepted.

All the answers should be in the form of a report. Only then it will be considered for Grading.

Detailed Calculation from SI units to gm/mm/ms unit system:

Fundamental Quantity: Length, Mass and time are fundamental quantities and can be converted directly so no calculation needed.

SI unit (Kg, m, s) gm/mm/ms unit system Conversion Factor

MASS 1kg 1000gm 1000
LENGTH 1m 1000mm 1000
TIME 1s 1000ms 1000

Derived Quantity:Derived quantities are quantities that are calculated from two or more measurements. Derived quantities cannot be measured directly. They can only be computed.

FORCE 1N = `kg*m/s^2` Force = mass x acceleration 1

1N = `kg*m/s^2`

= `1000g*(1000mm)/(1000ms)^2`

= `10^6/10^-6*(gm*(mm)/(ms^2))`

= `1 (gm*(mm)/(ms^2))`

STRESS 1Pa = `1N/m^2` `1N/m^2 = (1kg*m/s^2)/m^2` 10^-6

= `(1000g*(1000mm)/(1000ms)^2)/(1000mm)^2`

= `10^-6*(gm)/(mm.ms^2`

ENERGY 1J = 1Nm 1Nm = `(1kg*m/s^2)*m` 10^3

= `(1000g*(1000mm)/(1000ms)^2)*1000mm`

= `1 (gm*(mm)/(ms^2))*10^3mm`

= `10^3 (gm*(mm^2)/(ms^2))`

DENSITY 1Kg/m3 1Kg/m3 = `(1000g)/(1000mm)^3` 10^-6

= `10^-6(gm)/(mm)^3`

YOUNG'S Modulus 210GPa =210e+9 Pa = 210e+9N/m^2 210e+9N/m^2 = `210e+9*N/m^2 = 210e+9*(kg*m/s^2)/m^2`` 10^-6

= `210e+9*(1000g*(1000mm)/(1000ms)^2)/(1000mm)^2`

= `210*10^9*10^-6*(gm)/(mm.ms^2`

= `210*10^3*(gm)/(mm.ms^2`

Velocity 56.33KMPH 56.33KMPH = `56.33*(10^6mm)/(3600s)` 1

= `56.33*(10^6mm)/(3600*1000ms)`

= `56.33*(10^6mm)/(3.6*10^6ms)`

= `(56.33mm)/(3.6ms)`

= `15.6472 (mm)/(ms)`

GRAVITY 9.8m/s2 9.8m/s2 = `9.8*(1000mm)/(1000ms)^2` 10^-3

= `9.8*10^-3(mm)/(ms)^2`

	Mass	Length	Time	Force	Stress	Energy	Density	YOUNG'S Modulus	Velocity	Density
	1kg	1m	1s	1N	1Pa	1Nm	1Kg/m3	210GPa/ 210e+9Pa	56.33 KMPH	9.8m/s2
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`	`15.6472 (mm)/(ms)`	`9.8*10^-3(mm)/(ms)^2`
Conversion Factor	1000	1000	1000	1	10^-6	10^3	10^-6	10^-6	1	10^-3
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*10*(kg)/(cm.ms^2`	`1.5647 (cm)/(ms)`	`9.8*10^-4(cm)/(ms)^2`
Conversion Factor	1	100	1000	10^-4	10^-8	10^-2	10^-6	10^-8	0.1	10^-4
Kg cm s	1kg	100cm	1s	`10^2 (kg*(cm)/(s^2))`	`10^-2*(kg)/(cm.s^2`	`10^4 (kg*(cm^2)/(s^2))`	10^-6(kg)/(cm)^3	`210*10^7*(kg)/(cm.s^2`	`1564.7 (cm)/(s)`	`9.8*10^2(cm)/(s)^2`
Conversion Factor	1	100	1	10^2	10^-2	10^4	10^-6	10^-2	100	10^2
kg m s	1kg	1m	1s	`1 (Kg*(m)/(s^2))`	`1*(kg)/(m.s^2`	`(1kg*m^2/s^2)`	1Kg/m3	`210*10^9*(kg)/(m.s^2`	`15.6472 (m)/(s)`	9.8m/s2
Conversion Factor	1	1	1	1	1	1	1	1	1	1
g cm s	1000gm	100cm	1s	`10^5 (gm*(cm)/(s^2))`	`10*(gm)/(cm.s^2`	`10^7 (gm*(cm^2)/(s^2))`	`10^-3(g)/(cm)^3`	`210*10^10*(gm)/(cm.s^2`	`1564.7 (cm)/(s)`	`9.8*10^2(cm)/(s)^2`
Conversion Factor	1000	100	1	10^5	10	10^7	10^-3	10^-1	100	10^2
g cm us	1000gm	100cm	1000000us	`10^-7 (gm*(cm)/(us^2))`	`10^-11*(gm)/(cm.us^2`	`10^-5 (gm*(cm^2)/(us^2))`	10^-3(g)/(cm)^3	`210*10^-2*(gm)/(cm.us^2`	`1.56*10^-3 *(cm)/(us)`	`9.8*10^-10(cm)/(us)^2`
Conversion Factor	1000	100	1000000	10^-7	10^-11	10^-5	10^-3	10^-11	10^-2	10^-10
g mm s	1000gm	1000mm	1s	`10^6 (gm*(mm)/(s^2))`	`1*(gm)/(mm.s^2`	`10^9 (gm*(mm^2)/(s^2))`	`10^-6(gm)/(mm)^3`	`210*10^9*(gm)/(mm.s^2`	`1.56*10^4 *(mm)/(s)`	`9.8*10^3(mm)/(s)^2`
Conversion Factor	1000	1000	1	10^6	1	10^9	10^-6	1	10^3	10^3
ton mm s	0.001 tonne	1000mm	1s	1 tonne`(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`	`1.56*10^4 *(mm)/(s)`	`9.8*10^3(mm)/(s)^2`
Conversion Factor	0.001	1000	1	1	10^-6	10^3	10^-12	10^-6	10^3	10^3
slug ft s	0.06852	3.280ft	1s	`0.2246* slug*(ft)/s^2`	`0.0208*(slug)/(ft.s^2`	`0.7366 (slug*(ft^2)/(s^2))`	`1.93*10^-3(slug)/(ft)^3`	`210*0.0208*10^9*(slug)/(ft.s^2`	`51.33 (ft)/s`	`32.17 *(ft)/s`
Conversion Factor	0.06852	3.280	1	0.2246	0.0208	0.7366	1.93*10^-3	0.0208	0.9447	3.28
kg mm s	1Kg	1000mm	1s	`10^3 (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`	`1.56*10^4 *(mm)/(s)`	`9.8*10^3(mm)/(s)^2`
Conversion Factor	1	1000	1	10^3	10^-3	10^6	10^-9	10^-3	10^3	10^3
g cm ms	1000gm	100cm	1000ms	`10^-1 (gm*(cm)/(ms^2))`	`10^-5*(gm)/(cm.ms^2`	`10 (gm*(cm^2)/(ms^2))`	10^-3(g)/(cm)^3	`210*10^4*(gm)/(cm.ms^2`	`1.5647 (cm)/(ms)`	`9.8*10^-4(cm)/(ms)^2`
Conversion Factor	1000	100	1000	10^-1	10^-5	10	10^-3	10^-5	10	10^-4
kg mm ms	1Kg	1000mm	1000ms	`10^-3 (kg*(mm)/(ms^2))`	`10^-9*(kg)/(mm.ms^2`	`1 (kg*(mm^2)/(ms^2))`	`10^-9(Kg)/(mm)^3`	`210*(kg)/(mm.ms^2`	`15.6472 (mm)/(ms)`	`9.8*10^-3(mm)/(ms)^2`
Conversion Factor	1	1000	1000	10^-3	10^-9	1	10^-9	10^-9	1	10^-3

Conclusion:

All the required units are converted from SI units to different unit systems used in different industries.