Week - 1 - Consistency of units

Aim:

To Convert the given quantities into various system of units as mentioned and write detail calculation for convertion from SI to gm/mm/ms.

Procedure:

Conversion from SI to gm/mm/ms

• Mass = 1 kg units in SI system

        1 kg = 1000 gms -> 1gm = 10^-3 kg

        For conversion of mass from kg to gms we should multiply given mass with 10^-3

        So the conversion factor will be 10^-3.

• Length = 1 m units in SI system

        1 m = 1000 mm -> 1mm = 10^-3 m

         For conversion of length from m to mm we should multiply given length with 10^-3

         So the conversion factor will be 10^-3.

• Time = 1s Units in SI system

         1s = 1000 ms -> 1ms = 10^-3 s

         For conversion of Time from s to ms we should multiply given time with 10^-3

         So the conversion factor will be 10^-3

• FOrce =1 N Units in SI system

        1 N = Kg * m/ s^2 = 10^-3gm*10^-3 mm/ 10^-6 ms = gm mm/ ms = N

         Hence the units for force will be same . Conversion factor will be 1.

• Stress = 1 pa Units in SI system

        1 pa = 1 N/m^2 = 1 N / 10^-6 mm^2 = 10^6 N/ mm^2 = 1 MPa

        So the Conversion factor will be 10^6

• Energy = 1 Nm Units in SI system

        1 N-m = 1 N- 10^-3 mm = 10^-3 Nmm

        So the Conversion factor will be 10^-3

• Density = 1 Kg/ m^3 Units in SI system

        1 Kg/m^3 = 1000 gm / 10^9 mm^3 = 10^3 * 10^-9 gm/mm^3 = 10^-6 gm/ mm^3

        So the Conversion factor will be 10^-6

• YOUNGS Modulus = 210 GPa Units in SI system

         210 GPa = 210 * 10^9 N/ m^2 = 210 * 10^9 N/ 10^6 mm^2 = 210*10^9*10^-6 N/mm^2 = 210 *10 ^3 N/mm^2

        so the Conversion factor will be 10^-6

• Velocity = 56.33 KMPH Units in SI system

        56.33 KMPH = 56.33 * 1000 *1000 mm / 60*60*1000 ms = 56.33*5/18 mm/ms

        So the Conversion factor will be 5/18

• Gravity = 9.81 m/s^2 Units in SI system

        9.81 m/s^2 = 9.81 * 1000 mm/ 1000*1000 ms^2 = 9.81*10^-3 mm/ ms^2

        So the Conversion factor will be 10^-3

	Mass 1 Kg	Length 1 m	Time 1s	Force 1 N	Stress 1 Pa	Energy 1Nm	Density 1 Kg/m3	YOUNGS modulus 210 GPa	Velocity 56.33 KMPH	Gravity 9.8 m/s2
Kg cm ms	1 Kg	1e-2m	1e-3s	1e+4N	1e2Pa	1e-2J	1e-6 Kg/m3	2.1e+3	1.56	9.81e-4
Kg cm s	1 kg	1e-2m	1s	1e-2N	1e+2Pa	1e4J	1e-6 Kg/m3	2.1e+9	1560	981
gm mm ms	1e-3 kg	1e-3m	1e-3s	1N	MPa	1e-3J	1e-6Kg/m3	2.1e+5	15.65	9.81e-3
Kg m s	kg	m	s	N	Pa	Nm	Kg/m3	2.1e+11	15.65	9.81
g cm s	1e-3kg	1e-2m	1s	1 dyn	dyn/cm2	1e-7 J	1e-3Kg/m3	2.1e+12	1560	981
g cm us	1e-3Kg	1e-2m	1e-6s	1e+7N	100GPa	1e-5J	1e-3Kg/m3	2.1	1.56e-3	9.81e-10
g mm s	1e-3 Kg	1e-3m	1s	1e-6 N	Pa	1e-9J	1e-6Kg/m3	2.1e+11	1.56e+4	9810
ton mm s	1e+3Kg	1e-3m	1s	N	MPa	1e-3J	1e-12Kg/m3	2.1e+5	1.56e+4	9810
slug ft s	14.594Kg	0.305m	s	4.46N	50Pa	1.35J	526 Kg/m3	2.1e+11*50	51.33	32.17
kg mm s	Kg	1e-3m	s	1e-3N	1e3Pa	1e-6J	1e-9Kg/m3	2.1e+8	15650	9810
g cm ms	1e-3 Kg	1e-2m	1e-3s	10N	0.1Mpa	0.1J	1e-3Kg/m3	2.1e+6	1.56	9.81e-4
kg mm ms	Kg	1e-3m	1e-3s	1e+3N	1e+9Pa	1J	1e-9Kg/m3	2.1e+2	15.65	9.81e-3

  Conclusion:

Proper care should be taken while converting one system of units to another system of units.

Learning Outcomes:

• Conversion of one system of units to other.