Week - 1 - Consistency of units
Aim: The objective of this assignment is to convert the given measurements to the specified series of unit systems through a variety of conversion factors.
Conversions: The unit system used in the given measurements is the metric system. Some of the unit systems that the measurements need to be converted to are imperial. The measurements, the conversion and changed measurements are listed below.
1] Mass: 1 kg
Conversion to gm: 1 kg = 1000 gm
Conversion to ton: 1 ton = 2000 lb
1 kg = 2.2 lb = 2.2/2000 ton
Thus, 1 kg = 0.0011 ton
Conversion to slug: 1 slug = 14.5939 kg
Thus, 1 kg = 1/14.5939 = 0.0685 slugs
2] Length: 1 m
Conversion to cm: 1 m = 100 cm
Conversion to mm: 1 m = 1000 mm
Conversion to ft: 1 ft = 12 in = 12*0.0254 m
Thus, 1 m = 1/(12*0.0254) = 3.281 ft
3] Time: 1 sec
Conversion to ms: 1 sec = 1000 ms
Conversion to microsec: 1 sec = 1 X 10^6 microsec
4] Force: 1 N
1 N = 1 kg*m/s^2
Conversion to kg cm ms units: 1 N = 1*100/(1000)^2 = 0.0001 kg*cm/ms^2
Conversion to kg cm s units: 1 N = 1*100 = 100 kg*cm/ms^2
Conversion to gm mm ms units: 1 N = 1*1000*1000/(1000)^2 = 1 gm*mm/ms^2
Conversion to gm cm s units: 1 N = 1*1000*100 = 1 X 10^5 gm*cm/s^2
Conversion to gm cm microsec units: 1*1000*100/(10^6)^2 = 1 X 10^-7 gm*cm/microsec^2
Conversion to gm mm s units: 1 N = 1*1000*1000 = 1 X 10^6 gm*mm/s^2
Conversion to ton mm s units: 1 N = 1*0.0011*1000 = 1.1 ton*mm/s^2
Conversion to slug ft s units: 1 N = 1*0.0685*3.281 = 0.225 slug*ft/s^2
Conversion to kg mm s units: 1 N = 1*1000 = 1000 kg*mm/s^2
Conversion to gm cm ms units: 1 N = 1*1000*100/(1000)^2 = 0.1 gm*cm/ms^2
Conversion to kg mm ms units: 1 N = 1*1000/(1000)^2 = 0.001 kg*mm/ms^2
5] Energy: 1 Nm
1 Nm = 1 kg*(m/s)^2
Conversion to kg cm ms units: 1 Nm = 1*(100/1000)^2 = 0.01 kg*(cm/ms)^2
Conversion to kg cm s units: 1 Nm = 1*(100)^2 = 1 X 10^4 kg*(cm/s)^2
Conversion to gm mm ms units: 1 Nm = 1*1000*(1000/1000)^2 = 1000 gm*(mm/ms)^2
Conversion to gm cm s units: 1 Nm = 1*1000*(100)^2 = 1 X 10^7 gm*(cm/s)^2
Conversion to gm cm microsec units: 1 Nm = 1*1000*(100/10^6)^2 = 1 X 10^-5 gm*(cm/microsec)^2
Conversion to gm mm s units: 1 Nm = 1*1000*(1000)^2 = 1 X 10^9 gm*(mm/s)^2
Conversion to ton mm s: 1 Nm = 1*0.0011*(1000)^2 = 1100 ton*(mm/s)^2
Conversion to slug ft s units: 1 Nm = 1*0.0685*(3.281)^2 = 0.738 slug*(ft/s)^2
Conversion to kg mm s units: 1 Nm = 1*(1000)^2 = 1 X 10^6 kg*(mm/s)^2
Conversion to gm cm ms units: 1 Nm = 1*1000*(100/1000)^2 = 10 gm*(cm/ms)^2
Conversion to kg mm ms units: 1 Nm = 1*(1000/1000)^2 = 1 kg*(mm/ms)^2
6] Density: 1 kg/m^3
Conversion to kg cm units: 1 kg/m^3 = 1/(100)^3 = 1 X 10^-6 kg/cm^3
Conversion to gm cm units: 1 kg/m^3 = 1*1000/(100)^3 = 0.001 gm/cm^3
Conversion to gm mm units: 1 kg/m^3 = 1*1000/(1000)^3 = 1 X 10^-6 gm/mm^3
Conversion to kg mm units: 1 kg/m^3 = 1/(1000)^3 = 1 X 10^-9 kg/mm^3
Conversion to ton mm units: 1 kg/m^3 = 1*0.0011/(1000)^3 = 1.1 X 10^-12 ton/mm^3
Conversion to slug ft units: 1 kg/m^3 = 1*0.0685/(3.281)^3 = 1.94 X 10^-3 slug/ft^3
7] Young's modulus: 210 GPa
210 GPa = 210 X 10^9 kg/(m*s^2)
Conversion to kg cm ms units: 210 GPa = 210*10^9/(100*1000^2) = 2100 kg/(cm*ms^2)
Conversion to kg cm s units: 210 GPa = 210*10^9/100 = 2.1 X 10^9 kg/(cm*s^2)
Conversion to gm mm ms units: 210 GPa = 210*10^9*1000/(1000*1000^2) = 2.1 X 10^5 gm/(mm*ms^2)
Conversion to gm cm s units: 210 GPa = 210*10^9*1000/100 = 2.1 X 10^12 gm/(cm*s^2)
Conversion to gm cm microsec units: 210 GPa = 210*10^9*1000/(100*(10^6)^2) = 2.1 gm/(cm*microsec^2)
Conversion to gm mm s units: 210 GPa = 210*10^9*1000/1000 = 2.1 X 10^11 gm/(mm*s^2)
Conversion to ton mm s units: 210 GPa = 210*10^9*0.0011/1000 = 2.31 X 10^5 ton/(mm*s^2)
Conversion to slug ft s units: 210 GPa = 210*10^9*0.0685/3.281 = 4.386 X 10^9 slug/(ft*s^2)
Conversion to kg mm s units: 210 GPa = 210*10^9/1000 = 2.1 X 10^8 kg/(mm*s^2)
Conversion to gm cm ms units: 210 GPa = 210*10^9*1000/(100*1000^2) = 2.1 X 10^6 gm/(cm*ms^2)
Conversion to kg mm ms units: 210 GPa = 210*10^9/(1000*1000^2) = 210 kg/(mm*ms^2)
8] Velocity: 56.33 km/hr
Conversion to m s units: 56.33 km/hr = 56.33*1000/3600 = 15.647 m/s
Conversion to cm ms units: 56.33 km/hr = 56.33*1000*100/(3600*1000) = 1.565 cm/ms
Conversion to cm s units: 56.33 km/hr = 56.33*1000*100/3600 = 1564.7 cm/s
Conversion to mm ms units: 56.33 km/hr = 56.33*1000*1000/(3600*1000) = 15.647 mm/ms
Conversion to cm microsec units: 56.33 km/hr = 56.33*1000*100/(3600*10^6) = 1.565 X 10^-3 cm/microsec
Conversion to mm s units: 56.33 km/hr = 56.33*1000*1000/3600 = 0.016 mm/s
Conversion to ft s units: 56.33 km/hr = 56.33*1000*3.281/3600 = 51.336 ft/s
9] Gravitational constant: 9.8 m/s^2
Conversion to cm ms units: 9.8 m/s^2 = 9.8*100/1000^2 = 9.8 X 10^-4 cm/ms^2
Conversion to cm s units: 9.8 m/s^2 = 9.8*100 =980 cm/s^2
Conversion to mm ms units: 9.8 m/s^2 = 9.8*1000/1000^2 = 9.8 X 10^-3 mm/ms^2
Conversion to cm microsec units: 9.8 m/s^2 = 9.8*100/(10^6)^2 = 9.8 X 10^-10 cm/microsec^2
Conversion to mm s units: 9.8 m/s^2 = 9.8*1000 = 9800 mm/s^2
Conversion to ft s units: 9.8 m/s^2 = 9.8*3.281 = 32.152 ft/s^2