Week - 1 - Consistency of Units
Aim:
Convert the units of given values to the required unit systems as mentioned.
Procedure:
Conversion of SI unit to gm/mm/ms
1. Mass
Value: 1 kg
in gm/mm/ms : 1000gm; conversion factor: 1000
2. Length
Value: 1 m
in gm/mm/ms : 1000 mm; conversion factor: 1000
3. Time
Value: 1 s
in gm/mm/ms : 1000 ms; conversion factor: 1000
4. Force
Value: 1 N
Conversion to gm/mm/ms :
1N = 1 (kg *m)/s^2`
= 1 `(1000g*1000mm)/(1000*s)^2`
= 1 N; Conversion Factor: 1
5. Stress
Value: 1 Pa
in gm/mm/ms:
1 Pa = 1 N/m^2
= `(1*1N)/(1000mm)^2`
`= 10^-6 N/(mm)^2`
ie. 1000000*Pa = 1 Mpa
Conversion Factor = 1e-6
6. Energy
Value: 1 Nm
in gm/mm/ms:
= 1 `(1*N)*(1000mm)`
=1000Nmm
ie 1 Nmm= (1/1000)Nm = (1/1000) J = 1 mJ Conversion Factor = 1e3
7. Density
Value : 1`(kg)/m^3`
in gm/mm/ms:
=`(1000g)/(1000mm)^3`
= 1e-6 g/mm^3
= 1e-6 g/mm^3 Conversion Factor = 1e-6
8. Young's Modulus
value: 210 Gpa = 2.1e11 Pa
in gm/mm/ms:
since the unit of Young's modulus and stress is the same,
2.1e11 pa*(conversion factor for stress ie 1e-6) = 2.1e11 * 1e-6 = 2.1e5 Pa Conversion Factor: 1e-6
9. Velocity
Value: 56.33 Kmph
in gm/mm/ms:
= `(56.33*10^6 mm)/(60*60*1000)ms`
= `56330000/3600000`
= 15.65 mm/ms Conversion Factor: 15.65
10. Gravity
Value : 9.8 m/s^2
in gm/mm/ms:
=`(9.8*1000mm)/((1*1000)^2ms)`
= 9.8*1e-3 mm/ms^2 Conversion Factor: 1e-3
=9.8e-3 mm/ms^2
| MASS | LENGTH | TIME | FORCE | STRESS | ENERGY | DENSITY | Y's MODULUS | VELOCITY | GRAVITY | |
| kg cm ms | 1 kg | 100 cm | 1e3 ms | 1e-4 `(kg*cm)/(ms)^2` | 1e2 kg/cm.ms^2 | 1e-2`(kg*mm^2)/s^2` | 1e-6 kg/cm^3 | 2.1e3 kg/cm.ms^2 | 1.56 cm/ms | 9.81e-4 cm/ms^2 |
| kg cm s | 1 kg | 100 cm | 1 s | 1e-2 `(kg*cm)/s^2` | 1e2 kg/cm.s^2 | 1 `(kg*cm^2)/s^2` | 1e-6 kg/cm^3 | 2.1e9 kg/cm.s^2 | 1564 cm/s | 981 cm/s^2 |
| g mm ms | 1e3 g | 1e3 mm | 1e3 ms | 1 `(g*mm)/(ms)^2` | 1e3 g/mm.ms^2 | 1e3 `(g*mm^2)/(ms)^2` | 1e-6 g/mm^3 | 2.1e5 g/mm.ms^2 | 15.65 mm/ms | 9.8e-3 cm/ms^2 |
| g cm s | 1e3 g | 100 cm | 1 s | 1e5 `(g*cm)/s^2` | 1e11 g/cm.s^2 | 1e7 `(g*cm^2)/s^2` | 1e-3 g/cm^3 | 2.1 g/cm.s^2 | 1564 cm/s | 981 cm/s^2 |
| g cm us | 1e3 g | 100 cm | 1e6 us | 1e-7 `(g*cm)/(us)^2` | 1e-11 g/cm.us^2 | 1e-5 `(g*cm^2)/(us)^2` | 1e-3 g/cm^3 | 2.1 g/cm.us^2 | 1.564 cm/us | 9.81e-4 cm/us^2 |
| g mm s | 1e3 g | 1e3 mm | 1 s | 1e6 `(g*mm)/s^2` | 1 g/nm.s^2 | 1e9 `(g*mm^2)/s^2` | 1e-6 g/mm^3 | 2.1e11 g/nm.s^2 | 15.65e3 mm/s | 9.8e3 mm/s^2 |
| ton mm s | 1e-3 ton | 1e3 mm | 1 s | 1 `(ton*mm)/s^2` | 1e-6 ton/mm.s^2 | 1e3 `(ton*mm^2)/s^2` | 1e-12 ton/mm^3 | 1e-6 ton/mm.s^2 | 15.65e3 mm/s | 9.8e3 mm/s^2 |
| slug ft s | 0.07 slug | 0.3048 ft | 1 s | 2.28 `(slug*ft)/s^2` | 0.2052 slug/ft.s^2 | 7.6 `(slug*ft^2)/s^2` | 1.85e-3 slug/ft^3 | 0.2052 slug/ft.s^2 | 52.13 ft/s | 32.7 ft/s^2 |
| kg mm s | 1 kg | 1e3 mm | 1 s | 1e3 `(kg*mm)/s^2` | 1e-3 kg/mm.s^2 | 1e6 `(kg*mm^2)/s^2` | 1e-9 kg/mm^3 | 1e-3 kg/mm.s^2 | 15.65e3 mm/s | 9.8e3 mm/s |
| g cm ms | 1e3 g | 1e2 cm | 1e3 ms | 1e-1 `(g*cm)/(ms)^2` | 1e-5 g/cm.ms^2 | 10 `(g*cm^2)/(ms)^2` | 1e-3 g/cm^3 | 1e-5 g/cm.ms^2 | 1.56 cm/ms | 9.81e-4 cm/ms^2 |
| kg mm ms | 1 kg | 1e3 mm | 1e3 ms | 1e-3 `(kg*mm)/(ms)^2` | 1e-9 kg/mm.ms^2 | 1 `(kg*mm^2)/(ms)^2` | 1e-9 kg/mm^3 | 1e-9 kg/mm.ms^2 | 15.65 mm/ms | 9.8e-3 mm/ms^2 |