Week - 1 - Consistency of Units
Aim:
Procedure:
The given quantities are converted to consistent unit systems shown below:
| Unit System | Mass | Length | Time | Force | Stress | Energy | Density | Youngs Modulus | Velocity | Gravity |
| kg_cm_ms | 1 | 102cm | 1000 |
10-4 kg*cm/ms2 |
10-8 kg/(cm*ms2) | 10-2 kg*cm2/ms2 | 210*10e5 | 0.1564 | 9.8*10e-7 | |
| kg_cm_s | 1 | 102cm | 1 |
102 kg*cm/s2 |
10-2 kg/(cm*s2) |
104 kg*cm2/s2 |
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| gm_mm_ms | 103g | 103mm | 103ms |
1 g*mm/ms2 |
10-6 g/(mm*ms2) |
103 g*mm2/ms2 |
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| kg_m_s | 1 | 1 | 1 | 1 kg*m/s2 | 1 kg/(m* s2) | 1 kg*m2/s2 | ||||
| g_cm_s | 103g | 102cm | 1 |
105 g*cm/s2 |
10 g/(cm*s2) |
107 g*cm2/s2 |
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| g_cm_μs | 103g | 102cm | 106μs | 10-7 g*cm/μs2 | 10-11 g/(cm*μs2) | 10-5 g*cm2/μs2 | ||||
| g_mm_s | 103g | 103mm | 1 | 106 g*mm/ s2 | 1 | 109 g*mm2/s2 | ||||
| tonne_mm_s | 10-3ton | 103mm | 1 |
1 ton*mm/s2 |
10-6 ton/(mm*s2) | 103 ton*mm2/s2 | ||||
| slug_ft_s | 0.068slug | 3.28 ft | 1 | 0.2246 slug*ft/ s2 | 0.0208 slug/(ft*s2) | 0.7366 slug*ft2/s2 | ||||
| kg_mm_s | 1 | 103mm | 1 | 103 kg*mm/s2 | 10-3 kg/(mm*s2) | 106 kg*mm2/s2 | ||||
| g_cm_ms | 103g | 102cm | 103ms | 10-1 g*cm/ms2 | 10-5 g/(cm*ms2) | 10 g*cm2/ms2 | ||||
| kg_mm_ms | 1 | 103mm | 103ms | 10-3 kg*mm/ms2 | 10-9 kg/(mm*ms2) | 1 kg*mm2/ms2 |
Conversion of SI unit to gm/mm/ms :
MASS : 1kg = 1000gm Conversion factor : 103
LENGTH: 1m = 1000mm Conversion factor: 103
TIME : 1s = 1000ms Conversion factor : 103
FORCE : 1N = 1kg*1 m/s2 = (1000g*1000mm)/(1000ms)2= 106*10-6 (g*mm)/ms2= 1 (g*mm)/ms2
Conversion factor: 1
STRESS : 1Pa = 1N/m2 = {1kg*(1 m/s2)}/m2 = 1 kg/ (m* s2)= 1000g/{1000mm*(1000ms)2}= 10-6 g/ (mm*ms2)
Conversion factor: 10-6
ENERGY : 1J = 1Nm = (1kg*1 m/s2) * m = 1 (kg*m2/s2)= {1000g * (1000mm)2}/(1000ms)2= (109 g*mm2) / (106 ms2)= 103 (g*mm2/ ms2)
Conversion factor: 103
DENSITY : 1Kg/m3 = 1000g/(1000mm)3 = 10-6 g/mm3
Conversion factor: 10-6
YOUNGS MODULUS : 210GPa = 210e+9 kg/(m*s2) = 210e+9 * 10-6 g/ (mm*m s2)= 210e+3 g/ (mm*m s2) = 210*103 g/ (mm*m s2)
Conversion factor: 103
VELOCITY : 56.33 Kmph = 56.33 * {106mm/(3600*1000ms)}= 15.647 mm/ms
Conversion factor: 5/18
GRAVITY : 9.8m/s2 = 9.8 * 1000mm/(1000ms)2= 9.8* 10-3 mm/ms2
Conversion factor: 10-3
Result :
All the conversions have been carried out in the required unit system.