Week - 1 - Consistency of units
Objective:
1.to convert the Value of the following measurements to gm/mm/ms unit system
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
2.To create a conversion table for converting Si unit to other unit systems
Steps:
1.MASS 1kg
1 kg to 1000 gram
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2.LENGTH 1m
1 meter= 1000 millimeter
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3.TIME 1s
1second = 1000 millisecond
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4.FORCE 1N
1N=1 kg.m/s2
1 kg to 1000 gram
1 meter= 1000 millimeter
1second = 1000 millisecond
so 1kg.m/s2= 1000*1000/1000^2 gm.mm/ms2
1N=1gm.mm.ms2
so in other words we can enter the value of force in N for gm/mm/ms system
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5.STRESS 1Pa
1Pa= 1N/m^2
from above calculations force can be entered in N so we have to convert meter to millimeter
1N/m2= 1/1000^2 N/mm2
so 1Pa = 1E-6 N/mm2 or 1E6 pa =1N/mm2 so stress is measured in Mpa in gm/mm/ms system
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6.ENERGY 1Nm
1m =1000mm
1N= 1Kg.m/s2= 1gm.mm/ms2
1Nm= 1000 Nmm
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7.DENSITY 1Kg/m3
1 kg to 1000 gram
1 meter= 1000 millimeter
1kg/m3=1000/1000^3 gm/mm3
1kg/m3 = 1E-6 gm/mm3
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8.YOUNG'S Modulus 210GPa
1Pa= 1N/m^2
1GPa=1E9 Pa
and in gm/mm/ms system 1Pa = 1E-6 N/mm2
1GPa= E9*E-6 = 1000 N/mm2
so 210 GPa=210*E9Pa=210*E9*E-6 N/mm2
210 GPa= 210*1000N/mm2
210 GPa = 2.1 E5 N/mm2 = 2.1 E5 MPa
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9.Velocity 56.33KMPH
1kmph = 1000/(60*60)= 5/18 m/s
1m/s= 1000/1000 mm/ms
1m/s=1mm/ms
so 1Kmph = 5/18 mm/ms
56.33 Kmph = 56.33*(5/18) mm/ms
56.33 kmph = 15.65 mm/ms
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10.GRAVITY 9.8m/s2
1m= 1000 mm
1s =1000ms
1m/s2= 1000/1000^2 mm/ms2 = 1E-3 mm/ms2
9.8m/s2 = 9.8 E-3 mm/ms2
summary:
IIIly the value of youngs modulus and velocity and gravity in other unit system is obtained.
Conversion table : (for a model whose value of all mesurements is 1 in SI system)
