Week - 1 - Consistency of units
Assignment 1 - Consistency of units
1. Kg cm ms
1.1. MASS 1kg
This measurement is directly written according to the mass units considered by this system:
Mass 1 Kg = 1 Kg; Conversion factor (CF) = 1
1.2. LENGTH 1m
Converting from m to cm, this measurement is given by:
1 m = 100 cm; CF = 100
1.3. TIME 1s
Converting from s to ms, this measurement is given by:
1 s = 1000 ms; CF = 1000
1.4. FORCE 1N
A force measurement corresponds to a mass times an acceleration (F=ma).
By using the units of this system, the acceleration units are cm*ms^-2; while he units supported by the International System (I.S.) are: m/s^-2. This means that the total CF is 1/100x1000^2 = 10000 to express this quantity in I.S. units.
1 N = 1 Kg*m*s^-2 = 1/10000 Kg*cm*ms^-2 = 10^-4 Kg*cm*ms^-2
1.5. STRESS 1Pa
1Pa = 1N/m^2 = 10^-4 Kg*cm*ms^-2/m^2 = 10^-4 Kg*cm*ms^-2/(100cm)^2 = 10^-4/100^2 Kg*cm^-1*ms^-2 = 10^-8 Kg*cm^-1*ms^-2
CF = 10^-8
1.6. ENERGY 1Nm
Energy corresponds to a force times a displacement
1Nm = 1 J = 10^-4 Kg*cm*ms^-2 * 100 cm = 10^-2 Kg*cm^2*ms^-2
CF = 10^-2
1.7. DENSITY 1Kg/m3
The density is a mass divided by a volume
1Kg/m^3 = 1 Kg/(100 cm)^3 = = 10^-4 Kg*cm*ms^-2 * 100 cm = 10^-2 Kg*cm^2*ms^-2
CF = 10^-2
1.8. YOUNG'S Modulus 210GPa
1Pa = 10^-8 Kg*cm^-1*ms^-2 => 1GPa = 10 Kg*cm^-1*ms^-2 => 210GPa = 210*10 Kg*cm^-1*ms^-2 => 210GPa = 2100 Kg*cm^-1*ms^-2
CF = 10^-8 * 10^9 = 10
1.9. Velocity 56.33KMPH
The velocity corresponds to a ratio between a displacement and a time interval:
56.33 Km/h = 56.33 100000cm/(3600*1000 ms) = 1.56 cm/ms
CF = 100000/(3600*1000) = 0.0278
1.10. GRAVITY 9.8m/s2
The gravity acceleration has the units of a displacement divided by a time squared.
9.8 m/s2 = 9.8 100 cm/(1000 ms)^2 = 9.8e-4 cm/ms^2
CF = 10^-4
2. Kg cm s
2.1. MASS 1kg
This measurement is directly written according to the mass units considered by this system:
Mass 1 Kg = 1 Kg; Conversion factor (CF) = 1
2.2. LENGTH 1m
Converting from m to cm, this measurement is given by:
1 m = 100 cm; CF = 100
2.3. TIME 1s
Converting from s to ms, this measurement is given by:
1 s = 1000 ms; CF = 1000
2.4. FORCE 1N
A force measurement corresponds to a mass times an acceleration (F=ma).
1 N = 1 Kg*m*s^-2 = 1 Kg*100cm*s^-2 = 100 Kg*cm*s^-2
CF = 100
2.5. STRESS 1Pa
1Pa = 1N/m^2 = 100 Kg*cm*s^-2/(100 cm)^2 = 0.01 Kg*cm^-1*s^-2
CF = 0.01
2.6. ENERGY 1Nm
Energy corresponds to a force times a displacement
1Nm = 1 J = 100 Kg*cm*s^-2 * 100 cm = 10000 Kg*cm^2*s^-2
CF = 10000
2.7. DENSITY 1Kg/m3
The density is a mass divided by a volume
1Kg/m^3 = 1 Kg/(100 cm)^3 = = 10^-4 Kg*cm*ms^-2 * 100 cm = 10^-2 Kg*cm^2*ms^-2
CF = 10^-2
2.8. YOUNG'S Modulus 210GPa
1Pa = 1 Kg*m/(s^2*m^2) = 1 Kg*(100 cm)/(s^2*(100cm)^2) = 0.01 Kg*cm/(s^2*cm^2) =>
=> 210 GPa = 2.1e9 Kg*cm/(s^2*cm^2)
CF = 0.01e9
2.9. Velocity 56.33KMPH
The velocity corresponds to a ratio between a displacement and a time interval:
56.33 Km/h = 56.33 100000cm/(3600*s) = 1564.71 cm/s
CF = 100000/3600 = 27.8
2.10. GRAVITY 9.8m/s2
The gravity acceleration has the units of a displacement divided by a time squared.
9.8 m/s2 = 9.8 * 100 cm/s^2 = 980 cm/s^2
CF = 100
3. mg mm ms
3.1. MASS 1kg
1 Kg = 1000 mg
CF = 1000
3.2. LENGTH 1m
1 m = 1000 mm
CF = 1000
3.3. TIME 1s
1s = 1000 ms
CF = 1000
3.4. FORCE 1N
1 N = 1 Kg*m/s^2 = 1000 mg*(1000 mm)/(1000 ms) = 1000 mg*mm/ms
CF = 1000
3.5. STRESS 1Pa
1 Pa = 1N/m^2 = 1000 mg*mm/ms/(1000 mm)^2 = 0.001 mg/(mm*ms)
CF = 0.001
3.6. ENERGY 1Nm
1 J = 1Nm = 1000 mg*mm/ms*1000 mm = 1e6 mg*mm^2/ms
3.7. DENSITY 1Kg/m3
The density is a mass divided by a volume
1 Kg/m^3 = 1000 mg / (1000 mm)^3 = 1e-6 mg/mm^3
CF = 1e-6
3.8. YOUNG'S Modulus 210GPa
1Pa = 0.001 mg/(mm*ms) -> 1GPa = 1e6 mg/(mm*ms) -> 210 GPa = 210e6 mg/(mm*ms)
CF = 1e6
3.9. Velocity 56.33KMPH
The velocity corresponds to a ratio between a displacement and a time interval:
56.33 Km/h = 56.33 1e6 mm/(3600*1000 ms) = 15.647 mm/ms
CF = 0.278
3.10. GRAVITY 9.8m/s2
The gravity acceleration has the units of a displacement divided by a time squared.
9.8 m/s2 = 9.8 * 1000 mm/(1000 ms)^2 = 0.0098 mm/ms^2
CF = 0.001
4. kg m s
4.1. MASS 1kg
1 Kg = 1 Kg
CF = 1
4.2. LENGTH 1m
1 m = 1 m
CF = 1
4.3. TIME 1s
1s = 1 s
CF = 1
4.4. FORCE 1N
1 N = 1 Kg*m/s^2
CF = 1
4.5. STRESS 1Pa
1 Pa = 1N/m^2 = 1 Kg*m/s^2 /m^2 = 1 Kg/(m*s^2)
CF = 1
4.6. ENERGY 1Nm
1 J = 1Nm = 1 Kg*m/s^2*m = 1 Kg*m^2/s^2
CF = 1
4.7. DENSITY 1Kg/m3
The density is a mass divided by a volume
1 Kg/m^3 = 1 Kg/m^3
CF = 1
4.8. YOUNG'S Modulus 210GPa
1Pa = 1 Kg/(m*s^2) -> 1GPa = 1e9 Kg/(m*s^2) -> 210 GPa = 210e9 Kg/(m*s^2)
CF = 1e9
4.9. Velocity 56.33KMPH
The velocity corresponds to a ratio between a displacement and a time interval:
56.33 Km/h = 56.33 1000m/(3600 s) = 15.647 m/s
CF = 0.278
4.10. GRAVITY 9.8m/s2
The gravity acceleration has the units of a displacement divided by a time squared.
9.8 m/s2 = 9.8 m/s2
CF = 1
5. g cm s
5.1. MASS 1kg
1 Kg = 1000 g
CF = 1000
5.2. LENGTH 1m
1 m = 100 cm
CF = 100
5.3. TIME 1s
1 s = 1 s
CF = 1
5.4. FORCE 1N
1 N = 1 Kg*m/s^2 = 1000 g*100 cm/s^2 = 1e5 g*cm/s^2
CF = 1e5
5.5. STRESS 1Pa
1 Pa = 1N/m^2 = 1 Kg*m/s^2 /m^2 = 1000 g*100 cm/s^2/(100 cm)^2 = 10 g/(cm*s^2)
CF = 10
5.6. ENERGY 1Nm
1 J = 1Nm = 1 Kg*m/s^2*m = 1 Kg*100cm^2/s^2*100cm = 1e4 Kg*m^2/s^2
5.7. DENSITY 1Kg/m3
The density is a mass divided by a volume
1 Kg/m^3 = 1000 g/(100cm)^3 = 0.001 g/cm^3
CF = 0.001
5.8. YOUNG'S Modulus 210GPa
1Pa = 1000 g/(100cm*s^2) -> 1Pa = 10 g/(cm*s^2) -> 1 GPa = 1e10 g/(cm*s^2) -> 210 GPa = 210e10 g/(cm*s^2)
CF = 1e10
5.9. Velocity 56.33KMPH
The velocity corresponds to a ratio between a displacement and a time interval:
56.33 Km/h = 56.33 100000 cm/(3600 s) = 1564.72 cm/s
CF = 27.78
5.10. GRAVITY 9.8m/s2
The gravity acceleration has the units of a displacement divided by a time squared.
9.8 m/s2 = 9.8*100cm/s2 = 980 cm/s2
CF = 100
6. g cm us
6.1. MASS 1kg
1 Kg = 1000 g
CF = 1000
6.2. LENGTH 1m
1 m = 100 cm
CF = 100
6.3. TIME 1s
1 s = 1e6 us
CF = 1e6
6.4. FORCE 1N
1 N = 1 Kg*m/s^2 = 1000 g*100 cm/(1e6 us)^2 = 1e-7 g*cm/us^2
CF = 1e-7
6.5. STRESS 1Pa
1 Pa = 1N/m^2 = 1000 g*100 cm/(1e6 us)^2 /(100 cm)^2 = 1e-5 g*cm/us
CF = 1e-5
6.6. ENERGY 1Nm
1 J = 1Nm = 1000 g*(100 cm)/(1e6 us)^2*100 cm = 1e-5 g*m^2/s^2
CF = 1e-5
6.7. DENSITY 1Kg/m3
The density is a mass divided by a volume
1 Kg/m^3 = 1000 g/(100cm)^3 = 0.001 g/cm^3
CF = 0.001
6.8. YOUNG'S Modulus 210GPa
1Pa = 1e-5 g*cm/us -> 1 GPa = 1e4 g*cm/us -> 210 GPa = 210e4 g*cm/us
CF = 1e4
6.9. Velocity 56.33KMPH
The velocity corresponds to a ratio between a displacement and a time interval:
56.33 Km/h = 56.33 100000 cm/(3600*1e6 us) = 0.00156 cm/us
CF = 2.8e-5
6.10. GRAVITY 9.8m/s2
The gravity acceleration has the units of a displacement divided by a time squared.
9.8 m/s2 = 9.8*100cm/(1e6 us)2 = 9.8e-10 cm/s2
CF = 1e-10
7. g mm s
7.1. MASS 1kg
1 Kg = 1000 g
CF = 1000
7.2. LENGTH 1m
1 m = 1000 mm
CF = 1000
7.3. TIME 1s
1 s = 1 s
CF = 1
7.4. FORCE 1N
1 N = 1 Kg*m/s^2 = 1000 g*1000 mm/s^2 = 1 g*cm/s^2
CF = 1
7.5. STRESS 1Pa
1 Pa = 1N/m^2 = 1000 g*100 cm/s^2 /(100 cm)^2 = 1e-5 g*cm/us
CF = 1e-5
7.6. ENERGY 1Nm
1 J = 1Nm = 1000 g*(100 cm)/(1e6 us)^2*100 cm = 1e-5 g*m^2/s^2
CF = 1e-5
7.7. DENSITY 1Kg/m3
The density is a mass divided by a volume
1 Kg/m^3 = 1000 g/(100cm)^3 = 0.001 g/cm^3
CF = 0.001
7.8. YOUNG'S Modulus 210GPa
1Pa = 1e-5 g*cm/us -> 1 GPa = 1e4 g*cm/us -> 210 GPa = 210e4 g*cm/us
CF = 1e4
7.9. Velocity 56.33KMPH
The velocity corresponds to a ratio between a displacement and a time interval:
56.33 Km/h = 56.33 100000 cm/(3600*1e6 us) = 0.00156 cm/us
CF = 2.8e-5
7.10. GRAVITY 9.8m/s2
The gravity acceleration has the units of a displacement divided by a time squared.
9.8 m/s2 = 9.8*100cm/(1e6 us)2 = 9.8e-10 cm/s2
CF = 1e-10
8. ton mm s
8.1. MASS 1kg
1 Kg = 0.1 ton
CF = 0.1
8.2. LENGTH 1m
1 m = 1000 mm
CF = 1000
8.3. TIME 1s
1 s = 1 s
CF = 1
8.4. FORCE 1N
1 N = 0.1 ton*1000 mm/s^2 = 100 ton*mm/s^2
CF = 100
8.5. STRESS 1Pa
1 Pa = 1N/m^2 = 100 ton*mm/s^2 /(1000 mm)^2 = 1e-4 ton*mm/s
CF = 1e-4
8.6. ENERGY 1Nm
1 J = 1Nm = 0.1 ton*(1000 mm)/s^2*1000 mm = 1e5 ton*mm^2/s^2
CF = 1e5
8.7. DENSITY 1Kg/m3
The density is a mass divided by a volume
1 Kg/m^3 = 0.1 ton/(1000mm)^3 = 1e-10 g/cm^3
CF = 1e-10
8.8. YOUNG'S Modulus 210GPa
1Pa = 1e-4 ton*mm/s -> 1 GPa = 1e5 ton*mm/s -> 210 GPa = 210e5 ton*mm/s
CF = 1e5
8.9. Velocity 56.33KMPH
The velocity corresponds to a ratio between a displacement and a time interval:
56.33 Km/h = 56.33 1000000 mm/(3600s) = 15647.2 mm/s
CF = 277.78
8.10. GRAVITY 9.8m/s2
The gravity acceleration has the units of a displacement divided by a time squared.
9.8 m/s2 = 9.8*1000mm/s2 = 9800 mm/s2
CF = 1000