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Challenge

Week - 1 - Consistency of Units

JJayesh Pradhyumna9 Aug 2021

AIM:

To write the given measurements in the above different system of units and mention the conversion factors.

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

CONVERSION TO DIFFERENT UNITS:

SI unit / Measured quanitites

MASS

1 kg

LENGTH

1 m

TIME

1 sec

FORCE

1 N

STRESS

1 Pa

ENERGY 1 J

DENSITY

1 kg/m3

YOUNG'S Modulus

210 GPa

Velocity

56.33 kmph

GRAVITY

9.8 m/s2

Kg cm ms

x 1

x 100

x 10^3

x 10^-4

x 10^-8

x 10^-2

x 10^-6

x 10 x 210

x 1 / 36 x 56.33

x 10^-4

Kg cm s

x 1

x 100

x1

x 10^2

x 10^-2

x 10^4

x 10^-6

x 10^7 x 210

x 10^3/36 x 56.33

x 10^2

g mm ms

x 10^3

x 10^3

x 10^3

x 10^3

x 10^-3

x 10^6

x 10^-6

x 10^6 x 210

x 10/36 x 56.33

x 10^-3

kg m s

x 1

x 1

x 1

x1 kgm/s2

x 1 N/m2

x 1 Nm

x 1

x 10^9 x 210 N/m2

x 10/36 x 56.33

x 1

g cm s

x 10^3

x 100

x1

x 10^5

x 10

x 10^7

x 10^-3

x 10^10 x 210

x 10^3/36 x 56.33

x 100

g cm us

x 10^3

x 100

x 10^6

x 10^-7

x 10 ^-11

x 10^-5

x 10^-3

x 10^-2 x 210

x 1/36000 x 56.33

x 10^-10

g mm s

x 10^3

x 10^3

x1

x 10^6

x 1

x 10^9

x 10^-6

x 10^12 x 210

x 10^4/36 x 56.33

x 10^3

ton mm s

x 0.001

x 10^3

x1

x 1

x 10^-6

x 10^3

x 10^-12

x 10^3 x 210

x 10^4/36 x 56.33

x 10^3

slug ft. s

x 0.068

x 3.28

x 1

x 0.22

x 0.0205

x 7216

x 19

x 205x 10^5 x 210

x 0.911 x 56.33

x 3.28

kg mm s

x1

x 10^3

x1

x 10^3

x 10^-3

x 10^6

x 10^-9

x 10^6 x 210

x 10^3/36 x 56.33

x 10^3

g cm ms

x 10^3

x 100

x 10^3

x 0.1

x 10^3

x 10

x 10^-3

x 10^12 x 210

x 1 / 36 x 56.33

x 10^-4

kg mm ms

x1

x 10^3

x 10^3

x 10^-3

x 10^-9

x 1

x 10^-9

x 1 x 210

x 10/36 x 56.33

x 10^-4

Kg cm ms:

  • MASS - Conversion factor - x 1

  • LENGTH - Conversion factor - x 100

  • TIME - Conversion factor - x 10^3

  • FORCE - Conversion factor - x 10^-4

  • STRESS - Conversion factor - x 10^-8

  • ENERGY - Conversion factor - x 10^-2

  • DENSITY - Conversion factor - x 10^-6

  • YOUNG'S Modulus - Conversion factor - x 10

  • Velocity - Conversion factor - x 1/36

  • GRAVITY - Conversion factor - x 10^-4

Kg cm s:

  • MASS - Conversion factor - x 1

  • LENGTH - Conversion factor - x 100

  • TIME - Conversion factor - x 1

  • FORCE - Conversion factor - x 100

  • STRESS - Conversion factor - x 10^-2

  • ENERGY - Conversion factor - x 10^4

  • DENSITY - Conversion factor - x 10^-6

  • YOUNG'S Modulus - Conversion factor - x 10^7

  • Velocity - Conversion factor - x 1000/36

  • GRAVITY - Conversion factor - x 100

g mm ms:

  • Conversion of 1 kg Mass to g: kg -> g = x 1000 = x 10^3 g
  • Conversion of 1 m Length to mm: m -> mm = x 1000 = x 10^3 mm
  • Conversion of 1 s Time to ms: s -> ms = x 1000 = x 10^3 ms
  • Conversion of 1 N Force to gmm/ms2:

kg -> g = x 1000 = x 10^3

m -> mm = x 1000 = x 10^3

s -> ms = x 1000 = x 10^3

Therefore, (10^3 x 10^3)/10^3 = x 10^3 gmm/ms2

Conversion factor - x 10^3

  • Conversion of 1 Pa Stress to g/mm ms2:

1 Pa = 1 N/m2

From above conversion, 1 N = 10^3 kgmm/ms2

m -> mm = x 1000 = x 10^3

Therefore, 10^3 / (10^3 x 10^3) = x 10^-3 g/mm ms2

Conversion factor - x 10^-3

  • Conversion of 1 J Energy to gmm2/ms2:

1 J = 1 Nm

From above conversion, 1 N = 10^3 kgmm/ms2

m -> mm = x 1000 = x 10^3

Therefore, 10^3 x 10^3 = x 10^6 gmm2/ms2

Conversion factor - x 10^6

  • Conversion of 1 kg/m3 Density to g/mm3:

kg -> g = x 1000 = x 10^3

m -> mm = x 1000 = x 10^3

Therefore, 10^3 / (10^3 x 10^3 x 10^3) = x 10^-6 g/mm3

Conversion factor - x 10^-6

  • Conversion of 210 GPa Young's modulus to g/mm ms2:

GPa = x 10^9 Pa

From above conversion, 1 Pa = 10^-3 kgmm/ms2

Therefore, 10^9 x 10^-3 = x 10^6 g/mm ms2

Conversion factor - x 10^6

  • Conversion of 56.33 kmph Velocity to mm/ms:

km -> m = x 1000 = x 10^3, m -> mm = x 1000 = x 10^3, km -> mm = x 1000 = x 10^6

h -> min = x 60, min -> s = x 60, h -> s = x 60 x 60 = x 3600, s -> ms = x 1000 = x 10^3

Therefore, 10^6 / (3600 x 10^3) = x 10/36 mm/ms

Conversion factor - x 10/36

  • Conversion of 9.8 m/s2 Gravity to mm/ms2:

m -> mm = x 1000 = x 10^3

s -> ms = x 1000 = x 10^3

Therefore, 10^3 / (10^3 x 10^3) = x 10^-3 mm/ms2

Conversion factor - x 10^-3

kg m s:

  • MASS - Conversion factor - x 1

  • LENGTH - Conversion factor - x 1

  • TIME - Conversion factor - x 1

  • FORCE - Conversion factor - x 1

  • STRESS - Conversion factor - x 1

  • ENERGY - Conversion factor - x 1

  • DENSITY - Conversion factor - x 1

  • YOUNG'S Modulus - Conversion factor - x 10^9

  • Velocity - Conversion factor - x 10/36

  • GRAVITY - Conversion factor - x 1

g cm s:

  • MASS - Conversion factor - x 10^3

  • LENGTH - Conversion factor - x 100

  • TIME - Conversion factor - x 1

  • FORCE - Conversion factor - x 10^5

  • STRESS - Conversion factor - x 10

  • ENERGY - Conversion factor - x 10^7

  • DENSITY - Conversion factor - x 10^-3

  • YOUNG'S Modulus - Conversion factor - x 10^10

  • Velocity - Conversion factor - x 1000/36

  • GRAVITY - Conversion factor - x 100

g cm us:

  • MASS - Conversion factor - x 10^3

  • LENGTH - Conversion factor - x 100

  • TIME - Conversion factor - x 10^6

  • FORCE - Conversion factor - x 10^-7

  • STRESS - Conversion factor - x 10^10

  • ENERGY - Conversion factor - x 10^-11

  • DENSITY - Conversion factor - x 10^-5

  • YOUNG'S Modulus - Conversion factor - x 10^-3

  • Velocity - Conversion factor - x 1/36000

  • GRAVITY - Conversion factor - x 10^-10

g mm s:

  • MASS - Conversion factor - x 10^3

  • LENGTH - Conversion factor - x 10^3

  • TIME - Conversion factor - x 1

  • FORCE - Conversion factor - x 10^6

  • STRESS - Conversion factor - x 1

  • ENERGY - Conversion factor - x 10^9

  • DENSITY - Conversion factor - x 10^-6

  • YOUNG'S Modulus - Conversion factor - x 10^12

  • Velocity - Conversion factor - x 10^4 / 36

  • GRAVITY - Conversion factor - x 10^3

ton mm s:

  • MASS - Conversion factor - x 0.001

  • LENGTH - Conversion factor - x 10^3

  • TIME - Conversion factor - x 1

  • FORCE - Conversion factor - x 1

  • STRESS - Conversion factor - x 10^-6

  • ENERGY - Conversion factor - x 10^3

  • DENSITY - Conversion factor - x 10^-12

  • YOUNG'S Modulus - Conversion factor - x 10^3

  • Velocity - Conversion factor - x 10^4 / 36

  • GRAVITY - Conversion factor - x 10^3

slug ft. s:

  • MASS - Conversion factor - x 0.068

  • LENGTH - Conversion factor - x 3.28

  • TIME - Conversion factor - x 1

  • FORCE - Conversion factor - x 0.22

  • STRESS - Conversion factor - x 0.0205

  • ENERGY - Conversion factor - x 7216

  • DENSITY - Conversion factor - x 19

  • YOUNG'S Modulus - Conversion factor - x 205 x 10^5

  • Velocity - Conversion factor - x 0.911

  • GRAVITY - Conversion factor - x 3.28

kg mm s:

  • MASS - Conversion factor - x 1

  • LENGTH - Conversion factor - x 10^3

  • TIME - Conversion factor - x 1

  • FORCE - Conversion factor - x 10^3

  • STRESS - Conversion factor - x 10^-3

  • ENERGY - Conversion factor - x 10^6

  • DENSITY - Conversion factor - x 10^-9

  • YOUNG'S Modulus - Conversion factor - x 10^6

  • Velocity - Conversion factor - x 10^3 / 36

  • GRAVITY - Conversion factor - x 10^3

g cm ms:

  • MASS - Conversion factor - x 10^3

  • LENGTH - Conversion factor - x 100

  • TIME - Conversion factor - x 10^3

  • FORCE - Conversion factor - x 10^3

  • STRESS - Conversion factor - x 0.1

  • ENERGY - Conversion factor - x 10^3

  • DENSITY - Conversion factor - x 10

  • YOUNG'S Modulus - Conversion factor - x 10^-3

  • Velocity - Conversion factor - x 1/36

  • GRAVITY - Conversion factor - x 10^-4

kg mm ms:

  • MASS - Conversion factor - x 1

  • LENGTH - Conversion factor - x 10^3

  • TIME - Conversion factor - x 10^3

  • FORCE - Conversion factor - x 10^-3

  • STRESS - Conversion factor - x 10^-9

  • ENERGY - Conversion factor - x 1

  • DENSITY - Conversion factor - x 10^-9

  • YOUNG'S Modulus - Conversion factor - x 1

  • Velocity - Conversion factor - x 10/36

  • GRAVITY - Conversion factor - x 10^-4

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