Week - 1 - Consistency of Units

Aim : The Aim of this challenge is to convert data from one unit sytem to other unit system and 

         to write their conversion factors.

For conversion from SI unit to gm/mm/ms unit system:

The SI unit is written as by mass in 'kg', length in 'm' and time in 's'. Other quantities are calculated from the fundamental quantities. Given in the problem are:

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 

To convert the above mentioned quantities to gm/mm/ms system of units:

 1 kg = 1000 gm

1 m = 1000 mm

1 s = 1000 ms

FORCE

Force of 1 N in SI units is given by

Force(N) = Mass(m) X Acceleration due to gravity(g)

1 N = 1 kg X 1 m/s²

Converting the above into gm/mm/ms form we get,

 1N = (1000gm * 1000mm)/1000²ms²          

1 N = 1 gm mm/ms²

STRESS

 The definition of stress is given by force acting per unit area. Stress (σ) and its SI unit is Pa

Stress = Force/Area

1 Pa = 1 N/1 m²

1Pa = (1gm mm/ms²)/0.001²

1 Pa = 10⁶ gm /mm s²

ENERGY

The  energy is given by amount of work done i.e force * displacement. The unit of energy is Nm.

Energy = Force * displacement

1 N-m = 1 N * 1m

1 N-m  = 1.00 gm mm/ms² * 0.001 mm

1 N-m = 10^-3 gm-mm²/ms²

DENSITY

 Density is defined as mass per unit volume. The unit of density is kg/m³ in SI unit.

 Density = mass (kg) / volume(m³)

 1 kg/m³ = 0.001 gm / (0.001)³

 1 kg/m³ = 10⁶ gm/mm³

 YOUNG’S MODULUS

Young’s Modulus is the elastic strength of a material.

The unit of Young’s modulus is GPa.

For the given material, the value of Young’s modulus is 210 GPa.

To convert to gm/mm/ms

210 GPa = (210 * 10⁹ * 10⁶ gm mm/ms² )/ mm²

210 GPa = 2.10 * 10¹⁸ gm mm/ms²

VELOCITY

Velocity is displacement per unit time. Its unit in SI system is m/s. Given in the problem is 56.33 kmph.

56.33 kmph = 56.33 * 10³ * 0.001 / 3600 * 0.001

56.33 kmph = 15.37 mm/ms

GRAVITY

Gravity is same acceleration due to gravity and is calculated from the law of gravitational force equation. Its value on earth is estimated as 9.8 m/s² in SI unit.

 9.8 m/s² = 9.8 * 0.001 / 0.001²

 9.8 m/s² = 9800 mm/ms²     

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