Week - 1 - Consistency of Units

Week - 1 - Consistency of Units

Aim:

Convert the below unit as per SI UNITS.

Value of the following measurements are given as follows:

1. MASS 1kg
2. LENGTH 1m
3. TIME 1s
4. FORCE 1N
5. STRESS 1Pa
6. ENERGY 1Nm
7. DENSITY 1Kg/m3
8. YOUNG'S Modulus 210GPa
9. Velocity 56.33KMPH
10. GRAVITY 9.8m/s2

Now, here are a few system of units:

Kg cm ms

Kg cm s

gm mm ms

kg m s

g cm s

g cm us

g mm s

ton mm s

slug ft s

kg mm s

g cm ms

kg mm ms

PROCEDURE:

For that below values are direct taken from measurement.

MASS	g	Kg	ton	slug
	1000	1	0.001	0.0685

LENGTH -1m=1000mm=100cm

LENGTH	mm	cm	m	ft
	1000	100	1	3.281

TIME -1s

TIME	s	Milliseconds (ms)	microsecond (us)
	1	1000	1000000

For that below values are formulated value. - “gm/mm/ms”

FORCE (N)

FORCE(N)=Mass*acceleration

Mass- “kg”

Acceleration-change velocity/change in time -m.s^-2

F=kg*m/s² Or kg.m.s^-1.s^-1

or

F=g.mm.ms^-2

STRESS 1Pa

STRESS 1Pa=1N/m²

=Force/area

= kg*m.s^-2/m²

=kg/m.s²

1Pa=g/mm.ms^-2

ENERGY 1Nm

J=lenth*force

=m* kg*m/s² /1000

=mm*g*mm/ms²

ENERGY 1Nm =g*mm²/ms²

DENSITY 1Kg/m3

DENSITY =Mass/volume=kg/m³

DENSITY 1Kg/m3=g/mm³

YOUNG'S Modulus 210GPa

E=stress/stain

E= g/mm.ms^-2

E=210gpa=210*10⁹N/m²

=210*10⁹ (kg*m/s² )/m²

=210*10⁹ (kg*m/s.s )/m.m

=210*10⁹ (kg*m/s.s )/m.m

=210*10^{9 3}(g*1000)/1000.ms*1000.ms*1000.mm

E=210*10³.g/mm.ms²

Velocity 56.33KMPH

Velocity=Distance/ time .m/s

1 km = 1000 m, 1 hr has 3600 sec. So 1 km/hr = 1000m/3600s = 5/18 m/s. To convert the speed from km/hr to m/s, multiply the speed by 5/18(0.277).

56.33km/h=56.33*0.2778m/s

Velocity 56.33KMPH =15.648m/s

=15.603.mm/ms

GRAVITY 9.8m/s2

Gravity=9.81m/s²

=9.81*1000*mm/1000.ms*1000.ms

=9.81*1000*mm/1000.ms*1000.ms

=0.00981mm/ms²