Week - 1 - Consistency of Units

AIM : To Convert the Given Quantities to different unit systems. The Following are the given quantities

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

These Quantities have to be Converted to the following Units

1. Kg cm ms
2. Kg cm s
3. gm mm ms
4. kg m s
5. g cm s
6. g cm us
7. g mm s
8. ton mm s
9. slug ft s
10. kg mm s
11. g cm ms
12. kg mm ms

ANSWER :

1.Conversion for the Given SI Unit quantities in the respective desired Unit Systems

MASS 1Kg

Length 1m

Time 1s

Force 1N

Stress 1 Pa

Energy 1 Nm

Density 1Kg/m3

Young's Modulus 210 Gpa

Velocity 56.33 Kmph

Gravity 9.8 m/s2

Kg cm ms

1 kg

100 cm

1000 ms

10-4 kg*cm/(ms)2

1.0197x10-5 Kg/(cm)2

10.197162129779 Kg cm

10-6 kg/(cm)3

210x1013 Kg/(ms)2 *cm

1.564 cm/ms

980x10-6 cm/ms2

Kg cm s

1 kg

100 cm

1 s

102 Kg*cm/(s)2

1.0197x10-5 Kg/(cm)2

10.197162129779 Kg cm

10-6 kg/(cm)3

210x107 Kg/(s)2 *cm

1564.8 cm/s

980 cm/s2

Kg m s

1 kg

1 mt

1 s

1 Kg*mt/(s)2

0.1 Kg/(mt)2

0.102 Kg mt

1 Kg/m3

210x109 Kg/(s)2*mt

15.648 m/s

9.8 m/s2

g cm s

1000 g

100 cm

1s

105 g*cm/s2

1.0197x10-2 g/(cm)2

10197.162129779 g cm

10-3 g/(cm)3

210x1010 g/(s)2 *cm

1564.8 cm/s

980 cm/s2

g cm us

1000 g

100 cm

106 us

10-7 g*cm/(us)2

1.0197x10-2 g/(cm)2

10197.162129779 g cm

10-3 g/(cm)3

210x10-2 g/(us)2 *cm

1.564x10-3 cm/us

980x10-12 cm/us2

g mm s

1000 g

1000 mm

1 s

106 g*mm/(s)2

1.0197x10-4 g/(mm)2

101971.62129779 g mm

10-6 g/(mm)3

210x109 g/(s)2 *mm

15648 mm/s

9800 mm/s2

ton mm s

0.001 ton

1000 mm

1 s

10-3 ton*mm/(s)2

1.0036113565668x10-10 ton/(mm)2

0.10197 ton mm

10-12 ton/(mm)3

210x103 ton/(s)2 *mm

15648 mm/s

9800 mm/s2

slug ft s

0.0685218 slug

3.28084 ft

1 s

0.224808943 slug*ft/(s)2

0.0208854342 slug/(ft)2

0.2296 slug ft

0.0019403 slug/(ft)3

4.386x109 slug/(s)2 *ft

51.312 ft/s

32.152 ft/s2

kg mm s

1 kg

1000 mm

1 s

1000 kg*mm/(s)2

1.0197162129779x10-7 Kg/(mm)2

101.97 kg mm

10-9 kg/(mm)3

210x106 kg/s2mm

15648 mm/s

9800 mm/s

g cm ms

1000 g

100 cm

1000 ms

0.1 g*cm/(ms)2

0.010197162129779 g/(cm)2

10197.162129779 g cm

10-3 g/(cm)3

210x104g/(ms)2cm

1.564 cm/ms

980x10-6 cm/ms2

kg mm ms

1 kg

1000 mm

1000 ms

10-3 Kg*mm/(ms)2

1.0197162129779x10-7 Kg/(mm)2

101.97 kg mm

10-9 kg/(mm)3

210x102kg/(ms)2mm

15.64 mm/ms

9.8x10-3 mm/s2

2. Conversion from SI unit to g mm ms unit Systems

• MASS 1kg

1 kg=1000 g

• LENGTH 1m

1 mt = 1000 mm

• TIME 1s

1 s =1000 ms

• FORCE 1N

1N = 1 kg mt/`s^2`

= 1000 x 1000/`(1000)^2` g mm/`(ms)^2`

= 1 g mm/`s^2`

• STRESS 1Pa

1 pa = 1 Kg/mt`s^2`

= 1000 / (1000) x `(1000)^2` g/mm`(ms)^2`

= `10^-6` g/mm`(ms)^2`

• ENERGY 1Nm

1Nm = 1 kg / `s^2`

= 1000/ `(1000)^2` g/`s^2`

= `10^-3` g/`s^2`

• DENSITY 1Kg/`m^3`

1kg/`m^3`= 1000/`(1000)^3` g/`mm^3`

= `10^-6` g/`mm^3`

• YOUNG'S Modulus 210GPa

210 Gpa = 210 x `10^9` Kg/mt`s^2`

= (210 x `10^9`x 1000)/(1000)x `(1000)^2` g/mm`(ms)^2`

= 210 x `10^3` g/mm`(ms)^2`

• Velocity 56.33KMPH

56.33 Kmph = (56.33 x 1000)/3600 mt/s

= 15.64 mt/s

= (15.64 x 1000)/ (1000) mm/ms

= 15.64 mm/ms

• GRAVITY 9.8m/s2

9.8 m/`s^2` = (9.8 x 1000)/(1000)^2 mm/`(ms)^2`

= 9.8 x `10^3` mm/`s^2`

CONCLUSION : All the given quantities in the SI Unit were converted to the required Unit system successfully.