Talk to a counsellor
CoursesIIT ProgramsProjectsPlacementsFor BusinessBlogLog inTalk to a counsellor
Challenge

Week - 1 - Consistency of Units

AAsad K P22 Mar 2024
LS-DYNA

Week - 1 - Consistency of Units

Question

The values of the following measurements are given as follows

Sl No Property Value Unit
1 Mass 1 kg
2 Length 1 m
3 Time 1 s
4 Force 1 N
5 Stress 1 Pa
6 Energy 1 Nm
7 Density 1 kg/m^3
8 Young's Modulus 210 GPa
9 Velocity 56.33 KMPH
10 Gravity 9.8 m/s^2

Write the given measurements in the below different system of units. Also, mention the conversion factors.

  1. Kg cm ms

  2. Kg cm s

  3. gm mm ms

  4. Kg m s

  5. g cm s

  6. g cm `mus`

  7. g mm s

  8. ton mm s

  9. slug ft s

  10. kg mm s

  11. g cm ms

  12. kg mm ms

Answers

LS-DYNA doesn't have a default system of units. User needs to input material properties and physical dimensions according to a consistent system of units as per their choice.

The conversion can be done by following a table that is provided in the LS-DYNA support. The table is attached below.

The question involves the SI unit system comprising 'kg', 'm', and 's'. Utilize the table below for assistance. We need to convert it into the mentioned unit systems.

MASS LENGTH TIME FORCE STRESS ENERGY DENSITY YOUNG's 35MPH
56.33KMPH		 GRAVITY
kg m s N Pa J 7.83e+03 2.07e+11 15.65 9.806
kg cm s 1.0e-02 N 7.83e-03 2.07e+09 1.56e+03 9.806e+02
kg cm ms 1.0e+04 N 7.83e-03 2.07e+03 1.56 9.806e-04
kg cm us 1.0e+10 N 7.83e-03 2.07e-03 1.56e-03 9.806e-10
kg mm ms kN GPa kN-mm 7.83e-06 2.07e+02 15.65 9.806e-03
g cm s dyne dyne/cm² erg 7.83e+00 2.07e+12 1.56e+03 9.806e+02
g cm us 1.0e+07 N Mbar 1.0e+07 Ncm 7.83e+00 2.07e+00 1.56e-03 9.806e-10
g mm s 1.0e-06 N Pa 7.83e-03 2.07e+11 1.56e+04 9.806e+03
g mm ms N MPa N-mm 7.83e-03 2.07e+05 15.65 9.806e-03
ton mm s N MPa N-mm 7.83e-09 2.07e+05 1.56e+04 9.806e+03
lbf-s²/in in s lbf psi lbf-in 7.33e-04 3.00e+07 6.16e+02 386
slug ft s lbf psf lbf-ft 1.52e+01 4.32e+09 51.33 32.17
kgf-s²/mm mm s kgf kgf/mm² kgf-mm 7.98e-10 2.11e+04 1.56e+04 9.806e+03
kg mm s mN 1.0e+03 Pa 7.83e-06 2.07e+08 9.806e+03
g cm ms 1.0e+1 N 1.0e+05 Pa 7.83e+00 2.07e+06 9.806e-04
1. Kg cm ms

To convert values from 'kg m s' to the unit system outlined in the table below.


Sl. No

Parameters

 SI Unit System (kg m s) Conversion Factor Unit System (kg cm ms)
1 Mass 1 kg 1

1 kg
2 Length 1 m 10^2

10^2 cm
3 Time 1 s 10^3

10^3 ms
4 Force 1 N = 1 kg m/s^2 10^-4

10^-4 kg cm/ms^2
5 Stress 1 Pa = 1 N/m^2 10^-8

10^-8 kg/cm ms^2
6 Energy 1 J = 1 Nm 10^-2

10^-2 kg cm^2/ms^2
7 Density 1 kg/m^3 10^-6

10^-6 kg/cm^3
8 Young's Modulus 210 GPa = 210*10^9 N/m^2 10^-8

2100 kg/cm ms^2
9 Velocity 56.33 kmph = (56.33*1000)/(60*60) = 15.647 m/s 10^-1

1.5647 cm/ms
10 Gravity 9.8 m/s^2 10^-4

9.8*10^-4 cm/ms^2

The calculations for each unit conversion

  1. Mass (kg - kg)
    For the mass, both have the same units.

    Mass = 1kg
    Conversion Factor = 1
    After the conversion, Mass = 1*1 = 1kg



  2. Length (m - cm)
    To convert m to cm,
    1m = 10^2 cm

    So, Length = 1m,
    Conversion Factor = 10^2
    After the conversion, Length = 1*10^2 = 10^2 cm



  3. Time (sms)
    To convert s to ms,
    1s = 10^3 ms

    So, Time = 1s,
    Conversion Factor = 10^3
    After the conversion, Time = 1*10^3 = 10^3ms



  4. Force (N - kg-cm/ms^2)
    We know 1N = 1 kg m/s^2. To convert 'kg m/s^2' to 'kg-cm/ms^2',

    1 kg m/s^2 = 1*10^2/((10^3)^2)
    = 10^-4 kg-cm/ms^2

    So, Force = 1N,
    Conversion Factor = 10^-4
    After the conversion, Force = 1*10^-4 = 10^-4 kg cm/ms^2



  5. Stress (Pa - kg cm ms^2)
    We know 1Pa = 1 N/m^2 = 1 kg/m s^2. To convert 'kg/m s^2' to 'kg/cm ms^2',

    1 kg/m s^2 = 1/((10^2)*(10^3)^2)
    = 10^-8 kg/cm ms^2

    So, Stress = 1Pa,
    Conversion Factor = 10^-8
    After the conversion, Stress = 1*10^-8 = 10^-8 kg/cm ms^2



  6. Energy (J - kg cm^2/ms^2)
    We know 1J = 1 Nm = 1 kg m^2/s^2. To convert 'kg m^2/s^2' to 'kg cm^2/ms^2',

    1 kg m^2/s^2 = 1*(10^2)^2/((10^3)^2)
    = 10^-2 kg cm^2/ms^2

    So, Energy = 1J,
    Conversion Factor = 10^-2
    After the conversion, Energy = 1*10^-2 = 10^-2 kg cm^2/ms^2


  7. Density (kg/m^3 - kg/cm^3)
    To convert 'kg/m^3' to 'kg/cm^3',

    1 kg/m^3 = 1/((10^3)^2)
    = 10^-6 kg/cm^3

    So, Density = 1kg/m^3,
    Conversion Factor = 10^-6
    After the conversion, Density = 1*10^-6 = 10^-6 kg/cm^3


  8. Youngs Modulus (GPa - kg/cm^3)
    We know 1 GPa = 10^9 Pa = 10^9 N/m^2 = 10^9 kg/m s^2. To convert 'kg/m s^2' to 'kg/cm ms^2',

    10^9 kg/m s^2 = 10^9/((10^2)*(10^3)^2)
    = 10 kg/cm ms^2

    So, Youngs Modulus = 210 GPa = 210*10^9 Pa,
    Conversion Factor = 10^-8
    After the conversion, Youngs Modulus = 210*10^9*10^-8 = 2100 kg/cm ms^2




  9. Velocity (KMPH - cm/ms)
    We know 1 KMPH = 1000/(60*60) = 5/18 m/s. To convert 'm/s' to 'cm/ms',

    1 m/s = 10^2/10^3
    = 10^-1 cm/ms

    So, Velocity = 56.55 KMPH = (5/18)*56.55 m/s = 15.647 m/s,
    Conversion Factor = 10^-1
    After the conversion, Density = 15.647*10^-1 = 1.5647 cm/ms



  10. Gravity (m/s^2 - cm/ms^2)
    To convert m/s^2 to cm/ms^2,

    1 m/s^2 = 1*10^2/(10^2)^3
    = 10^-4 cm/ms^2

    So, Gravity = 9.81 m/s^2
    Conversion Factor = 10^-4
    After the conversion, Density = 9.81*10^-4 = 9.81*10^-4 cm/ms^2

Similarly, we can convert all the SI unit systems to the given unit system

2. Kg cm s

To convert values from 'kg m s' to the unit system outlined in the table below.

Sl. No

Parameters

 SI Unit System (kg m s) Conversion Factor Unit System (kg cm s)
1 Mass 1 kg 1

1 kg
2 Length 1 m 10^2

10^2 cm
3 Time 1 s 1

1 s
4 Force 1 N = 1 kg m/s^2 10^-2

10^-2 kg cm/s^2
5 Stress 1 Pa = 1 N/m^2 10^-2

10^-2 kg/cm s^2
6 Energy 1 J = 1 Nm 10^4

10^4 kg cm^2/s^2
7 Density 1 kg/m^3 10^-6

10^-6 kg/cm^3
8 Young's Modulus 210 GPa = 210*10^9 N/m^2 10^7

210*10^7 kg/cm s^2
9 Velocity 56.33 kmph = (56.33*1000)/(60*60) = 15.647 m/s 10^2

1564.7 cm/s
10 Gravity 9.8 m/s^2 10^2

9.8*10^2 cm/s^2
3. gm mm ms

To convert values from 'kg m s' to the unit system outlined in the table below.

Sl. No

Parameters

 SI Unit System (kg m s) Conversion Factor Unit System (gm mm ms)
1 Mass 1 kg 10^3

10^3 gm
2 Length 1 m 10^3

10^3 mm
3 Time 1 s 10^3

10^3 ms
4 Force 1 N = 1 kg m/s^2 1

1 gm mm/ms^2
5 Stress 1 Pa = 1 N/m^2 10^-6

10^-6 gm/mm ms^2
6 Energy 1 J = 1 Nm 10^3

10^3 gm mm^2/ms^2
7 Density 1 kg/m^3 10^-6

10^-6 gm/mm^3
8 Young's Modulus 210 GPa = 210*10^9 N/m^2 10^3

210*10^3 gm/mm ms^2
9 Velocity 56.33 kmph = (56.33*1000)/(60*60) = 15.647 m/s 1

15.647 mm/ms
10 Gravity 9.8 m/s^2 10^-3

9.8*10^-3 mm/ms^2
4. kg m s

To convert values from 'kg m s' to the unit system outlined in the table below.

Sl. No

Parameters

 SI Unit System (kg m s) Conversion Factor Unit System (kg m s)
1 Mass 1 kg 1

1 kg
2 Length 1 m 1

1 m
3 Time 1 s 1

1 s
4 Force 1 N = 1 kg m/s^2 1

1 kg m/s^2
5 Stress 1 Pa = 1 N/m^2 1

1 kg/m s^2
6 Energy 1 J = 1 Nm 1

1 kg m^2/s^2
7 Density 1 kg/m^3 1

1 kg/m^3
8 Young's Modulus 210 GPa = 210*10^9 N/m^2 1

210*10^9 kg/m s^2
9 Velocity 56.33 kmph = (56.33*1000)/(60*60) = 15.647 m/s 1

15.647 m/s
10 Gravity 9.8 m/s^2 1

9.8 m/s^2
5. gm cm s

To convert values from 'kg m s' to the unit system outlined in the table below.

Sl. No

Parameters

 SI Unit System (kg m s) Conversion Factor Unit System (gm cm s)
1 Mass 1 kg 10^3

10^3 gm
2 Length 1 m 10^2

10^2 cm
3 Time 1 s 1

1 s
4 Force 1 N = 1 kg m/s^2 10^5

10^5 gm cm/s^2
5 Stress 1 Pa = 1 N/m^2 10

10 gm/cm s^2
6 Energy 1 J = 1 Nm 10^7

10^7 gm cm^2/s^2
7 Density 1 kg/m^3 10^-3

10^-3 gm/cm^3
8 Young's Modulus 210 GPa = 210*10^9 N/m^2 10^10

210*10^10 gm/cm s^2
9 Velocity 56.33 kmph = (56.33*1000)/(60*60) = 15.647 m/s 10^2

1564.7 cm/s
10 Gravity 9.8 m/s^2 10^2

9.8*10^2 cm/s^2
6. gm cm `mus`

To convert values from 'kg m s' to the unit system outlined in the table below.

Sl. No

Parameters

 SI Unit System (kg m s) Conversion Factor Unit System (gm cm `mus`)
1 Mass 1 kg 10^3

10^3 gm
2 Length 1 m 10^2

10^2 cm
3 Time 1 s 10^6

10^6 `mus`
4 Force 1 N = 1 kg m/s^2 10^-7

10^-7 gm cm/`mus`^2
5 Stress 1 Pa = 1 N/m^2 10^-11

10^-11 gm/cm `mus`^2
6 Energy 1 J = 1 Nm 10^-5

10^-5 gm cm^2/`mus`^2
7 Density 1 kg/m^3 10^-3

10^-3 gm/cm^3
8 Young's Modulus 210 GPa = 210*10^9 N/m^2 10^-11

210*10^-11 gm/cm `mus`^2
9 Velocity 56.33 kmph = (56.33*1000)/(60*60) = 15.647 m/s 10^-4

15.647*10^-4 cm/`mus`
10 Gravity 9.8 m/s^2 10^-10

9.8*10^-10 cm/`mus`^2
7. gm mm s

To convert values from 'kg m s' to the unit system outlined in the table below.

Sl. No

Parameters

 SI Unit System (kg m s) Conversion Factor Unit System (gm mm s)
1 Mass 1 kg 10^3

10^3 gm
2 Length 1 m 10^3

10^3 mm
3 Time 1 s 1

1 s
4 Force 1 N = 1 kg m/s^2 10^6

10^6 gm mm/s^2
5 Stress 1 Pa = 1 N/m^2 10^3

10^3 gm/mm s^2
6 Energy 1 J = 1 Nm 1

1 gm mm^2/s^2
7 Density 1 kg/m^3 10^-6

10^-6 gm/mm^3
8 Young's Modulus 210 GPa = 210*10^9 N/m^2 10^9

210*10^9 gm/mm s^2
9 Velocity 56.33 kmph = (56.33*1000)/(60*60) = 15.647 m/s 10^3

15.647*10^3 mm/s
10 Gravity 9.8 m/s^2 10^3

9.8*10^3 mm/s^2
8. ton mm s

To convert values from 'kg m s' to the unit system outlined in the table below.

Sl. No

Parameters

 SI Unit System (kg m s) Conversion Factor Unit System (ton mm s)
1 Mass 1 kg 10^-3

10^-3 ton
2 Length 1 m 10^3

10^3 mm
3 Time 1 s 1

1 s
4 Force 1 N = 1 kg m/s^2 1

1 ton mm/s^2
5 Stress 1 Pa = 1 N/m^2 10^-6

10^-6 ton/mm s^2
6 Energy 1 J = 1 Nm 10^3

10^3 ton mm^2/s^2
7 Density 1 kg/m^3 10^-12

10^-12 ton/mm^3
8 Young's Modulus 210 GPa = 210*10^9 N/m^2 10^3

210*10^3 ton/mm s^2
9 Velocity 56.33 kmph = (56.33*1000)/(60*60) = 15.647 m/s 10^3

15.647*10^3 mm/s
10 Gravity 9.8 m/s^2 10^3

9.8*10^3 mm/s^2
9. slug ft s

To convert values from 'kg m s' to the unit system outlined in the table below.

Sl. No

Parameters

 SI Unit System (kg m s) Conversion Factor Unit System (slug ft s)
1 Mass 1 kg 0.068

0.068 Slug
2 Length 1 m 3.28

3.28 ft
3 Time 1 s 1

1 s
4 Force 1 N = 1 kg m/s^2 0.22304

0.22304 slug ft/s^2
5 Stress 1 Pa = 1 N/m^2 0.02073

0.02073 slug/ft s^2
6 Energy 1 J = 1 Nm 0.73157

0.73157 slug ft^2/s^2
7 Density 1 kg/m^3 0.00192

0.00192 slug/ft^3
8 Young's Modulus 210 GPa = 210*10^9 N/m^2 20.7317*10^6

4.35365*10^9 slug/ft s^2
9 Velocity 56.33 kmph = (56.33*1000)/(60*60) = 15.647 m/s 3.28

51.32216 ft/s
10 Gravity 9.8 m/s^2 3.28

32.144 ft/s^2
10. kg mm s

To convert values from 'kg m s' to the unit system outlined in the table below.

Sl. No

Parameters

 SI Unit System (kg m s) Conversion Factor Unit System (kg mm s)
1 Mass 1 kg 1

1 kg
2 Length 1 m 10^3

10^3 mm
3 Time 1 s 1

1 s
4 Force 1 N = 1 kg m/s^2 10^3

10^3 kg mm/s^2
5 Stress 1 Pa = 1 N/m^2 10^-3

10^-3 kg/mm s^2
6 Energy 1 J = 1 Nm 10^6

10^6 kg mm^2/s^2
7 Density 1 kg/m^3 10^-9

10^-9 kg/mm^3
8 Young's Modulus 210 GPa = 210*10^9 N/m^2 10^6

210*10^6 kg/mm s^2
9 Velocity 56.33 kmph = (56.33*1000)/(60*60) = 15.647 m/s 10^3

15647 mm/s
10 Gravity 9.8 m/s^2 10^3

9800 mm/s^2
11. gm cm ms

To convert values from 'kg m s' to the unit system outlined in the table below.

Sl. No

Parameters

 SI Unit System (kg m s) Conversion Factor Unit System (gm cm ms)
1 Mass 1 kg 10^3

10^3 gm
2 Length 1 m 10^2

10^2 cm
3 Time 1 s 10^3

10^3 ms
4 Force 1 N = 1 kg m/s^2 10^-1

10^-1 gm cm/ms^2
5 Stress 1 Pa = 1 N/m^2 10^-5

10^-5 gm/cm ms^2
6 Energy 1 J = 1 Nm 10

10 gm cm^2/ms^2
7 Density 1 kg/m^3 10^-3

10^-3 gm/cm^3
8 Young's Modulus 210 GPa = 210*10^9 N/m^2 10^4

210*10^4 gm/cm ms^2
9 Velocity 56.33 kmph = (56.33*1000)/(60*60) = 15.647 m/s 10^-1

1.5647 cm/ms
10 Gravity 9.8 m/s^2 10^-4

9.8*10^-4 cm/ms^2
12. kg mm ms

To convert values from 'kg m s' to the unit system outlined in the table below.

Sl. No

Parameters

 SI Unit System (kg m s) Conversion Factor Unit System (kg mm ms)
1 Mass 1 kg 1

1 kg
2 Length 1 m 10^3

10^3 mm
3 Time 1 s 10^3

10^3 ms
4 Force 1 N = 1 kg m/s^2 10^-3

10^-3 kg mm/ms^2
5 Stress 1 Pa = 1 N/m^2 10^-9

10^-9 kg/mm ms^2
6 Energy 1 J = 1 Nm 1

1 kg mm^2/ms^2
7 Density 1 kg/m^3 10^-9

10^-9 kg/mm^3
8 Young's Modulus 210 GPa = 210*10^9 N/m^2 1

210 kg/mm ms^2
9 Velocity 56.33 kmph = (56.33*1000)/(60*60) = 15.647 m/s 1

15.647 mm/ms
10 Gravity 9.8 m/s^2 10^-3

9.8*10^-3 mm/ms^2

Please note that for Young's Modulus, the SI unit is considered to be GPa, and the conversion factor calculations are based on GPa.

Conclusion

The conversion of SI units to the specified unit systems has been completed, and the values have been individually tabulated.

Your portfolio, next

Ship work like this
in your own course.

Talk to a career counsellor

Free 20-minute call. We'll map the right course to where you want to work.

By submitting you agree to our Terms and Privacy Policy.