Just confusing myself with the standard form I think

[Probability]

I am just practicing some examples from a text book Mechanical Engineering Principles.

On page 10 there are some examples of Hooke's Law questions.

I have posted in this section because I think I am misunderstanding the basics somewhere in the conversions of units.

The question asks;

A circular bar is 2.5m long and has a diameter of 60mm. When subjected to a compressive load of 30kN the bar shortens by 0.20mm.

Determine the Young's Modulus E

I was ok going through the book up to this point then I thought what am I doing wrong?

I said; Note this line / means divide.

Stress = Force / Area, and

strain = extension x / original length L, and

E = stress / strain

so,

I know that F = 30 x 10^3 N

Area = pi x d^2 / 4 implies

A = Pi x 0.06^2 / 4

A = 2.83 x 10^ -6 m^2

Stress = 30 x 10^3 N / 2.83 x 10^-6 m^2

Stress = 10.61 x 10^9 N/m^2

Strain = extension x / original length L

Strain = 0.0002 / 0.0025

Strain = 0.08

E = 10.61 x 10^9 N/m^2 / 0.08

E = 132.6 x 10^9 pa or 132.6 Gpa

The area is the part I thought I was getting a little mixed up with during conversion

Thanks for any advice received.

 

[HallsofIvy]

I am just practicing some examples from a text book Mechanical Engineering Principles.

On page 10 there are some examples of Hooke's Law questions.

I have posted in this section because I think I am misunderstanding the basics somewhere in the conversions of units.

The question asks;

A circular bar is 2.5m long and has a diameter of 60mm. When subjected to a compressive load of 30kN the bar shortens by 0.20mm.

Determine the Young's Modulus E

I was ok going through the book up to this point then I thought what am I doing wrong?

I said; Note this line / means divide.

Stress = Force / Area, and

strain = extension x / original length L, and

E = stress / strain

so,

I know that F = 30 x 10^3 N

Area = pi x d^2 / 4 implies

A = Pi x 0.06^2 / 4

A = 2.83 x 10^ -6 m^2

Your first multiplication is wrong. this should be 10^-3, not 10^-6.

Stress = 30 x 10^3 N / 2.83 x 10^-6 m^2

Stress = 10.61 x 10^9 N/m^2

Strain = extension x / original length L

Strain = 0.0002 / 0.0025

Where did "0.0025" come from? I thought you were working in meters and the length was given as 2.5 m, not 0.0025 m.

Strain = 0.08

E = 10.61 x 10^9 N/m^2 / 0.08

E = 132.6 x 10^9 pa or 132.6 Gpa

The area is the part I thought I was getting a little mixed up with during conversion

Thanks for any advice received.

 

[wjm11]

I am just practicing some examples from a text book Mechanical Engineering Principles.

On page 10 there are some examples of Hooke's Law questions.

I have posted in this section because I think I am misunderstanding the basics somewhere in the conversions of units.

The question asks;

A circular bar is 2.5m long and has a diameter of 60mm. When subjected to a compressive load of 30kN the bar shortens by 0.20mm.

Determine the Young's Modulus E

I was ok going through the book up to this point then I thought what am I doing wrong?

I said; Note this line / means divide.

Stress = Force / Area, and

strain = extension x / original length L, and

E = stress / strain

so,

I know that F = 30 x 10^3 N

Area = pi x d^2 / 4 implies

A = Pi x 0.06^2 / 4

A = 2.83 x 10^ -6 m^2

Stress = 30 x 10^3 N / 2.83 x 10^-6 m^2

Stress = 10.61 x 10^9 N/m^2

Strain = extension x / original length L

Strain = 0.0002 / 0.0025

Strain = 0.08

E = 10.61 x 10^9 N/m^2 / 0.08

E = 132.6 x 10^9 pa or 132.6 Gpa

The area is the part I thought I was getting a little mixed up with during conversion

Thanks for any advice received.

Watch your units; you seem to have made multiple errors that cancelled out during your calculations:

Your area calculation is off by three orders of magnitude: A = Pi x 0.06^2 / 4 = 2.83 x 10^-3 m^2 (not 10^-6)

Your strain calculation is off by three orders of magnitude. Strain = .0002 m/2.5 m = .00008 = 8 x 10^-5

P/A = Stress = 30 x 10^3 N / 2.83 x 10^-3 m^2= 1.06 x 10^7 N/m^2

E = stress/strain = (1.06 x 10^7 N/m^2)/( 8 x 10^-5) = 1.33 x 10^11 N/m^2 = 1.33 x 10^11 pa = 1.3 x 10^2 Gpa = 130 Gpa

Note: you only get two significant digits in your answer, based on the problem statement inputs.

Please check my calculations for accuracy.

 

[Probability]

Watch your units; you seem to have made multiple errors that cancelled out during your calculations:

Your area calculation is off by three orders of magnitude: A = Pi x 0.06^2 / 4 = 2.83 x 10^-3 m^2 (not 10^-6)

Your strain calculation is off by three orders of magnitude. Strain = .0002 m/2.5 m = .00008 = 8 x 10^-5

P/A = Stress = 30 x 10^3 N / 2.83 x 10^-3 m^2= 1.06 x 10^7 N/m^2

E = stress/strain = (1.06 x 10^7 N/m^2)/( 8 x 10^-5) = 1.33 x 10^11 N/m^2 = 1.33 x 10^11 pa = 1.3 x 10^2 Gpa = 130 Gpa

Note: you only get two significant digits in your answer, based on the problem statement inputs.

Please check my calculations for accuracy.

Thank you, do I assume then that the answer given in the text book as 132.6 Gpa is incorrect then?

 

[wjm11]

Thank you, do I assume then that the answer given in the text book as 132.6 Gpa is incorrect then?

Depends on the problem statement. To be technically correct regarding significant digits, if the problem stated 60mm instead of 60.mm, then you only have one significant digit. Same with the "30kN". In that case, your final answer should only have one significant digit: 100 Gpa. The answer of "132.6" displays four significant digits.

 

[Probability]

Your first multiplication is wrong. this should be 10^-3, not 10^-6.


Where did "0.0025" come from? I thought you were working in meters and the length was given as 2.5 m, not 0.0025 m.

With regards my first multiplication which you advise is wrong, where you say this should be 10^-3, not 10^-6.

I tried that method but could not achieve the correct answer according to the text book.

My reasoning for my methods is this;

The circular bar in the question is quoted as 2.5m in length, and the shortened length when loaded is 0.20mm.

I thought the industry agreed standard was to convert mm to m when working out area, so I did convert as follows;

A = Pi x d^2 / 4 = Pi x (60/1000)^2 / 4 = 0.002827433

Now in standard form that area looks like this;

2.83 x 10^-6 m^2

Do you agree with me so far?

Now if I take stress = force / area like this;

30 x 10^3 N / 2.83 x 10^-6 m^2 = 10.61 x 10^9 N/m^2

Because

30 / 2.83 = 10.60 and moving the base 10^-6 to the numerator position becomes 10^3 + 10^6 = 3 + 6 = 10^9

so the stress is 10.61 x 10^9 N/m^2

Then strain = extension x / original length L

So,

strain = (0.20/1000) / (2.5/1000) = 0.0002 / 0.0025 = 0.08

extension x is the amount of movement we are looking for, so it seems right to measure it in mm and not m

so my conclusion

10.61 x 10^9 N/m^2 / 0.08 = E

E = 132.6 x 10^9 pa or 132.6 Gpa

Do you not agree?

 

[Deleted member 4993]

With regards my first multiplication which you advise is wrong, where you say this should be 10^-3, not 10^-6.

I tried that method but could not achieve the correct answer according to the text book.

My reasoning for my methods is this;

The circular bar in the question is quoted as 2.5m in length, and the shortened length when loaded is 0.20mm.

I thought the industry agreed standard was to convert mm to m when working out area, so I did convert as follows;

A = Pi x d^2 / 4 = Pi x (60/1000)^2 / 4 = 0.002827433

Now in standard form that area looks like this;

2.83 x 10^-6 m^2..................... Incorrect Area = 2.83*10^-3 m²

Do you agree with me so far? ..... No ... see above

Now if I take stress = force / area like this;

30 x 10^3 N / 2.83 x 10^-3 m^2 = 10.61 x 10^6 N/m^2

Because

30 / 2.83 = 10.60 and moving the base 10^-6 to the numerator position becomes 10^3 + 10^6 = 3 + 6 = 10^9..... No ... see above

so the stress is 10.61 x 10^6 N/m^2

Then strain = extension x / original length L

So,

strain = (0.20/1000) / (2.5/1000) = 0.0002 / 0.0025 = 0.08 .... Incorrect Strain = (0.20/1000)/2.5 m/m = 0.00008 = 80 * 10^-6

Modulus = (10.

extension x is the amount of movement we are looking for, so it seems right to measure it in mm and not m

so my conclusion

10.61 x 10^6 N/m^2 / (0.08 *10^-3)= E

E = 132.6 x 10^9 pa or 132.6 Gpa

Do you not agree? ..... Yes and No ... Yes to the numerical answer but No to the arithmetic involved (Or may be it should be No and Yes as Mark suggested)

.

 

[Probability]

.

Something does not add up there Subhotosh Khan, surely if your arithmetic is correct and mine is way out then you should at least end up somewhere near the correct answer?

Up to now I have worked through this book and managed to get every answer they provide correct, and on this last one struggled a little until the end, but managed to achieve their answer provided, yet your answer is;

1.32625 x 10^11?

when they say;

132.6 x 10^9

I know I am no expert but if you were lining a rocket to go to the moon, you just sent your rocket to the sun

 

[Probability]

.

I Probability advised;

Now in standard form that area looks like this;

2.83 x 10^-6m^2

and you advised

2.83 x 10^-6 m^2..................... Incorrect Area = 2.83*10^-3 m²

Are you sure?

60mm / 1000 = 0.06 m

That means if I am correct that 0.06 is representing 60mm as 0.06 of a metre, not metres squared?

If the dividing factor is indeed 1000, then 1000 converts to meters, but 1000 x 1000 is 10^6, which represents m^2 surely?

 

[Deleted member 4993]

I Probability advised;

Now in standard form that area looks like this;

2.83 x 10^-6m^2

and you advised

2.83 x 10^-6 m^2..................... Incorrect Area = 2.83*10^-3 m²

Are you sure?

60mm / 1000 = 0.06 m

That means if I am correct that 0.06 is representing 60mm as 0.06 of a metre, not metres squared?

If the dividing factor is indeed 1000, then 1000 converts to meters, but 1000 x 1000 is 10^6, which represents m^2 surely?

You are having serious problems in working with decimals!!

I suggest you do this problem step-by-step - as shown below - without skipping any intermediate steps.

π * d²/4 = π/4 * (60/1000)² = π/4 * (6/100)² = π/4 * 36 * 10^-4 = 9*π*10^-4 = 28.27433 *10^-4 = 28.27433*10^-1 *10^-3 = 2.827433 *10^-3 = 2.83 *10^-3

Please make sure you understand every step of the calculation done above.

 

[Probability]

You are having serious problems in working with decimals!!

I suggest you do this problem step-by-step - as shown below - without skipping any intermediate steps.

π * d²/4 = π/4 * (60/1000)² = π/4 * (6/100)² = π/4 * 36 * 10^-4 = 9*π*10^-4 = 28.27433 *10^-4 = 28.27433*10^-1 *10^-3 = 2.827433 *10^-3 = 2.83 *10^-3

Please make sure you understand every step of the calculation done above.

It seems that I am not alone in this matter?

You say;

You are having serious problems in working with decimals!!

I suggest you do this problem step-by-step - as shown below - without skipping any intermediate steps.

π * d²/4 = π/4 * (60/1000)² = π/4 * (6/100)² = π/4 * 36 * 10^-4 = 9*π*10^-4 = 28.27433 *10^-4 = 28.27433*10^-1 *10^-3 = 2.827433 *10^-3 = 2.83 *10^-3

Please make sure you understand every step of the calculation done above.

The two lines of RED decimals are correct, they equal each other, and are the same as my workings, however just so we are clear on this, 10^-1 and 10^-3 do not equal 10^-3, they do indeed = 10^-4.

The green decimals above to the power 10^-3 are therefore not equal as you state, but I will accept that they being to the power 10^-3 represent meters, but until you can explain with common sense how you got from 10^-4 to 10^-3, and explain how 10^-3 represents m^2 I believe you also have an arithmetic learning curve to achieve

The original question said that the diameter was 60mm and not mm^2

 

[Deleted member 4993]

It seems that I am not alone in this matter?

You say;

You are having serious problems in working with decimals!!

I suggest you do this problem step-by-step - as shown below - without skipping any intermediate steps.

π * d²/4 = π/4 * (60/1000)² = π/4 * (6/100)² = π/4 * 36 * 10^-4 = 9*π*10^-4 = 28.27433 *10^-4 = 28.27433*10^-1 *10^-3= 2.827433 *10^-3 = 2.83 *10^-3

Please make sure you understand every step of the calculation done above.

The two lines of RED decimals are correct, they equal each other, and are the same as my workings, however just so we are clear on this, 10^-1 and 10^-3 do not equal 10^-3, they do indeed = 10^-4.

The green decimals above to the power 10^-3 are therefore not equal as you state, but I will accept that they being to the power 10^-3 represent meters, but until you can explain with common sense

how you got from 10^-4 to 10^-3,→ by moving the decimal point one position to left (or dividing by 10) ← 28.27 * 10^-4 = 2.827 * 10^-3 watch the decimal point


and explain how 10^-3 represents m^2 ← one has nothing to with the other


I believe you also have an arithmetic learning curve to achieve

The original question said that the diameter was 60mm and not mm^2 → irrelevant statement - π * d²/4 calculates area using d and squaring it ← d ^2 or d ²

.

 

[Probability]

Keeping things as simple as I can here.

I have 60mm and I want the area A

A = Pi * d^2 / 4

A = 2827,433388 mm

Now I want it in metres m

A = Pi * d^2 / 4

A = Pi * (60/1000)^2 / 4

A = 0.002827433 m^2 (this I take you to mean it is in metres squared)

From this point you have multiplied by 1000 to move 3 place values to the right to get;

2.83 * 10^-3 m^2

Now studying the information and decimal place value the maths book I have does not make reference to counting from the right hand end of the numbers, i.e.

0.002827433 (counting from the right to the left)

2.83 * 10^-6 m^2

I see your point and initially as previously said I did try to work out the problem using that method but could not achieve the solution provided, yet when I follow the text book examples and their methods I achieve their solutions.

It seems the rules must change between every day maths and engineering when looking at practical examples. Researching the authors work they are not actually following the same maths reasoning as you, by example;

Keeping with my example on this thread.

Stress = Force / Area

Stress = 30 x 10^3 / 2.83 x 10^-6 m^2

I can see the difference here now between the book and you.

You are following the maths arithmetic idea of multiplying by 1000 to get from;

0.02827433 to end up with 2.83 x 10^-3, but

the author of the book seems to have done this;

0.02827433 and counted six places to the left to end up with;

2.83 x 10^-6

can you see what they have done?

Now in standard form the author has done this;

Stress = 30 x 10^3 N / 2.83 x 10^-6 m^2 = 30 / 2.83 = 10.60070671

Then the author has moved the base 10 up to the numerator position and added the powers so that 10^3 + 10^6 = 10^9

If you don't follow this reasoning the magnitude of the answer is significantly different.

This is why maths is so difficult because one cannot just apply text book ideas because practical work seems to move the goal posts, and if this were not so then the forces etc would be a mile out.

Don't worry I am confused and learning all the time as well

 

[Deleted member 4993]

Keeping things as simple as I can here.

I have 60mm and I want the area A

A = Pi * d^2 / 4

A = 2827,433388 mm..............Incorrect .... Dimension of area is mm² (or mm^2)

A = π/4 * d² = 3.14159 * (60)²/4 mm² = 2827.433 mm² = 2827.433 * 10^-6 m² = 2.827433 * 10^-3 m²

Now I want it in metres m

A = Pi * d^2 / 4

A = Pi * (60/1000)^2 / 4

A = 0.002827433 m^2 (this I take you to mean it is in metres squared)

From this point you have multiplied by 1000 to move 3 place values to the right to get;

2.83 * 10^-3 m^2

Now studying the information and decimal place value the maths book I have does not make reference to counting from the right hand end of the numbers, i.e.

0.002827433 (counting from the right to the left)

2.83 * 10^-6 m^2

I see your point and initially as previously said I did try to work out the problem using that method but could not achieve the solution provided, yet when I follow the text book examples and their methods I achieve their solutions.

It seems the rules must change between every day maths and engineering when looking at practical examples ( no they don't - you are misinterpreting the process). Researching the authors work they are not actually following the same maths reasoning as you, by example;

Keeping with my example on this thread.

Stress = Force / Area

Stress = 30 x 10^3 / 2.83 x 10^-6 m^2

I can see the difference here now between the book and you.

You are following the maths arithmetic idea of multiplying by 1000 to get from;

0.02827433 to end up with 2.83 x 10^-3, but

the author of the book seems to have done this;

0.02827433 and counted six places to the left to end up with;

2.83 x 10^-6

can you see what they have done?

Now in standard form the author has done this;

Stress = 30 x 10^3 N / 2.83 x 10^-6 m^2 = 30 / 2.83 = 10.60070671

Then the author has moved the base 10 up to the numerator position and added the powers so that 10^3 + 10^6 = 10^9

If you don't follow this reasoning the magnitude of the answer is significantly different.

This is why maths is so difficult because one cannot just apply text book ideas because practical work seems to move the goal posts (that is because you are not paying proper attention), and if this were not so then the forces etc would be a mile out.

Don't worry I am confused and learning all the time as well

.It seems that you are taking "on-line" course or trying to teach yourself. Bad idea!!

Please get a face-to-face teacher to have these FUNDAMENTAL OPERATIONS explained.

 

[Probability]

In all "probability", .......

Well I dug out some old maths information from college over 10 years back, and I have to say guys that I am somewhat disappointed with your misunderstanding of maths regards this question and worked solution I posted, as I said previously we all need to learn this subject properly.

I pointed out that 2.83 x 10^-6 m^2 was correct because I said 1000 x 1000 = 10^6, but it seems some of you were not having this and saying I was wrong, well actually I am right, and here is why.

60mm^2 = 3600mm and 3600 / 1000 = 3.6 x Pi / 4 = 2.83 x 10^9

Now another way

(60/1000)^2 * Pi / 4 = 0.002827433 which in standard form is 2.83 x 10^-3

But it seems that the author of the book has completed it this way

60mm^2 implies

mm^2 to m^2

1mm = 1 x 10^-3 m

1mm^2 = (10^-3m)^2

1mm^2 = 10^-6 m^2

So in the example

2.83 x 10^-6 m^2 is correct by this method.