Determining yield stress via a bar subjected to tensile force

[Al_Pa_Cone]

Homework Statement

Homework Equations

All Equations Below

The Attempt at a Solution

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[PhanthomJay]

You are using the wrong area for the cylinder. What should it be?

 

[Al_Pa_Cone]

Do I use the area of a circle as the force is acting on the circular end? pi r^2

 

[Chestermiller]

Do I use the area of a circle as the force is acting on the circular end? pi r^2

Of course. The force is equal to the stress times the cross sectional area.

 

[Al_Pa_Cone]

Does This look better?

 

[mjc123]

Once again, 1 m² is NOT 1000 mm²! And GN m is not a unit of force.

 

[Al_Pa_Cone]

I should have noticed that given the fact I only did it last week! As for the units, I think GPa is the correct unit to use in my answer? I am getting mixed up by force measured in Newtons and Newton meters as a measurment. I have reworked my answer again?

 

[Chestermiller]

I should have noticed that given the fact I only did it last week! As for the units, I think GPa is the correct unit to use in my answer? I am getting mixed up by force measured in Newtons and Newton meters as a measurment. I have reworked my answer again?
View attachment 111305

Looks OK, except for the units. GPa is a unit of stress, not force. It would be better to just give the answer in N.

 

[Al_Pa_Cone]

That would be 117.6 Pascals then.

Thanks!

 

[mjc123]

No it wouldn't. You have a stress in GPa and you multiply it by an area in m². What are the units of the answer?

 

[Al_Pa_Cone]

Sorry I did not read the last comment properly,

Looks OK, except for the units. GPa is a unit of stress, not force. It would be better to just give the answer in N.

I only caught half of it in my emails (Looks OK, except for the units. GPa) and assumed it was ok.

As my undertanding goes with these units:

A Pascal is a unit which can be used for internal pressure acting in all directions equally within a material
A Newton is a unit which can represent force which acts upon a structure or an object
meters and millimeters is obviously a measurement of distance
meters^2 is a measurement of 2 dimensional area
meters^3 is a measurement of 3 dimensional area

The part where I get mixed up is when I have a GN m^-2

a Giga Newton is type of unit and a m^-2 is another but when do you choose to drop the distance/ area measurement out of the final answer giving a Force answer in simply Newtons or Giga Newtons rather than Newton meters ect

So... I am unsure whether my answer should be in Newtons or Newton meters
As the calculations go I presume they are ok so my attempted answer is:

 

[Chestermiller]

Much better.

 

[mjc123]

You don't "choose to drop the distance/area measurement", as if this was optional. It disappears as a result of being multiplied by a distance/area measurement. N m^-2 * m² = N.
Remember, quantity equals number plus unit. Until you get the hang of this I would strongly advise you to write your units in your calculations, e.g.
Force = 6 x 10^-3 GN m^-2 * 1.96 x 10^-5 m² = 1.176 x 10^-7 GN
And you should just learn the basic units for common quantities, e.g:
Force: N = kg m s^-2
Energy: J = N m = kg m² s^-2
Pressure and Stress: Pa = N m^-2
Strain: m/m = dimensionless (sometimes we use "units" like με = 10^-6 m/m)
etc.

 

[Al_Pa_Cone]

I think I need to read up some more on common units and measurements, It was introduced into the earlier assignments without covering in the maths bridging course I completed before starting this HNC,. Once again I thank you!