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ptc-30073261-Visitor
1-Visitor
November 17, 2011
Question

Mathcad confusing two very different types of quantities

  • November 17, 2011
  • 2 replies
  • 18829 views

Hi,

I am trying hard to get used to Mathcad. I am running into a very simple issue when using SI units.

At first I calculated the amount of work done using the equation: Work = Force x Distance and the answer was dispalyed in "J" or Joules.

But then I defined a new unit called "Nm" to identify torque quantities.

After creating the "Nm" unit, the work equation is giving an answer in "Nm" instead of "J". It is very frustrating. Can anybody help?

CSR

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2 replies

M
MikeArmstrong1-Visitor
1-Visitor
November 17, 2011

I don't understand. 1 Joule = 1 N*m. So what's the problem?

Mike

P
ptc-30073261-VisitorAuthor
1-Visitor
November 17, 2011

Joule (J) is used as a unit of ENERGY or WORK DONE. When the force (N) acts along the same direction as the displacement (m), we end up with energy.

Newton.Meter (Nm) is a unit to measure TORQUE. In this case, the force (N) acts perpendicular to the diatance (m).

Mathcad may not know which instance of the multiplication is being called for, i.e. whether we calculating an ENERGY or TORQUE. I would like to go and change the incorrect assignment of Nm to J for all my energy calculations.

M
MikeArmstrong1-Visitor
1-Visitor
November 17, 2011

In the International System of Units (SI), a newton meter is known as a unit of torque. It can also be used as a unit of energy. N*m is also used when calculating bending moments.

Mathcad may not know which instance of the multiplication is being called for, i.e. whether we calculating an ENERGY or TORQUE. I would like to go and change the incorrect assignment of Nm to J for all my energy calculations.

You can tell Mathcad which unit to choose in the options.

Mike

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PhilipOakley1-Visitor
1-Visitor
November 18, 2011

The units of Torque aren't simply Newton.metres, rather it is Newton.metres per radian. That is, you need to multiply Torque by Angle turned to compute the work (Energy - joules) expended.

The fact that SI doesn't get it right from the point of view of dimenion checking for 'out of plane' lengths is a matter of regret. You sould not be able to divide a length in direction X by a length in direction Y (X-Y-Z 3d corrdinates) without introducing a some notation that indicates the cancellation of a Length dimension - that 'Unit' is Angle, with some discussion about the choice of default unit - is it the revolution (cycle) or the Radian.

There has been extensive previous discussions on the point. I also wrote http://communities.ptc.com/docs/DOC-1522 and http://communities.ptc.com/docs/DOC-1501 (variants on a theme 😉

Thank you for bringing up the subject again!

Philip

    F
    Fred_Kohlhepp23-Emerald I
    23-Emerald I
    November 18, 2011

    Philip Oakley wrote:

    The units of Torque aren't simply Newton.metres, rather it is Newton.metres per radian. That is, you need to multiply Torque by Angle turned to compute the work (Energy - joules) expended.

    The fact that SI doesn't get it right from the point of view of dimenion checking for 'out of plane' lengths is a matter of regret. You sould not be able to divide a length in direction X by a length in direction Y (X-Y-Z 3d corrdinates) without introducing a some notation that indicates the cancellation of a Length dimension - that 'Unit' is Angle, with some discussion about the choice of default unit - is it the revolution (cycle) or the Radian.

    There has been extensive previous discussions on the point. I also wrote http://communities.ptc.com/docs/DOC-1522 and http://communities.ptc.com/docs/DOC-1501 (variants on a theme 😉

    Thank you for bringing up the subject again!

    Philip

    If you are looking for work done then I agree. But when I put a wrench on a bolt and tighten it I'm doing work until the bolt stops turning. At that point I have a torque (Newton metres) without work. At that point torque and bending moment both are correctly force times shortest distance. No?

    (Welcome back! Seems like I haven't seen you name in quite a while)

    P
    PhilipOakley1-Visitor
    1-Visitor
    November 18, 2011

    Fred Kohlhepp wrote:

    Philip Oakley wrote:

    The units of Torque aren't simply Newton.metres, rather it is Newton.metres per radian. That is, you need to multiply Torque by Angle turned to compute the work (Energy - joules) expended.

    <snip>

    At that point torque and bending moment both are correctly force times shortest distance. No?

    Correct; It's 'No'.

    The reason/problem that the two are different is that the Newton is force, which is mass * acceleration, and acceleration is length per time^2, so overall we have the confusion between Length * Lenght, and Length * Length, without any way to discriminate between the Length axes in use.

    If we had Lx, Ly and Lz as independent (unit) dimensions, which clearly they are as geometry dimensions, then it would all be obvious (Proposed by Williams in ~1896 or thereby!). So we could see N_x.m_y as being Torque, while N_x.m_x as Energy. But William's ideas never got anywhere....

    [Aside: the (1/2)m.v^2 kinetic energy is the same as E=mc^2 with relativity applied to the root(1-(v/c)^2) relativity term (with first order approximation), i.e. energy is the square of Length, not an area L_x.L_y ...]

    The alternative to William's Lx;Ly;Lz is to monitor how often we cancel out independant terms, i.e Lx/Ly, which is "Angle", though it is used as an (in)correctness monitor. That's why we do dimensional analysis - to detect mistakes.

    Historically all calculations were by hand, so could be done separately, but now with computers we no longer do those checks, especially if we code algorithms. But at least MathCAD will detect most unit/dimensions errors (not like MatLab....8-).

    BUT PTC FAILS TO DISTINGUISH Nm from mN (apparently somewhere in Pro/e you had to use that convention for the difference).

    PS You can define a variable called "Torque(Nm)" (using chemical notation) which can be put in the units place holder where required. You can even 'cheat and define Torque(Nm) := Joule instead of Torque(Nm) := metre.Newton <wink> . This will at least give the reader a proper understanding of the calculation result.

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