If I calcuate "energy per m^3", do I express the unit for my answer as "J" or "J/m^3"?

You will need to express this as J/m^3 to be fully correct, but it seems the answers assume it is not necessary because the question states ‘per m^3’.

If you’re calculating this as a precursor to a stress-strain analysis of the cable, you’ll be needing the work per cross-sectional area or J/m^2. If this is a stand-alone question, you can leave it in the J/m^3 form, since that’s what the question is asking for. There’s no need to cancel out the meters implied in the definition of Joule.

Ok thank you for the confirmation!
It appears that the textbook simply had a misprint in the back. J/m^3 it is :)

Technically, I don’t think the book is wrong, and neither are you.

“Calculate the work (energy) done per m^3 of this cable”.

One could say the work done per cubic meter of the cable is X joules. (this is what the book did)

One could also say that the work done on the cable is X J/m^3. (what you are saying)

Both say the same thing with slightly different phrasing.

Alright, thank you!
Sometimes exam questions try and trick students in multiple choice where the correct answer with units of J or J/m^3 are options.
But exam questions will presumably be phrased better.

Thanks lilikoi :)

@julia999 I wouldn’t count on it :)

Especially on some of the more cutthroat engineering exams such as the early college weed-out courses, or the post-grad FE. Someone forgot to tell the engineering profs that in the real world of engineering, you have much more than 2 minutes to put together an exact answer, and units only count if you’re working with a particularly difficult or foreign customer. Even in that case, most people I talk to on an every day basis know when I say “pound” it could mean psia, psig, lb-mass, or I could even be referring to the class rating of a flange. In all of these situations, the word “pound” means very different things, but it is said with a high degree of confidence in the understanding of your audience.

But to address the reality here – we’re talking about a college exam where reality-based situations have never crossed most professors’ minds. This fact proves to be probably the only dose of literary irony you will ever see in your engineering coursework.

Sorry for the downer – I’m 4 years in as a career engineer, and I love it, but I found college material useless then, and that feeling has only strengthened in the years since. Long rant here with little reason, but I hope all went well with your end of semester – good luck and take the FE immediately.