GPE.

[Derek Plattis]

Found this illustration in a student's physics text book. The question beside it was about gravitational potential energy.

GP Energy001.jpg

Perhaps our cause is spreading!

Derek

[Jim]

The question beside it was about gravitational potential energy.

What was the question?

[crfriend]

How new is the textbook? The character in the aeroplane seat is more than just a bit reminiscent of one of our lot here.

And, yes, "What was the question?"

[Derek Plattis]

How new is the textbook? And, yes, "What was the question?"

The text book is dated 2008 and the question is one of a string, each of which is dependent on the previous one. For that reason it is too long to quote here but it involves calculating whose wig ( toupee) it is. Data such as the heights involved, the mass of the wig and the loss of GPE when the wig fell is either given or derived from previous answers - fairly simple stuff designed to give practice in using equations.

Apparently, the man in the baggage compartment is there because he wanted to avoid the in-flight meal

I still can't quite get my head round the picture - it would only be necessary to have two bald-headed men in the picture. The seated man's outfit is an added bonus!

Derek

[Tor]

Two possibilities that come to minde regarding the picture is someone with a sense of humour trying to use the picture to elicit false assumptions as to the owner of the toupee - or some text writing trying to push the limits, like hackers trying to get assembler codes describing things unmentionable here past management at big corporations. I bet Carl could give you quite a list of the latter off the top of his head.

[ChrisM]

Despite the artist's intent to draw "Einstein in drag", my first glance thought was "Yep, that's me, that's what I look like and I'm OK with that."

Chris

Err: Just to be clear: I am claiming to look like the Doc in skirt, not the guy in the baggage bin!

[Derek Plattis]

Incidentally, it turns out that the wig belongs to the guy in the baggage compartment because in order to lose the given GPE it had to fall 2.5m. - So we're alright there then!

Derek

[Tor]

The wig fell 2.5m? Given my experience with aeroplanes that means it would probably have to have fallen from pretty much the ceiling - if that is even 2.5m. I'm never close to standing underneath the overhead baggage compartments, and I'm about 2m tall.

[Derek Plattis]

The wig fell 2.5m? Given my experience with aeroplanes that means it would probably have to have fallen from pretty much the ceiling - if that is even 2.5m. I'm never close to standing underneath the overhead baggage compartments, and I'm about 2m tall.

Yes, we may be reading too much into this I think, - It's only a GCSE textbook. (for 15-16 year old students).
however, it certainly couldn't have fallen off the head of the skirted man.
Anyway, I wish I had legs like his!

Derek

[crfriend]

Incidentally, it turns out that the wig belongs to the guy in the baggage compartment because in order to lose the given GPE it had to fall 2.5m. - So we're alright there then!

Ah, but we're dealing in inertial space here, and had the airliner been subject to a particularly violent downdraught then it's entirely possible for the entire space to go into negative-G for a short period of time which could have tossed the seated bloke's toupee off his head. (This is why the question was important.) (Several folks are injured this way every year, sometimes very severely.)

Clearly under a constant "down-force" of 1G then the math becomes pretty easy and the "potential energy" is a function of the "time to impact" (which equates very nicely to height if one has taken calculus) -- but, in many scenarios we are not subject to a constant gravitational acceleration, nor is gravity a constant planet-wide (OK, I'm really picking nits with that assertion, but the fact holds). Any ride on a high-speed roller-coaster will be enough to convince anyone of that, even if they can't keep their lunch onboard.

Even on low-speed conveyances this can become apparent. I walk at a fast enough pace and with a long enough stride that I am frequently in "inertial space" on trains; if I'm starting a step and the train enters a curve, my leading foot does not land where I originally intended it to unless I actively correct for the change.

Also, I rather suspect that GPE needs to be calculated for objects in a vacuum, which would not have been good at all for our seated skirted subject. (And, yes, I saw that drawing and immediately thought "ChrisM". Sorry, sir, but that's just the way my addled brain works.)

[Derek Plattis]

O.K. - as I said, this is only a GCSE physics question. I'd like to give you the whole thing but I'm too conscious of any further copyright violations.

All good fun!

Derek

[Tor]

I walk at a fast enough pace and with a long enough stride that I am frequently in "inertial space" on trains; if I'm starting a step and the train enters a curve, my leading foot does not land where I originally intended it to unless I actively correct for the change.

I sometimes marvel at how many ways we seem to be so similar despite the years, miles, and lineage that separate us. Despite not having experience with walking on trains (due to a dearth of trains in these parts), I have no doubt that the ground eating pace I tend to travel at would have me in the same position. One thing I have seen is that due to my long stride and propensity to use it at a fairly rapid rate I've been known to have quite a bit of inertial momentum in loaded shopping carts, despite not having made the change in inertial position to anything other than a fast walk. Those little casters can get a bit noisy even on those smooth floors.

Derek, last I checked, academic inquiry (which this arguably has become) tends to have much more relaxed copyright restrictions, but it is up to you.