Carl wrote:
>
> Chap 14 #11. Two hundred grams hung on a spring stretches it 8.4 cm.
> How much energy is stored when stretched 8.4 cm?
I am mystified by this thread. It looks like
nit-picking to me.
And the nits seem even less important than usual.
The spring, as approximated by Hooke's law, is
linear. The gravitational field (over laboratory
length scales) is linear, indeed constant.
So no matter how you parse the question, you get
a force-versus distance diagram that is triangular,
Y high and X long, so it has area XY/2. If you
really work at it you can quibble about the sign,
but even so the intended sign is pretty obvious
from the statement of the problem.
The only thing that really needs to be assumed
is that the stretching begins or ends in some
equilibrium condition -- which seems like the
only natural notion of stretching, unless
otherwise specified.
-- Could the problem have been stated in more detail?
Sure.
-- Would the details have made any difference?
No, not as far as I can see.
It's not correct to claim that the answer is
"anything you want" because of gauge invariance
or the like; there's a perfeclty good gauge-
invariant interpretation of the question.