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[Phys-l] Deltas in equations



At 3:42 PM -0400 4/27/06, Edmiston, Mike wrote:
Larry, what book is that? I am intrigued not only for the wording of
cause/effect, but also because of the use of delta-V. I keep telling
students of cases where the textbook should be writing delta-something,
but they just write something, and that isn't such a good idea. I
haven't seen any textbooks that get serious about writing delta when
they should. Does this textbook also use delta in other places it
should be used, such as delta-U(spring) = 1/2 k delta-(x^2)?

The book (which will be out this fall) is the College Physics (by Jones,
Field, Knight http://www.aw-bc.com/info/knight_college/ ) version (bio,
pre-med, allied health version) of Randy Knight's Physics for Scientists
and Engineers.

Knight's PSE is also usually very good about the Delta's. For example, his
kinematic equation for uniform acceleration is
s_f = s_i + v_is Delta-t + (1/2) a_s (Delta-t)^2;
Hooke's law is
(F_sp)_s = -k Delta-s
Elastic potential energy is
U_s = (1/2) k(Delta-s)^2
Work is
W = \vec{F} dot Delta-\vec{r}
All the circuit equations use Delta-V
and he uses the Delta's very consistently, not just upon introduction of a
given concept.


But back to cause and effect.
Knight states (page 109) after giving N2 as (Eqn 4.3) \vec{a} = \vec{F}_net / m
"We can rewrite Newton's second law in the form \vec{F}_net = m \vec{a}
which is how you'll see it presented in many textbooks. Equations 4.3 and
4.4 are mathematically equivalent, but Equation 4.3 better describes the
central idea of Newtonian mechanics: A force applied to an object causes
the object to accelerate."

Larry