There has been disagreement on how a spring balance is used to measure a
force. Here are my instructions. I'd appreciate comments from everybody,
even Marlow.
BTW let me again publically state that I appreciate the effort Marlow has
taken in this thread, I have read literature I would never have read
otherwise. And if I may quote Churchill in his description of Erwin Rommel,
may I say across the great divide of conflict I have formidable opposition.
Which is good as it forces me to more precise than I otherwise be. Hence,
why I've asked for clarifications in the Kepler problem.
Instructions for how to use a spring balance to measure a force:
These set of instructions are for use in an inertial frame of reference!!
In studying forces (they will be real forces since we are in an inertial
frame of reference) acting on an object (say my cat, or to satisfy the live
subjects committee at the university a solid massive block); Fred, our
scientist, (apologies to anybody whose name is Fred, no similarity is
implied) discovers a force acting on the object. He does this by observing
an acceleration in the object, legitimate conclusion in an inertial frame
(everybody agrees to this, I hope). And by taking into all other forces on
the object he discovered this force. Let's call it "Fred's force" to give
it a name.
He also finds that he can easily repeat the experimental set-up.
Repeatability is necessary in order to use a spring balance, and in fact to
do science.
(1) Fred, being an intrepid scientist wants to measure this force and he
decides to do this with a spring balance. Now how does he do this and draw
his conclusions. Well, he must arrange matters so that the force of the
spring will balance Fred's force.
(2) In order to do this he must orient the spring so that the direction of
the spring force on the block is oppositely pointed to the direction of
Fred's force on the object.
As a corollary to this step I might add that he has to anchor the other end
of the spring to some fixed surface in the laboratory (the inertial frame)
(3) And to be in balance means that he must also arrange it such that the
acceleration of the block is zero. (or else we haven't set up a balance,
this is what Marlow means when he says you have to wait until the
oscillations die out) In others words we must set up a static equilibrium
situation.
(I will note, parenthetically, setting up an equilibrium situation is
implicitly measuring the acceleration of the block, because you must measure
its acceleration to be zero to know that you are in an equilibrium
situation)
(4) This being done you read the scale reading on the spring balance, which
has been previously calibrated against known forces.
(5) Fred's force, being a good force, is a vector and has magnitude and
direction.
(6) The magnitude of Fred's force is the scale reading from the spring
balance.
(7) The direction of Fred's force acting on the object is opposite to the
direction of the spring force on the object.
Warning: You may have difficulty in using this device to measure velocity
dependent forces and the manufacturer implies no warranty on the device or
measurements made by the device when used in such a manner.
(I haven't thought long enough on how one would use the spring balance for a
velocity dependent force, the equilibrium situation can't be v=0 and a=0 for
your object since that removes the force you are trying to measure, so for
now the instructions above are for position dependent forces only.)