Re: N2

[Mark Sylvester <msylvest@SPIN.IT>]

At 12:56 PM 7/3/00 -0700, John Barrer wrote:
>    Assuming that students are already familiar with
> the kinematics of linear acceleration as well as the
> relationship between mass and weight (force of Earth
> on an object), the modified Atwood requires very
> little hand waving. In the "Modeling" approach, the MA
> lab is at the start of the investigation of how force
> relates to acceleration. Use of a Pasco lab cart on a
> (level) lab table along with a low friction pulley to
> change pull direction gives very good results. Keeping
> system mass constant (means shifting masses from the
> cart to the hanger) produces a very nice straight line
> plot of acceleration vs. force whose slope is
> 1/(system mass). Or, keep the hanging mass (applied
> force) constant and vary the load in the cart to
> produce a straight line plot of acceleration vs.
> inverse mass whose slope is the applied force (due to
> hanging mass). Acceleration measurement is done with a
> photogate and a "picket fence" on the Pasco cart. Note
> that there is no need to measure the force applied to
> the cart since we're dealing with the acceleration of
> the SYSTEM (although you could so with a force probe -
> but that's too much at the outset, IMHO.)

But if you *do* use a force probe then you can make the lab more elementary
because you no longer have to analyze an Atwood Machine. The pulley and the
mass at the end of the string are merely a way to apply the force, which is
measured at the point of application. No need for mg either. The next step
is to get rid of the string and just push and pull the cart randomly by the
force sensor, while logging F and a. Pasco should modify the software so
that the force probe can be calibrated in arbitrary units. For this
experiment you don't want to measure force in newtons.

Related to this, I found something really nice when we were playing with
the Pasco track a few months back. The idea was to show that the
acceleration of a body projected upwards doesn't change as it goes up and
comes down again. The v-t graph should be a straight line, starting with
positive velocity, passing through zero at the top of the motion, and going
negative as the body comes down. (Of course a terribly difficult graph to
predict, sometimes even for people with a lot of basic physics behind
them). So we set the track at an incline and pushed the cart up, letting it
come down again, while logging the motion with the little ultrasound
sensor. We got a distinct kink in the graph as it passed through zero
velocity. The acceleration while the cart is going up has bigger magnitude
than while it's coming down, and the graph makes two pretty good straight
lines. Assuming that this is because the friction changes sign at the top
of the motion, one can go on to estimate the size  of the friction force
from this graph (you also need the mass of the cart). I was struck by how
easy it was to see and measure the effect with the datalogging stuff.

Mark