Re: Kinematics

[Bernard Cleyet <anngeorg@PACBELL.NET>]

"Having students run provides a kinesthetic
experience that can aid learning, but it is
difficult for a runner to maintain a constant
acceleration for an extended time.

We perform a somewhat similar experiment
using a cart accelerated across a table by a
hanging mass.  We use a spark timer to record
the displacement of cart every 0.1 s.  This
experiment provides an acceleration that is
essentially constant, but does not provide
a kinesthetic experience."


Every physics lab should include a round about (merry go round), thereby, one may experience a constant acceleration.  Furthermore, one may vary it my changing ones distance from the axis in addition to spinning it faster.  These devices are rare for insurance and legislative reasons.  UCSC has one directly incorporated in an intro. lab.  It is fitted with a removable plate on which one may observe the motion of balls and the precession of pendula.


I hope someday to construct a scaled up version of the hanging mass cart.  I hope 1/10 g  is sufficient to kinesthetically observe (feel?) acceleration.  In which case, one would need (for 5 s. of acceleration) ~ 40' of rope, two pulleys, a lightweight low friction cart and ~ 10 kg mass for the weight.  Terminal speed ~ 11 m/s.  Stopping* is the problem. Some students may land running (stand on cart with handle), if sitting, roll off the cart into a sand pit (long jump), or have a double pulley system.  One with about 20 kg and the other 10. Longer ropes and a method to release the larger mass at the midpoint.  This system is superior as one can "feel" the reversed direction of the acceleration.  Measurement can be done by the usual methods, viz. acoustical ranging spark timer, video, etc.  Of course, there is already Amusement Park Physics.

* If there is a method of avoiding the rope and a longer run, nearly constant speed is "experienced" after the weight lands.

I've already posted the reaction cart "experience" using a cart and a SCUBA tank.


bc

Dan Crowe wrote:

> If the acceleration is constant, then the average
> velocity during a time interval (t1 < t < t2)
> equals the instantaneous velocity at the midpoint
> of the time interval [t =3D (t1 + t2)/2].  If the
> midpoint of the time interval is used with the
> data given by Ludwik, then the calculated
> acceleration is inconsistent with the assumption
> that it is constant.
>
> I obtain the following values:
>
> t (s)        0.75     2.0     2.9     3.55
> Vav (m/s)    1.33     2.0     2.5     4.0
> Aav (m/s^2)      0.536   0.556    2.31
>
> The first two calculated values of acceleration
> are consistent with the assumption that the
> acceleration is constant, but the third value
> is clearly inconsistent with that assumption.
>
> If the acceleration is increasing (decreasing)
> monotonically, then the average velocity equals
> the instantaneous velocity at a time later
> (earlier) than the midpoint of the interval.
>
> If the final time reading was 4.0 s, then the
> final average velocity would be 2.86 m/s and
> would correspond to the instantaneous velocity
> at t =3D 3.65 s, assuming that the acceleration
> was constant.  In that case, the acceleration
> for the final interval would be 0.514 m/s^2,
> which would be more consistent with the
> assumption of constant acceleration.
>
> Having students run provides a kinesthetic
> experience that can aid learning, but it is
> difficult for a runner to maintain a constant
> acceleration for an extended time.
>
> We perform a somewhat similar experiment
> using a cart accelerated across a table by a
> hanging mass.  We use a spark timer to record
> the displacement of cart every 0.1 s.  This
> experiment provides an acceleration that is
> essentially constant, but does not provide
> a kinesthetic experience.
>
> Daniel Crowe
> Oklahoma School of Science and Mathematics
> Ardmore Regional Center
> dcrowe@sotc.org
>
>
> -----Original Message-----
> =46rom: Ludwik Kowalski [mailto:kowalskil@MAIL.MONTCLAIR.EDU]
cut