This is one of my favorite demonstrations. I supervise it, but students
do the work. I do it similar to the way Vicki Frohne decribed, with the
added feature that I place a penny on the floor where we predict the
ball will land. I use a one-inch ball bearing, and it leaves a dent on
the penny. I can hit Abraham Lincoln on the cheek every time.
There are some tools/tricks you can do to help guarantee success. It is
instructive for the students to see all these tools/tricks at work.
(1) The end of the ramp is about a meter from the end of the table. We
measure the velocity of the ball as it rolls across this one meter
distance before falling off the table. A C-clamp holds a small board at
the end of the table to stop the ball so it won't roll off during our
measurement of the velocity.
(2) For best results we use a magnetic release to start the ball down
the ramp. If using hand release, let students practice and see who can
get the most consistent velocities.
(3) For best results, use two photogates placed 0.5 to 1.0 meter apart
to measure delta-t and then calculate the velocity. In the absence of
photogates you can use a stop watch, but measure delta-t a bunch of
times so you can get a reasonably good measure of the velocity.
(4) Once you know the velocity, and you know the height of the table,
you can calculate the range of the ball. Now the difficult part is
locating this distance from the edge of the table in-line with the
velocity of the ball.
I have a piece of 1/2-inch electrical conduit about 2 meters long.
Starting about 5-cm from one end, I ruled the conduit with a centimeter
scale using a "Sharpie" marker. I remove the clamp from the end of the
table and one student holds the zero-end of the conduit on the table
with the zero mark lined up with the end of the table where the ball had
been hitting the clamped board.
Another student holds the other end of conduit on top of a two-by-four
cut the same length as the table-to-floor distance. This student can
sight down the center of the conduit and move it back and forth until
she sees the end of the ramp through the conduit. This should line the
conduit up with the path of the ball. Other students can sight this
from the ramp, or from behind the student holding the end, to help
confirm it is in-line with the predicted trajectory of the ball.
A string and weight are used as a plumb line. The top of the string is
tied in a loop that sides over the conduit. A third student slides the
plumb-line loop along the conduit, watching the cm-scale, and
positioning the top of the plumb-line at the calculated distance from
the end of the table. A fourth student steadies the plumb-line from
swinging, and marks the spot on the floor where we predict the ball will
land. In our lab we mark it on a cement floor with a marker, but you
can use a piece of tape.
Remove the conduit, the clamp is already removed, place Abraham Lincoln
at the predicted landing spot. Before releasing the ball, see who wants
to bet a dollar against you hitting the penny. With a magnetic release,
photogate timers, and supervising the alignment, I've never missed.
With stopwatch timers and hand release you might want to use a nickel or
a quarter. Students usually want to see it again. Once the spot on the
floor is marked you can do it again and again, another nice lesson that
physics is not a fluke. Be prepared to pass out slightly-dinged pennies
as souvenirs.
Michael D. Edmiston, Ph.D.
Professor of Physics and Chemistry
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu
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