Acceleration Due to Gravity
Behr Free-Fall Apparatus and Spark Timer
You will perform an experiment to measure the acceleration due to gravity using the Behr spark timer
apparatus. You will measure distances on the spark timer tape, and then fit linear and quadratic functions
to your data and plot theoretical and experimental results.
A metal object, the “bob”, is held at the top of a vertical post by an
electromagnet. At regular time intervals, high-voltage sparks pass
between the bob and a ground plane, passing through a strip of
waxed paper and leaving a black burn hole. When the release button
is pressed, the electromagnet releases the bob at the same time as the
first spark is generated. As the bob falls, every one-sixtieth of a
second, an additional mark is created on the paper tape. By
measuring the distances from the starting point on the tape to each
successive point, you can create a record of the position of the bob
as a function of time.
The position of a freely falling object is given by:
y = 12 gt 2  v0 t + y0
where g (= 9.81 m/s2) is the acceleration due to gravity.
Let the next spark mark be Point 1 at distance y1 m and time t1 =
1/60 s, the next one be Point 2 at distance y2 m and time t2 = 2/60 s,
and so on. The position of the bob yn at time tn is given by:
yn = 12 gt 2n  v0 t n + y0
(1)
and the instantaneous velocity:
v n = gt n  v0
(2)
In principle, then, you can obtain an experimental value for g from
our spark tape data by three different methods: 1) Fit a quadratic
curve to a plot of yn vs. tn (the coefficient of the “t2” term would be
equal to 1/2g, the coefficient of the “t” term would be equal to v0,
and the coefficient of the “1” would be equal to y0 (=0)), 2) Fit a
straight line of slope ½g to a plot of yn vs. tn2, or 3) Fit a straight line
of slope g and intercept v0 to a plot of vn vs. tn.
PROCEDURE
1. Wheel the Behr apparatus into position. Use the three adjustable feet to plumb the column using
the bubble level on the back of the column.
2. One student can feed the tape from the bottom roll while a
second student pulls the tape up the column, then over the
top, and attaches it to the clip on the back of the column.
The first student then takes up the slack at the bottom roll.
Examine the tape to make sure there are no extraneous
preliminary marks on it. The tape is easily scratched so
treat it gently while preparing for a run and then removing
the tape for measuring.
3. Switch on the spark timer power.
4. Hang the bob from the electromagnet at the top and make sure it is at rest.
5. Press and hold the spark timer button at the end of the cord. Release the
button when the bob hits the catch cup and the bottom.
6. Switch off the spark timer power.
7. Carefully remove the tape and take it to your bench.
MEASURING THE TAPE
1. Create a table with three columns: Spark Dot n,
Time tn, and Distance yn. The length will be
about 30-32 rows.
2. Place the spark tape on the table and tape down
its ends.
3. The first few spark dots do not necessarily
represent “free fall” due to the relaxation time
of the electromagnet in dropping to zero field
strength when you first depress the sparker
button. Therefore, we will start with, say, the
third spark dot rather than the first dot. This
defines the starting dot from which we will
make all measurements.
Label third spark dot as the starting dot n = 0.
This will be the starting point for measuring
distance and time (t0 = 0 and y0 = 0).
4. Turn a 2-meter stick on edge and line up its
scale markings with the spark dots on your tape.
Make sure the 0-point of the meter stick remains
lined up with your n=0 spark dot during all of
your distance measurements.
5. For each dot, calculate the time elapsed tn,
measure the distance fallen yn, and record the
values in your table. Note that since the sparks
occur at the rate of every 1/60th of a second:
t n  n  ( 160) .
6. Calculate the average velocity over each time
interval by finding the change in distance
between two points and dividing it by 1/60th of a
second. Note that this would be the velocity at
the midpoint of the time interval for this pair of
points.
PLOTTING
If you are plotting by hand in a classroom and want to easily find the slope, plot either vn vs. tn2 or vn vs.
tn. From either straight line you can find the value of g and compare it with the standard value.
Here are some typical plots with Excel.