A Level Physics Notes: Experimental Physics – Measuring the Acceleration Due to Gravity Using Light Gates
Apparatus:
Free fall apparatus consisting of two sets of light gates, ball bearing and batteries, timer.
Diagram:
Procedure:
1. The apparatus should be mostly set up already as shown in the
diagram. However, you will need to connect the timer to the light
gates and align these gates. If the set up is correct, then as the
falling mass passes through the first gate the timer should start and
when the mass passes through the second gate the timer should stop.
In each case the mass interrupts the light beam at the gates. the
timer will read time,
to
± 0.01 second. The upper gate is fixed in position a distance
from
the top of the apparatus.
2. The lower light gate should be positioned initially about 55 cm
below the upper gate, measure this distance,
3. Allow the mass to fall from the top of the guide tube and so
obtain a time for the fall between the two light gates. Repeat twice
more and so obtain a mean value of
to
three significant figures.
4. Repeat stage 4 for seven further different distances of
fall,
between
55 cm and 120 cm.
Theory, Graph and Calculation:
Throughout the fall through distance,the
acceleration is assumed to be constant and equal to
the acceleration due to gravity. The velocity at the first light gate
equals
and
that at the second equals
with
time of fall equal to
Then
becomes
Also
becomes
but
therefore:
and so
which
we can write as
This equation has form
so
if a graph of
is
plotted on the
-
axis againston
the
-
axis it should be a straight line of gradient
Plot this graph and hence determine