Physics 2LA
Acceleration Due To Gravity
(contains pre lab assignment**)
This laboratory involves an experimental determination of a value for the acceleration due to
gravity at the surface of the earth,
g
.
You will:
•
Measure g for different fall distances.
•
Measure
g
for different falling objects.
•
Consider sources of error, and estimate their influence on the measurement.
An emphasis of this experiment is on
recognizing
and
estimating
the various uncertainties that
contribute to
error
in measurement. We have learnt about Random (or Statistical) errors and
Resolution (or precision) errors in lab 1. Here we will also consider
Systematic Errors
.
Please
re read your lab 1 section on error analysis if you are still not comfortable with the concept. Also
review the
video module on error analysis and significant figures
. The prelab assignment
provides you with practice on calculating and propagating errors.
Please turn in the prelab
assignment at the start of the lab.
Apparatus
•
Free fall apparatus
•
Steel balls
•
Computer with data acquisition
interface and analysis software
•
2meter stick
•
Precision balance
•
Vernier calipers
The Physics
For a body starting at rest (
v
0
= 0) falling with a constant acceleration due to gravity, the equation
of motion is
2
2
1
gt
y
−
=
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View Full Documentwhere
y
is the distance (height) the object falls,
t
is the time of fall, and
g
is the acceleration of
gravity.
Sources of Error
Experimental error can usually be divided into three broad categories.
1.
Random
(
Statistical) Error (
Δ
ran
):
These are errors related to the random errors involved in
making the measurements. It is usually be reduced by repeating the act of measurement
many times. An example is the measurement of time intervals with clocks where there are
errors in starting and stopping the clock, which means that every time you drop something, it
takes a slightly different time interval to reach the floor.
The value of this error as we saw in
lab 1 is given by
n
ran
σ
=
Δ
, where
is the standard deviation and
n
is the number of
measurements made.
2.
Resolution (Precision) Errors (
Δ
res
):
This is an error related to the smallest size of length
or interval of time that you can measure with the instruments that you are using. For
example,
we cannot measure distance to better than about 1 mm with the meter stick you
will be using.
Also, the time interval measurement has a minimum resolution of
0.001s due
to the method used.
3.
Systematic Errors (
Δ
sys
)
: These are errors that skew the measurements in one direction due
to a imperfection in the equipment or a factor that is neglected in the analysis. For example
the wooden meter stick you are using was marked at 90
o
F in the factory but is now a slightly
different size as the room temperature is 75
o
F.
Systematic errors are common to all of the
measurements, and therefore cannot be reduced by simply repeating the experiment.
Other
more possible systematic errors in the free fall measurement are:
(a) Air resistance.
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 Spring '09
 robertclare
 TA, Observational error, ΔG

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