Sample Formal Laboratory Report for Physics on the Picket Fence Lab without the
parachute
Purpose:
The purpose of this experiment is to verify the acceleration due to gravity using
the picket fence with a photogate, LabPro and LoggerPro software by measuring it with a
precision of 0.5% or better.
Theory:
All objects, regardless of mass, fall with the same acceleration due to gravity
assuming that there is no air resistance. Objects thrown upward or downward and those
released from rest are falling freely once they are released. Any freely falling object
experiences acceleration directed downward, regardless of the direction of its motion at
any instant. The symbol “g” is used for this special acceleration at the Earth’s surface.
The value of g is approximately 9.8 m/sec2. Since we are neglecting air friction and
assuming that the free fall acceleration is constant, the motion of a freely falling object is
equivalent to motion in one dimension under constant acceleration. Therefore the
constant acceleration equations can be applied. Objects falling downward only under the
influence of gravity can be graphically analyzed with a displacement versus time graph
shown by a parabolic curve described in graph 1. This graph shows that as the object is
falling, the displacement it travels each second is greater than the prior second. This
graph can be mathematically illustrated by the equation
1
y  vi t  at 2
2
which is the equation for displacement as a function of time.
y
v
t
graph 1
t
graph 2
Graph 2 shows the velocity as a function of time which is a linear relation for constant
acceleration shown by the equation v f  vi  at . Keeping acceleration constant, the
graph of acceleration versus time would be a horizontal line at the value of acceleration.
Definition of symbols used:
t = time
vi = initial velocity
a = acceleration
y = vertical displacement
vf = final velocity
g = acceleration due to gravity
Method:
1.
Set up the photogate in a stand as shown below, connected to a LabPro which is
connected to a PC. The photogate is attached to a ring stand to allow the picket
fence to fall between the legs of the photogate.
Picket
fence
2.
Open the loggerpro program, experiment 5 (picket fence) in the physics with
computers file.
3.
Hold the picket fence above the photogate so that it is oriented as shown above.
4.
Click on Collect, when the collect button turns to Stop, drop the picket fence
through the photogate—use a soft landing spot after the picket fence is clear. Be
sure to drop it vertically and ensure it does not touch the photogate as it falls.
5.
The computer will measure and graph the time it takes for each black line to pass
through the photogate. A displacement versus time and velocity versus time
graph will appear on the screen.
6.
Click on the velocity versus time graph to activate it and then click on the linear
fit button and include a best fit line to calculate the slope of the data. Record the
slope in data table 1.
7.
Do procedure 3-6 five more times.
8.
Complete the rest of table 1.
Data Collected:
Trial #
Slope
Accel. “g”
(m/sec2)
1
9.81
TABLE 1—Velocity Versus Time Graph
2
3
4
9.79
9.87
9.76
9.81
9.79
9.87
9.76
Average acceleration due to gravity, gavg = 9.815 m/s2  0.055
Accepted acceleration due to gravity, gaccepted = 9.8 m/s2
Precision = 0.56%
Percent difference = 0.15%
Analysis of Data:
The value for part one trial number 3 is significantly higher than the other trials.
Part one calculations
Average acceleration:
sum all 5 accelerations and divide by 5
( 9.81 + 9.79 + 9.87 + 9.76 + 9.82 m/s2) / 5 = 9.815 m/s2
Uncertainty: (maximum a – minimum a) / 2
(9.87  9.76 m/s2) / 2 = 0.055 m/s2
Precision: precision % 
uncertainty
100%
ave acceleration
5
9.82
9.82
0.055m / s 2
100%  0.56%
9.815m / s 2
Error calculation:
% difference 
%diff 
accepted value - measured value
accepted value
9.8  9.815 m / s 2
9.8 m / s 2
100
100  0.15%
Discussion:
The purpose of the experiment was to verify the acceleration due to gravity which
was done with 0.15% error and 0.56% precision. Since both the error and precision are
small, it shows that the experimental was fairly consistent and the average value is very
close to the accepted value of acceleration due to gravity. Since the picket fence fell
through a short distance close to sea level, the acceleration due to gravity remained
constant throughout the entire fall through the photogate. Each equidistant black line on
the picket fence passed through the gate in shorter and short time increments because it
was accelerating, resulting in the graphs used to collect the data.
Air resistance did have an effect on the falling fence but it was so minute, it did not affect
the data. If air resistance was large enough to affect the data, the acceleration due to
gravity would be less than 9.8 m/sec2. Performing this experiment in a vacuum would
eliminate the error due to air resistance, but both the experiment results and limitations of
the lab equipment show it is an unnecessary improvement. Other things that could cause
a change in experimental value of acceleration would be if the fence fell crooked or was
pushed down slightly. If the photogate fell crooked it would cause a slight decrease in
distance between black lines ultimately causing a change in acceleration. Having the
fence short keeps that error minimal. A reading such as part 1 trial 3 (9.87) which is
above the actual value of g indicates there may have been a minor problems with this
drop. Proper dropping technique will minimize many errors associated with this lab. An
automated dropping device would significantly improve the precision of this lab.
Equipment measurement precision does not have much affect on error because the
computer can record to many decimal places—depending on how it gets set by the user.
Ultimately, the laboratory was partially successful in verifying the acceleration due to
gravity given the low percent error comparing to the accepted value, however the
objective to measure g to a precision of 0.5% was not achieved. When trial 3 is removed
and the precision is recalculated, the objective is achieved. Based on this, the experiment
results could be improved by performing the experiment again with an improved method
for dropping the picket fence and more trials.