Physics Lab
Scott Hildreth
In this experiment, you’ll determine the acceleration due to earth’s gravitational force with three different freefall methods. We say an object is in free fall when the only force acting on it is the earth’s gravitational force. No other forces can be acting; in particular, air resistance must be either absent or so small as to be ignored. When the object in free fall is near the surface of the earth, the gravitational force on it is nearly constant. As a result, an object in free fall accelerates downward at a constant rate. This acceleration is usually represented with the symbol g.
Your goals for the exercise are:
 Explore
the use of graphs and equations for distance vs. time, and velocity
vs. time, to determine “g”, the earth’s gravitational
acceleration.
 Master
the difference between precision  measuring carefully and accounting
for uncertainty in your measurement  and accuracy  measuring correctly and coming close to
the “right” answer.
 Work together in a group setting, dividing up the work fairly and doublechecking one another. You will need at least two people to take data, two people to draw graphs using Excel, someone to keep the team on task, and someone to ensure that the write up is completed and turned in ontime.
Turn in one full write up for the team, on or before Wednesday,
17 February. Include:
a) the names and lab duties of each of the participants, and
short abstract
b) the organized data tables for all experiments
c) the graphs you drew, and the calculations of the slope of
the velocity vs. time curve that determine the value of “g”
d) analysis of sources of errors and uncertainties in your work.
You are encouraged to work together using our online forum, http://clpccd.blackboard.com.

You may do these experiments in any order.
 The value of “g” (actual) to use for comparison is 9.81 meters/sec^{2}
Determining the Acceleration of Gravity
Procedure:
[Uncertainty]/[Measured
Value] x 100%
For the example: [0.2 cm] / [100.2 cm]
x 100% = 0.2%
Relative uncertainty in acceleration of gravity (dg/g) = 2 (dt/t) + (dy/y)
Note that the time element’s uncertainty
appears multiplied by (2) because the equation for acceleration depends upon
the SQUARE of the time. So the time
variable appears “twice”, and each time its uncertainty
matters.
6. (cont.)
The percentage uncertainty in “g” will
then be an estimate of your overall precision for the experiment:
% Uncertainty in “g” = 100% x dg/g = 2 x (% uncertainty in time) + (% uncertainty in distance)
[“g”(actual) – “g”(experimental)] x 100% / (”g” actual)
Example: Your experimental value of “g” was 8.90 m/sec^{2}; the actual is 9.81, and your actual percentage error would be:
[9.81 – 8.90] x 100% / (9.81) = 9.3%
Experiment 1 Data
Table

Drop Distance +/ ? 
Estimated Uncertainty in Individual Drop
Time: 

Drop Times: 
T1:

T2: 
T3: 
T4: 
T5: 

T6:

T7: 
T8: 
T9: 
T10: 
Average Drop Time:


% Uncertainty:




Average “g” 

% Uncertainty



Experiment 1 Questions:
You’ll use a spark timer to make marks on a tape as an
object falls. The timer will produce a
spark every 1/60^{th} of a second (+/ 0.005 seconds). We’ll do this experiment once, but
analyze the resulting data in two different ways. A
suggested data table for this experiment is attached, but you are free –
and encouraged – to create your own.
Method 2A uses the total distance fallen and the total elapsed time to estimate
an “average” velocity in each time interval, which can be used to
create a graph of velocity vs. time, and from that, acceleration.
Method 2A Procedure:
1. Each team will create their own freefall data strip using the spark timer. The sparks will mark the tape at constant intervals of 1/60^{th} of a second. Pick one spot at the top of the tape, label that spot “top”, and then mark the tape, numbering the spots from the first spot beneath the “top” to the bottom (from t_{1} … t_{i}_{ }).
v_{i}_{ (avg) }= 2y_{i}/ t_{i}
The uncertainty in your value of “g” will be influenced both the average uncertainty in time, the average uncertainty in measurements of distances travelled, and the number “n” of data points you recorded. The uncertainty in time is used twice (once to get velocities, and again to get acceleration); the uncertainty in distance is used once. Note that “n” increase, your overall uncertainty decreases by the square root of n.
%dgA = [(2 x %
Average Uncertainty in Time) + (Average % uncertainty in distance)]/ √n
[“g”(actual) – “g”(experimental)] x 100% / [”g” actual]
Method 2B uses the
displacements between each mark as the object falls, and the known time
interval to estimate an “instantaneous” velocity for that interval,
that will continue to increase as the object is accelerated
downwards by the force of gravity. If
you graph this instantaneous velocity at each point vs. time, you can estimate
the slope of the line and therefore, the acceleration of gravity.
Method
2B Procedure:
v_{i}_{
}= Dy_{i}/
t_{ }where t is 1/60^{th}
of a second
Record both your value of the slope and its uncertainty as g_{B}
+/ dg_{B}
%.
Experiment 2 Questions:


FreeFall Tables for Experiment 2Lab Data








Measurement Data 
Calculated 

Spot
# 
Total Distance from “top” spot on Tape y_{i} 
Instantaneous Displacement Between
Adjacent Points Dy_{i}_{ }=
y_{i} – y_{i1} 
Elapsed Time t_{i}_{} 
Avg. Velocity v_{i (avg) }= 2y_{i}/ t_{i}_{} 
Instantaneous Velocity v_{i }= Dy_{i}/ t 

cm 
cm 
sec 
cm/sec 
cm/sec 

+/ cm 
+/ cm 
+/ sec 
Displacement/ 
Distance/ 






1 





2 





3 





4 





5 





6 





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27 











Experiment 3 uses
the automated data collection system created by Vernier
Corporation, using LoggerPro software to analyze the data. I’ll walk you through how the system
works, and how you can quickly generate velocity vs. time graphs for a falling
object, analyze those graphs for the slope, and establish an experimental value
for the acceleration of gravity.
In this experiment, you will have the advantage of using a
very precise timer connected to the computer and a Photogate.
The Photogate has a beam of infrared light that
travels from one side to the other. It can detect whenever this beam is
blocked. You will drop a piece of clear plastic with evenly spaced black bars
on it, called a Picket Fence. As the Picket Fence passes through the Photogate, the computer will measure the time from the
leading edge of one bar blocking the beam until the leading edge of the next
bar blocks the beam. This timing continues as all eight bars pass through the Photogate. From these measured times, the program will
calculate the velocities and accelerations for this motion and graphs will be
plotted.
1. Observe the reading in the status bar of Logger Pro at the bottom of the screen. Block the Photogate with your hand; note that the Photogate is shown as blocked. Remove your hand and the display should change to unblocked.
2. Click _{} to prepare the Photogate.
Hold the top of the Picket Fence and drop it through the Photogate,
releasing it from your grasp completely before it enters the Photogate. Be sure
you are dropping the fence directly into the bucket below, cushioned with a
towel to ensure the fence is not damaged.
Be careful when releasing the Picket Fence. It must not touch the sides of the Photogate as it falls and it needs to remain vertical.
Click _{} to end data collection.
3. Examine your
graphs. The slope of a velocity vs.
time graph is a measure of acceleration. If the velocity graph is approximately
a straight line of constant slope, the acceleration is constant. If the
acceleration of your Picket Fence appears constant, fit a straight line to your
data. To do this, click on the velocity graph once to select it, then click _{} to fit the line y = mx + b to the data.
Record the slope in the data table below.
4. To establish the reliability of your slope measurement, repeat Steps 2 and 3 at least five more times. Do not use drops in which the Picket Fence hits or misses the Photogate. Record the slope values in the data table.
Experiment 3 Data
Table
Trial 
1 
2 
3 
4 
5 
6 
Slope (m/s^{2}) 







Minimum 
Maximum 
Average 

Acceleration (m/s^{2}) 







Acceleration due to gravity, g 
± m/s^{2} 

Precision 
% 

Experiment 3 Questions
g. From
your six trials, determine the minimum, maximum, and average values for the
acceleration of the Picket Fence. Record them in the data table.
h. Compare
the precision and accuracy of this experiment with the first two. Overall which experiment produced the most
precise data? Was that also the most
accurate? Explain.