Name _________________________
Measurement of Acceleration of a Freely Falling Object
(Simulated Data)
In this experiment you will measure the position vs time record of a freely-falling object by
recording its position as a function of time, and then analyze the graphs of position vs time
and velocity vs time to obtain a value for the acceleration of the object in free fall.
Procedure and notes:
1. After demonstrating the experimental apparatus and analysis procedure the lab
instructor will distribute to each lab group a previously recorded data record containing
the position vs time record of a freely falling object. The data record will be in the form
of a long spark-sensitive tape with y vs t marks appearing as something like Fig.1
below.
Fig. 1
2. The time interval between consecutive marks corresponds to 1/30 sec. Record all
lengths in meters.
Secure the data tape to the tabletop with masking tape at a few spots to keep it from
slipping while you are measuring distances between the marks on the tape. You will be
using an Excel spreadsheet to enter your data directly into a data table that looks like the
one below.
3. The beginning of the motion is at the end of the tape where the marks are closer
together. Skip the first three marks. Circle the 4th mark and denote it as the origin point.
Measure the distance y from this point to each of the succeeding points and record it as
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yi for i = 1,2,3,… in Data Table 1. The corresponding time values for each point are t=0
sec for the origin point, t=1/30 (=0.03333..) for point y1and increasing in 1/30 sec
increments for each succeeding point.
4. Plot the y vs t data as Graph 1 using Excel. Be sure to label the graph completely.
Describe the apparent form of the graph verbally.
5.
Calculate the average velocity over each of the time intervals. The average velocity
over any 1/30 sec time interval is an approximation for the instantaneous velocity at the
middle of the interval over which the average was calculated. For example, the average
velocity v2 between time t1 = 1/30 sec and t2 = 2/30 sec is to be associated with the time
t = 1.5/30 sec, that is t = 3/60 sec. Record this information in Data Table 1 in the Avg.
Vel. column on the right. The entries for the average velocities can be calculated using
the formula
vi (t = (ti + ti-1)/2 ) = ( yi – yi-1) / ( 1/30 sec)
Eq. 1.
6. Plot a velocity-vs-time graph by plotting the average velocity over each 1/30th second
interval. Note that the graph corresponds to a straight line with a positive constant slope.
Since the equation of the velocity for constant acceleration “a” is given by
v = v0 + a t
Eq. 2
then the acceleration can be interpreted as the slope of the velocity – time graph.
Use a linear “best fit” trendline with your plotted points in the v vs t graph. Select the
slope and regression options. This will display the slope of this trendline line on your
graph. Report this as your measured value for the free-fall acceleration
Calculate the percent error between your experimental value of g and the accepted value
of 9.80 m/s2.
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Data Table 1
Time
y (m)
0.000
0
Delta y (m)
Avg Time
(sec)
0.033
0.017
0.067
0.050
0.100
0.083
0.133
0.117
0.167
0.150
0.200
0.183
0.233
0.217
0.267
0.250
0.300
0.283
0.333
0.317
0.367
0.350
0.400
0.383
0.433
0.417
0.467
0.450
0.500
0.483
0.533
0.517
0.567
0.550
0.600
0.583
Avg Vel
(m/sec)
In your analysis use the Excel Worksheet Function LINEST to determine the uncertainty in
your slope.
Final Results - include uncertainty
gExp = ____________ ± Uncertainty = _____________
% Uncertainty =
% Error =
__________________
__________________
Estimate the uncertainty in your measurements. How do these compare with the percentage
error between your experimental value of g and the accepted value?
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