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FREE FALL OBJECTIVE To measure the acceleration of (University of South Carolina)

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FREE FALL
OBJECTIVE
To measure the acceleration of a freely falling object.
INTRODUCTION
There is an old story that Galileo dropped similar spheres off the leaning
tower of Pisa to prove that objects do not, as reported by Aristotle, fall
with accelerations proportional to their masses. There is strong evidence
that Galileo never did the experiment as described in the story, but
gathered his data in an equivalent but much slower manner using inclined
planes. We will do the experiment as described in the traditional story but
using modern electronic timing equipment.
Galileo showed that an object falling freely in a uniform gravitational field
is constantly accelerated. The force that causes the acceleration is the
result of the mutual attraction between the falling mass and the earth. Of
course, if there are other forces present, such as friction or air resistance,
the motion of the falling object would not be one of constant acceleration.
However, if the distance of fall is not too great and the object is sufficiently
dense, the effects of air resistance are very small and may be ignored. If
we use Newton's second law to find the acceleration a of a mass m
subjected to a force F, we get
F
a =
(1)
m
If the force is the gravitational force, we call the acceleration g, the
acceleration due to gravity. This experiment is to study the motion of a
falling object in order to measure the acceleration g.
An object falling from rest with constant acceleration g for a time t will fall
a distance d given by
(2)
d = 1/2gt
2
It this experiment you will measure the height of fall d and the time t for
different heights and use the data to determine the value of g.
1
ACTIVITY 1
USING THE ELECTRONIC TIMER
1. Assemble the timer with the free fall adapter so the steel ball has an
unobstructed path to the stop pad. The distance the ball falls is
measured from the bottom of the ball when held in the ball dropping
mechanism to the top of the stop pad. Push in the spring-held rod
slightly and tighten the thumb screw. Place the ball between the two
metal contacts on the drop mechanism so that it is held in place. You
can then release the ball by loosening the thumb screw.
2. Adjust the height of the ball to about 1.25 m. Measure the height and
record your measurement.
3. Set the timer modes to “Stopwatch.” Press the “Start/Stop” key. The
timer will beep and “*” will appear on the second line of the display.
Dropping the ball will start the timer. When the ball hits the stop pad the
timer will stop and display the elapsed time.
ACTIVITY 2
5. Drop the ball 5 times. Record the times and compute the
average.
ACTIVITY 3
6.
Transcribe all data from the generated data file to your table.
Compute the average fall times.
ACTIVITY 4
7.
From your data table, calculate the average fall time squared and
multiply the height values by 2. Record these values into data table
2.
ACTIVITY 5
8.
Using a spreadsheet, preferably Microsoft Excel, or other graphing
software, prepare a graph of 2*d versus t
2
. Make sure to label the
axes and give your plot a title.
2
9.
Using the trendline function, add a linear trendline to your plot. Make
sure you turn on the trendline values to see the equation of the line.
10.
The slope of the trendline is the experimental value for g.
ACTIVITY 6
12.
Compare your experimental value of g to the standard value of
9.81 m/s
2
by computing the percent error. The percent error is
given by the difference between your result and the standard value
divided by the standard value and converted to a percent.
experimental value - standard value
percent error =
×100%.
standard value
SUMMARY
Answer the following questions on your data sheet.
How well does your measurement compare with the
“standard value” for the gravitational acceleration? What
factors could contribute to any differences between what
you have found and what you expected?
3
Name –––––––––––––––––
FREE FALL
DATA SHEETS
ACTIVITY 1: Electronic timer
1. Height of ball above pad:
ACTIVITY 2: Measurements of time of fall.
Units = __________________
Average value of time of fall .
ACTIVITY 3: Generate data table
Table 1:
Height
1
st
time
2
nd
time
3
rd
time
4
th
time
5
th
time
average
ACTIVITY 4: Preparing to plot
Table 2:
2*d (meters)
t
2
(seconds
2
)
ACTIVITY 5: The plot
Include a copy of your plot with this assignment. Make sure your plot
is in the proper format. For example, are your axes labeled and show
the proper units?
ACTIVITY 6: Percent error
Compare your experimental value to the standard value of 9.81 m/s2
by computing a percent error.
Computed percent error:___________________________
Answer the summary questions and include in this assignment.
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Completed 23 August 2021

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