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Experiment 2 Acceleration Due to Gravity
2.1 Introduction
“Why does a ripe fruit fall from its tree to the ground?”
-
Isaac Newton reportedly wondered about this phenomenon.
Thanks to him and other great minds that followed, we now
know why it's because of the force called gravity that acts
between any two objects. Gravity is an attractive force, which is
why in Newton's model, the apple falls towards the Earth as
opposed to flying off into the cosmos. The rate that the apple (or
any falling object) accelerates is a constant value for any location
on Earth. This is the acceleration due to gravity, g.
In this experiment, you will determine the value for the
acceleration due to gravity for Mobile, Alabama, and compare it
to the accepted local value.
2.2 Theory
Consider Newton's 2nd Law: the force that acts on each object
results in an acceleration of that object – in other words, F = m x
a. For the case of an object experiencing free-fall, the value of
this acceleration is due to the gravitational force between the
Earth and the object. The gravitational force between the Earth
and the object is given by:
F-G
M.m
d?
where G is called the universal gravitational constant and has
value of 6.67 x 10-11 Nm²/kg?, M is Earth’s mass, m is object's
mass and d is distance between their centers.
The numerical value for the acceleration due to gravity is nearly
constant everywhere on the Earth, no matter whether the object in
motion is a falling apple, a person skydiving, or a baseball flying
over the center-field wall.
Suppose we have an object that is initially at rest and then
dropped from a height, h, just above the surface of the Earth. If
air resistance is negligible, the time it takes for the object to fall to
the ground (t) is related to the height it was dropped from (h) by
the acceleration due to gravity (g) as:
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air resistance is negligible, the time it takes for the object to fall to
the ground (t) is related to the height it was dropped from (h) by
the acceleration due to gravity (g) as:
h-
Experimentally, it is much easier to measure the height that an
object is dropped from and the time it takes to fall to the Earth,
and use these values to mathematically determine our own value
for 'g':
2h
Note that this determination does not depend on the mass of the
object at all!
In this exercise, you will drop an object from several different
heights, record the time of free-fall, and determine your own
value for the acceleration due to gravity.
2.3 Equipment
• Free-Fall Apparatus
· Stand with Clamps
• Meter Stick
• Computer
2.4 Experimental Procedure
2.4.1 Data Acquisition
The apparatus for this experiment consists of a ball-release
mechanism, steel ball, electronic timer and target pad, set up as
shown in Figure 2-1.
Bal Release Mechanism
TIMER
Target Pad
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TIMER
Target Pad
Figure 2-1: Free-Fall Apparatus
• Place the steel ball in the launcher by holding the trigger
release and turn the timer on.
• Make sure that the ball is held by the launcher jaws. On
making contact the display on the timer will go blank.
• Place the target pad below the position of the steel ball, so that
when the ball drops, it will strike the pad squarely.
• Measure the height (in meters) from the bottom of the ball to
the top of the target pad and record this value in the
spreadsheet, h.
• To release the ball and begin timing, press release trigger with
a quick motion.
· Record the time (in seconds) taken for the fall - enter this
value into the spreadsheet, t.
• Repeat this procedure two more times.
The spreadsheet will determine the average of the height
measurements and the average of the time measurements.
These values will be used to calculate the acceleration due
to gravity (g) for each height.
.
Change the height of the release and repeat the above procedure
for two additional heights. Once you are finished, you should
have completed a total of nine (9) trials - three experimental runs
each for three different heights. Each set of trials will be used to
obtain a value for g.
*** Please be sure to turn off the timer at the end of the
experiment. ***
2.4.2 Data Analysis
The spreadsheet will determine the average value for your
experimental g. How does your value compare (greater, lesser, or
the same) with the accepted value at the University of South
Alabama: g = 9.793394 m/s?? What is the percent difference
between your experimental value and the accepted local value? In
general, a 10% difference in values (or less) is considered a
'good' estimate of the actual value. If your value is much larger
than 10%, please check your entries into the spreadsheet or, time
permitting, repeat the experiment.
2.5 Discussion Questions
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• 10 release the ball and begin timing, press release trigger with
a quick motion.
• Record the time in seconds) taken for the fall – enter this
value into the spreadsheet, t.
• Repeat this procedure two more times.
The spreadsheet will determine the average of the height
measurements and the average of the time measurements.
These values will be used to calculate the acceleration due
to gravity (g) for each height.
Change the height of the release and repeat the above procedure
for two additional heights. Once you are finished, you should
have completed a total of nine (9) trials - three experimental runs
each for three different heights. Each set of trials will be used to
obtain a value for g.
*** Please be sure to turn off the timer at the end of the
experiment. ***
2.4.2 Data Analysis
The spreadsheet will determine the average value for your
experimental g. How does your value compare (greater, lesser, or
the same) with the accepted value at the University of South
Alabama:
g = 9.793394 m/s?? What is the percent difference
between your experimental value and the accepted local value? In
general, a 10% difference in values (or less) is considered a
'good' estimate of the actual value. If your value is much larger
than 10%, please check your entries into the spreadsheet or, time
permitting, repeat the experiment.
2.5 Discussion Questions
1. Is there an influence of air drag on your final results of
measured g? Explain your reasoning.
2. If we were to repeat the same experiment with two balls of
the same size but different masses, which ball will
experience greater g? Justify your answer.
3. Suppose you performed the same experiment in a lab that is
located 2000 miles above the Earth's surface. Would you
expect to get the same, less or greater result for g? Explain
your reasoning
:
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