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Free Fall Experiment

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Free Fall Experiment

One of the major topics discussed in Physics is the study of free
fall, or the effect of the force of gravity on any object. This
experiments aimed to investigate the mechanics or the action of
gravity an object by analyzing certain vectors related to free fall
versus time graphs. These studies on free fall are important if
further studies of projectile motion are being made.

The objective of the study is to show that velocity, acceleration and
distance are related such that one is actually the slope of the other.
The slope of velocity is acceleration. The slope of distance is
velocity. Hence, changes in one of the factors involving a certain
object, the other related factors are also inevitably altered. This
exercise also seeks to prove the constant of acceleration due to
gravity.

The first activity utilized the ULI, photogate and Logger Pro systems
to analyze graphs for free fall. The photogate system was first
assembled and connected to the computer using the ULI. Three graphs
were analyzed by the Logger Pro program namely distance vs. time,
velocity vs. time, and acceleration vs. time graphs. A chopper was
dropped in between the photogate, and data of various components such
as acceleration were recorded and plotted on the different graphs in
the program. After data collection, a linear fit and a quadratic curve
was tested upon the graph of distance vs. time. It was found out that
a quadratic curve would fit better for the distance vs. time graph
rather than a linear fit. This shows that the distance follows a
parabolic curve as time progress during a free fall. This is shown by
the equation X = X0 + V0t – 1/2gt2, or D= V0t – 1/2gt2 .A quadratic
equation has a form ax2 + bx + c = 0, where ax2 is –1/2gt2 , bx is V0t,
and c is X – X0 which is also the displacement or as scalar quantity,
the distance D. The graph of velocity vs. time is a linear equation,
in which a slope may be taken by the equation y = mx + b. Our equation
is V0 = gt. If the derivative of the graph of distance vs. time were
taken, the resulting derivative would be the linear graph of velocity
vs. time. Furthermore, if the derivative of the graph of velocity vs.
time were taken, we would have the graph of acceleration vs. time,
which has the equation y = m, or a horizontal graph. This graph is
logical for acceleration, since in a free fall, the acceleration of
the object is at a constant 9.8m/s2.

The average slope of the graph of velocity vs. time in five trials was
taken to compare with the theoretical acceleration of gravity (9.8m/s2).
In computing, we had a value of 9.428 m/s2, which was 3.79% off from
the theoretical. We computed for the percentage error by the equation
(theoretical – actual) / theoretical * 100. This is a large percentage
error as compared to percentage errors acquired by other groups.
Several causes of error may be attributed to this. Mechanical errors,
or errors in the equipment may have caused this. The photogate wasn’t
working at first and had to be replaced. We even had to work with
another computer, since the computer assigned to our table was
malfunctioning.

The second activity utilized an accelerometer to measure the amount of
acceleration of an object at various heights/point from the ground. A
representative wore the accelerometer with the indicator arrow facing
upward, and then positioned himself in a trampoline. He would then
jump up in down within a certain time of about five seconds. The
acceleration was then graphed in the computer by a series of crests
and troughs. The pattern of the graph was somewhat uniform all
throughout, with crests and troughs at close to regular intervals
paralleled to the different points at the jump of the representative.
It was noticed that at a higher point during the jump, the graph
shifted downward. Inversely, when the representative landed in the
trampoline, the graph shot upward. This was reasonable. The force of
gravity increases as an object is closer to the ground. This why the
graph moved upwards when the representative landed on the trampoline.
Crests represented high rates of acceleration. Similarly, crests
indicate that the representative nearer to ground. The troughs, on the
other hand, indicate lower rates of acceleration. The force of gravity
decreases as an object is farther from the ground. At the peak of the
representative’s jump, the graph would move downward, creating the low
points of the graph.

However, the orientation of the graph may be changed. Remember that
before jumping, the indicator arrow was flipped upwards. The effect on
the graph was it shot downwards at peaks of the jump, and it moved
upwards whenever the representative landed. If the indicator arrow is
flipped downward, the previous graph will also be flipped. Instead of
an increasing positive value as one descends, the meter will read an
increasingly negative value. This is simply an indication of the
direction of the acceleration., which going down.

In this activity, we have learned the relationships between time,
distance, velocity and acceleration. In addition, we are also able to
confirm the presence of acceleration due to gravity. Even if the
theoretical is 9.8m/s2 , the presence of factors like air resistance
lessens this value.

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