IntroductionEvery body on earth or near its surface has a gravitational
force acting on it. When an any given body falls from a height, it is subject
to a gravitational acceleration, which on Earth is approximately g=9.8 m/s2.
Due to the fact that g is the same for everyone, the acceleration in this case
doesn’t depend on the mass of the body that is falling. However, air resistance
acts as an opposing force.This experiment proves that The concept of free-fall
provides underpinning knowledge in order to understand air resistance and
consequently how fast objects fall. Without proper knowledge of these concepts,
it wouldn’t be possible for people to use parachutes or go skydiving. The objective of the experiment was to neglect the drag
force caused by air resistance and try to calculate the acylation using suvat
equations. Comparing the results with the actual acceleration then gives
insight on how air resistance affects these bodies. TheoryTo understand the concept of free-fall, it is first necessary
to refer to Newton’s Second Law of Motion, which states and is commonly known by
the formula:

 (1)Where F is the force (N), m is the mass (kg) and a is
acceleraton (m/s²).In the scenario of any given object falling freely within
the Earth’s gravitational field, its acceleration will always be the one due to
gravity, amounting to approximately 9.8 m/s². This acceleration is independent
of the mass of the object since gravity will act equally on each object.If there weren’t any other forces acting on the objects,
then every object in free fall under the same conditions would fall at the time.
However, this doesn’t happen due to an opposing Force exerted by the again,
known as drag. In any body falling towards Earth, the acceleration will be
directed downwards and the drag upwards.This drag force helps deaccelerate the body and is expressed
by the formula:                       Experimental methodIn order to calculate the acceleration of the two balls, we
used a set of devices that when connected between each other could precisely
calculate the time between the ball dropped and it reached the floor.A magnet drop box was placed at the top in a way that when
it was on, it would hold the balls (a small magnet was added to the plastic
balls so it could be held suspense). Once the timer was activated, the drop box
released the ball and when it reached the detector pad at the bottom, the smart
timer would give the total amount of time taken. This can see in more detail on
the pictures below: The drop box was also set up in a way where its height was adjustable,
and it was possible to try the experiment with several different heights. The
total distance was calculated used a measuring tape.

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Figure 1: The system set up with one of the balls being held
by the drop box. Figure 2: One the time was pressed, the ball would instantly drop.

Figure 3: One the ball reached the detector pad, the smart
timer would have the total amount of time taken for the given distance.After collecting the time measurements for different
distances for each ball, a plot of time squared against distance was done using
equation … and the gradient of that times 2 would give us the acceleration.Alternatively, it was also possible to rearrange the formula
in terms of a and get the acceleration from that. In this experiment, however,
the first method was used for both balls. With that data, it was then possible to compare the results
with the expected acceleration due to gravity. Results  Looking at the graph, it is noticeable that both lines are close
to each other, but that their gradient, and consequently their acceleration, is
different.The calulation of the gradient  was done using equation … and then it was
multiplied by 2. For the plastic ball the gradient was Mpb =9.12m/s2 and for
the steel ball it was Msb = 9.67 m/s2.Using error progration fomulas on ….. we get that the error
for the plastic ball as … and the steel ball was …      

 

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