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, for
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.
To 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
Where F is the force (N), m is the mass (kg) and a is
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 air, 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:
Where p is the density of the air, A is the area of the
object that is in contact with the air, Cd is the drag coefficient and v is the
As the body starts to deaccelerate, it reaches one point
where equation 1 will be equal to equation two and at that point the velocity
will be constant.
This concept is crucial as it helps is predict how fast an
object will fall and what to do to reduce its landing speed.
On the other hand, there are cases where the drag force is
too small that it can be ignored and in these instances we can use SUVAT
equations to determine either the time, the acceleration of the distance of something
Given the suvat equation :
Where s is the total distance, u0 is the initial velocity, t
is time a is acceleration.
If we wish to the acceleration, given that the initial
velocity is 0, we can rearrange formula 3 to get:
Using equation 5 you can find out the acceleration, but
there’s also the possibility of plotting a graph of the time squared against
the distance, which would mean that the slope of the graph would be half the
amount of a, due to the fact that in the formula we’re using 2s.
In 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.
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.
Looking at the graph, it is noticeable that both lines are close
to each other, but that their gradient, and consequently their acceleration, is
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 …