Motion in air
investigation.
There are some
things that must be clear before getting in depth. First of all it's important
to know that free fall motion works different from falling with something like
a parachute, which creates air resistance, we must also recall that without air
resistance, 2 objects with different weights will fall at the same time, this
happens because of Newton's second law (Fnet=m*a) where the acceleration is
directly related to the net force while the mass is inversely related, however,
only in a vacuum this situation happens, as in any other place there will be
air resistance. What determines how fast something fall is acceleration that=
Fnet/m (Physicsclassroom.com, 2015), in a vacuum it is the same for objects of different weights.
Speed increases
air resistance, and a point comes when it balances the force of gravity,
and in that moment it reaches a terminal velocity, the higher the weight, the
higher the speeds before the terminal velocity will be, and therefore falling
faster.
The air resistance
depends in a lot of factors, the speed, the cross-sectional area, the shape and
the density of the air, air density depends on the humidity, the altitude and
the temperature. The shape of the object determines the drag coefficient which
is determined by Cd=2Fd (drag force)/p(mass
density)v(speed)2(squared)*A(reference area).
How does changing
the surface area affect the time it takes to reach the floor?
Before starting
with the variables, I want to state I would prefer throwing the object like a
fall, not from a ramp or a slingshot, as they are not precise.
Independent:
Surface area, I will cut papers in x squared, each time making it bigger.
Dependent: I will
be measuring the time it takes the object to reach the floor, I would throw the
object with one hand and start the stopwatch with the other hand, once I hear
it touches the floor I will stop it, this is not complete precise.
Control: Height, I
will always be throwing it from the same height (2 meters, from the door). Air
density, I will be doing the tries consecutively, therefore humidity and
temperature will not change, and as i'm throwing from the same place, the
height doesn't change either. Will be done with the same material. Initial
speed, this may not be completely precise, but I will use my hand and just open
it to let the object fall, that way the initial speed stays at 0.. I will also
be using the same amount of plasticine for each one.
Material:
1 A3 Piece of
paper, to get the object that I will later shape.
Scissors, to cut
the piece of paper in similar pieces.
(Possibility) 1
Glue, to help me make shapes and stay like that.
1 Stopwatch, to
measure the time it takes.
A piece of
plasticine, this way, the time it takes to fall is not affected, however, it
makes the paper not be able to be moved (and stopped) by temporary wind
changes.
Stairs to get to
the 2 metres.
Method:
1. Cut the piece
of A3 in 5 pieces of: 2,5*2,5cm, 5*5cm, 7,5*7,5cm, 10*10cm and finally
12,5*12,5cm.
2. Take those
pieces and shape them, I can use a bit of glue to stick them.
3. Add the staples
to give more weight.
4. Go on top of
the stairs.
5. Open the hand
and let the object fall, start the stopwatch.
6. When the object
hits the floor, stop the stopwatch.
7. Annotate
results.
8. Repeat three times
for all the objects.
Physicsclassroom.com, (2015). Introduction to
Free Fall. [online] Available at:
http://www.physicsclassroom.com/class/1Dkin/u1l5a [Accessed 1 May 2015].
Study.com, (2015). Factors That
Affect Wind: Pressure Gradient Forces, Coriolis Effect & Friction - Video
& Lesson Transcript | Study.com. [online] Available at:
http://study.com/academy/lesson/factors-that-affect-wind-pressure-gradient-forces-coriolis-effect-friction.html
[Accessed 1 May 2015].
Howthingsfly.si.edu, (2015). Air in Motion |
How Things Fly. [online] Available at:
https://howthingsfly.si.edu/aerodynamics/air-motion [Accessed 1 May 2015].
Grc.nasa.gov, (2015). What is Drag?. [online] Available at:
https://www.grc.nasa.gov/www/k-12/airplane/drag1.html [Accessed 1 May 2015].
Prediction:
The one with more surface area
will be the slowest one, this has to do with how air resistance works, air
resistance is what determines how fast something falls, the mass doesn't change
this, however the surface does (this is where aerodynamic comes from, having
the less air resistance as possible) affect the air resistance, making it
slower, therefore, the bigger ones should fall slower.
Results:
Size
|
Try
1 (in sec)
|
Try
2 (in sec)
|
Try
3 (in sec)
|
Average
(in sec)
|
5cm2
|
0.60
|
0.50
|
0.53
|
0.54
|
25cm2
|
0.87
|
0.67
|
0.60
|
0.71
|
56,25cm2
|
1.03
|
1.16
|
1.06
|
1.08
|
100cm2
|
1.53
|
1.62
|
1.34
|
1.49
|
156,25cm2
|
1.64
|
1.82
|
1.68
|
1.71
|
Conclusion:
The results went as expected, we can see how,
at 5cm2 the time to reach the floor is really low, and at 156,25cm2, because of
the air resistance, it's really slow compared to the previous one, the pattern
isn't broken in any moment, it is how it should be, I was lucky there wasn't
any anomalous results, in general, the average increased consistently. The
difference were in a reasonable margin, between 0,15s and 0,30s, which is
understandable, even with the pieces of plasticine, the wind could change,
which would affect the results, something like an open door could make
differences. The only thing I think wasn't perfect was using the same amount
of. The smaller ones would fall perfectly, only being stopped by the air
resistance, in a straight lines, the 100cm2 and 156.25 didn't fall completely
straight. To improve the experiment, I should have tried to change the amount
of plasticine in a proportional positive correlation with the surface area.
Evaluation:
I did the experiment by myself, that and humans
not being perfect, made the experiment not be perfect, my timing wasn't
perfect, it didn't make a big difference (0,05s at most), but wasn't perfect,
even if I had done it perfectly, I would have still found the same conclusion,
as it wasn't a big difference, but it's something that when looking for
precision, I have to take in account. My coordination between my two hands
wasn't perfect (adding to that, it takes around 0,05s to click the stopwatch).
If I had the opportunity, I would have
developed a way to release the piece of completely 0 as initial speed, I tried
to just leave the paper and let it fall, but a system in which I can start with
no initial speed would help it be precise.
This two problems, aren't that that much of a
trouble, specially because they always happen, so the pattern, a bit higher
(the average of all result), but with the same differences in between them, as
it happens the same to all of them, however, it's not correct for this to
happen, specially because, we can't find percentages and it's not always the
same wrong, I sometimes coordinate perfectly, and sometimes make it change by
more than 0,05 seconds, however, as I threw each piece 3 times, we could find
an average, and in case one of them was really far away from the rest, we could
ignore it and leave it as anomalous, or just delete it and repeat it. We can
see how this wasn't much of a trouble, and that there wasn't any moment in
which I did it really unprecisely in how there isn't any moment in which the
results of a piece never overlap with the results from other.
