Background
The motion of an object varies depending on the initial speed, the
acceleration and the forces that interfere with it (School-for-champions.com,
2015). Some of these forces are:
Gravity is a constant (g) affected by the altitude of the object (9,98m/s).
Air friction depends
on the speed and the volume of the object, and the density of the air.
If we change one of these factors, the distance, the speed or the time in
which the object will fly will vary.
As we are investigating how mass varies the displacement of a projectile,
these formulas seem relevant:
Newton’s second law: F = M × A (Teachertech.rice.edu, 2015)
*Force is measured in Newtons (kg·m/s2)
A kinematic equation: d = vi × t +1/2 × a × t2 (Formulas.tutorvista.com, 2015)
*Displacement is measured in metres.
Time of flight: t = 2v0 × sin2 q (Physicsclassroom.com, 2015)
The first formula shows that if the mass increases, the acceleration
decreases proportionally. If the acceleration decreases, the force is smaller.
The second formula suggests that the displacement of an object will vary
depending on the initial velocity, the time and the acceleration. If the
initial velocity is higher there will be a bigger displacement. If the
acceleration is higher the same thing will happen. This is because it acquires
a bigger force and therefore is able to fly a bigger distance.
Research Question
How does changing the mass of a spherical object affect the distance of its
flight?
Hypothesis
The higher the weight of the object is the shorter will be its flight. This
can be proven with the formulas. Firstly, looking at Newton’s Second Law
(F = M × A) if the mass is bigger and the force remains the same all
along, the acceleration will have to be smaller. If the acceleration is
smaller, it will fly a shorter distance.
Also, if we look at the kinematic equation stated earlier (d = vi ×
t +1/2 × a × t2), we can see that is the
acceleration is lower, because of what we have concluded from the first
equation, the resulting displacement must also be lower.
Variables
·
Independent: what I
will be changing in this experiment is the mass of the plasticine balls that I
will use as projectiles. To do this I will do 5 balls of plasticene with
different masses (30g, 40g, 50g, 60g, 70g). We will measure
the masses using a scale.
·
Dependent: what
will change because of the different mass plasticene balls will be the distance
that it will fly. Therefore, what we are measuring in this experiment is the
distance in metres. I will measure this with a tape
measure.
·
Controlled:
− What must remain unchanged during all the experiment is the force with
which I throw the ball with the slingshot. We will achieve this by measuring
how much we pull the elastic band of the slingshot.
− I will also not change the shape of the plasticene balls. They will always
be spheres as similar to each other as possible.
− Density and gravity will also be the same all along because if we stay in
the same classroom and we are not manipulating the air density or the gravity
then it will stay the same.
Materials
− Slingshot
(two sticks and one elastic band)
− Plasticine
− Scale
− Tape
measure
Method
1. Break the plasticine in seven parts and shape it into a sphere
weigh it on the scale and keep adding more plasticene until it weighs the
desired weight (30g, 40g, 50g, 60g, 70g).
2. Create the slingshot tying two sticks together with an elastic band.
3. Place the measuring metre on the floor. Extend it until it reaches
about 3 metres.
4. Place one of the plasticene balls on the elastic band and
pull it 5 centimetres. Let the band loose.
5. Record the
distance the projectile has flown.
6. Repeat the
previous steps 4 more times with different mass plasticene balls (30g,
40g, 50g, 60g, 70g).
Table
The following
table shows how the weight of the plasticene spheres affects the distance they
fly, taking into account that the shape and the initial velocity remain the
same.
Mass (g)
|
Distance flown trial 1
|
Distance flown trial 2
|
Distance flown trial 3
|
Distance flown trial 4
|
Distance flown trial 5
|
Distance flown Average
|
5
|
320
|
330
|
320
|
325
|
330
|
325
|
7
|
310
|
325
|
325
|
315
|
300
|
315
|
9
|
380
|
310
|
315
|
310
|
330
|
329
|
11
|
220
|
250
|
220
|
245
|
200
|
227
|
13
|
150
|
130
|
155
|
160
|
145
|
148
|
Graph
Conclusion
As we can
see in the results table, the distance flown was smaller the bigger the mass of
the plasticine spheres were. With this experiment we also proved the kinematic
equation (d = vi × t +1/2 × a × t2) because we saw that if the mass was bigger, the smaller the force was
and therefore, the less distance the object flew.
However,
there was an anomaly: when the mass reached 9 grams, the average distance flown
increases unexpectedly, from 315 to 329, and then goes down again to 227 and
continues decreasing normally. This could have been caused by the fact that Amaia threw the 9g spheres. This will proably been the cause to this anomaly because the way she threw the spheres with the slingshot was different to the way Marina threw it. A solution to this would have been to let the same person do it all along.
Evaluation
A possible error
that could have altered the results of the experiment would be the angle with
which we threw the balls with the slingshot. We didn’t measure the angle we
would position the slingshot every time, so it will most probably have varied.
This could have affected the results because if we threw it from below, the
plasticine spheres will have flown higher and lost energy during the process.
The actual distance flown would have probably been shorter. In the
contrary, if the was thrown from above, the spheres would have flown a
different distance because they would have hit the floor sooner.
A solution to this
problem would be to measure at what distance the slingshot’s rubber bands are
being hold tense from our hand before letting go and letting the ball fly. If
we made sure this distance was always the same, we would know the angle is
always the same and would avoid this error.
We can also say
that the fact that the slingshot was made of pens made it quite unstable.
Because of this, we had to redo it various times changing the ways in which it
was built (the length of the string, the way it was attached to the pens...),
which may have had repercussions in the results. This could have altered the
results because the initial force put into the object would have probably
varied depending on the composition of the slingshot.
The only solution
for this is to make another type of slingshot which is more stable. It would be
a good idea to put some more effort into making the slingshot by using to
wooden sticks that meet at the bottom to have the real slingshot structure. We
also could attach the elastic band to the wooden part by tying a knot. A small
piece of leather could also be stuck to the elastic band to make sure it
supports the plasticine balls.
In addition, we have
to consider that the plasticine balls bounced in different locations each
time they were thrown and as we had to work together in order to correctly
throw them with the slingshot, we could not see the exact place where
they first landed.
In order to solve
this, we should either change the technique of the slingshot, so it is easier
to use it, or take another type of projectile which doesn't bounce.
If we were to keep
the spheres as they were, we could put some paint on them so that the first
time it bounces a spot is left on the floor.
Another solution to this last problem could be filming the experiments so that, after, we could see exactly where the balls bounced. Moreover, we could play it as many times as necessary.
References
Teachertech.rice.edu, (2015). Newton's 3 Laws of Motion. [online] Available
at: http://teachertech.rice.edu/Participants/louviere/Newton/law2.html [Accessed 27 Apr.
2015].
School-for-champions.com, (2015). Force Affects Motion by Ron Kurtus -
Succeed in Understanding Physics: School for Champions. [online] Available at: http://www.school-for-champions.com/science/force_motion.htm#.VT3h7yE5_IU [Accessed 19 Apr.
2015].
Formulas.tutorvista.com, (2015). Projectile Motion Formula | Formula for
Projectile Motion | Formulas@TutorVista.com. [online] Available at: http://formulas.tutorvista.com/physics/projectile-motion-formula.html [Accessed 20 Apr.
2015].
Physicsclassroom.com, (2015). Kinematic Equations. [online] Available at: http://www.physicsclassroom.com/class/1DKin/Lesson-6/Kinematic-Equations [Accessed 27 Apr.
2015].
