MOTION IN AIR

MOTION IN AIR INVESTIGATION AND LAB REPORT

Objective: to study the effect of angular projection in a parabolic projection.

BACKGROUND INFORMATION

1.-Energy

Oxford dictionaries define energy as “the property of matter and radiation which is manifest as a capacity to perform work” (Oxforddictionaries.com, 2015).

2.-Mechanics

Mechanics is a field of Science which studies motion, force and energy.

2.1.-Kinematics: Motion

Kinematics is the branch of Mechanics which studies motion, which, at the same time refers to the change in position of an object in relation with time. According to the Encyclopedia Britannica, motion, in physics, is a “change with time of the position or orientation of a body” (Britannica, 2015). The aim of mechanics is to describe, through graphs, tables and equations the motion of an object.

3.-Basic concepts

3.1.-Scalars and Vectors

Mathematical quantities can be either expressed by scalars or vectors depending on their magnitude and direction. Concurrently, scalars are quantities that can be expressed by a single magnitude in the form of numerical number. Vectors however, need to be expressed by both; a magnitude and a direction.

3.2.-Distance and Displacement

Distance and Displacement are totally different concepts in physics. On the one hand, distance is a scalar quantity that relates to the “interval between two points” (physics.org, 2015). On the other hand, displacement is a vector quantity which represents the distance between two points of the previous interval. Moreover, displacement must always be the shortest interval connecting all, initial and final points.

3.3.-Speed and Velocity.

“Speed is a scalar quantity that refers to "how fast an object is moving”, therefore it can be expressed by a single magnitude. In other words, speed refers to the time taken for an object to cover a specified distance. Average speed is given by the following formula:

Average Speed = distance/time  (m/s)

Similarly velocity is vector quantity which “refers to the rate at which an object is moving” (physics.org, 2015). Hence, when calculating velocity we must take into account units of displacement which represent two magnitudes and thus, direction and magnitude must be both studied when calculating velocity. The magnitude of the studied object will be its speed, whilst the direction of the velocity vector will be the same as the direction in which the object moves.

3.4.-Acceleration

“Acceleration is a vector quantity that is defined as the rate at which an object changes its velocity” (Physicsclassroom.com, 2015). Therefore, we assume that an object accelerates when it changes its velocity, that at the same time refers to spontaneous speed and direction. In order for an object to accelerate it must change velocity. Acceleration is given by the following formula:

Acceleration= (Final velocity – Initial Velocity) (m/s) / time (s)

4.-Newton’s Laws

4.1.-Newton’s First Law: Law of inertia

The law of inertia claims that an object which is at rest will stay at rest and an object which is moving will keep moving (same speed and direction) unless an external unbalanced force acts upon it. Moreover, when objects are resting or moving at a constant speed their forces are balanced due to the equilibrium between the forces acting upon them. In normal conditions forces of a moving objects will not be often balanced due to other external forces such as friction that will unbalance the equilibrium.

Objects however tend to stay in their stay of motion and this resistance against change of motion is called inertia. Motion is likewise linked with velocity and therefore inertia must be the tendency of an object to stop its acceleration. (Physicsclassroom.com, 2015)

4.2.-Newton’s Second Law: the law of Motion

This law states that for acceleration of an object to occur, the equilibrium of balanced forces that causes inertia must be broken and hence, forces must be unbalanced. At the same time, the acceleration of an object will depend on the net of force hitting the object and its mass. Once these forces are unbalanced there will be an acceleration. This statement is defined with the following formula:

Acceleration= Net force acting upon he object (N) / mass of the object in grams

(Teachertech.rice.edu, 2015)

4.3.-Newton’s Third Law

Newton’s third Law claims that forces are a result from the interaction between objects. At the same time it classifies forces into push and pull; some of them being a result of a interactions such as inertia and others resulting from action-at-a-distance interactions like gravity. This law reveals that when two objects A and B interact with each other they are exerting forces upon each other. Therefore, if object A was to push object B there would be a response to their interaction which would be for instance its change of speed.

According to Newton, “For every action, there is an equal and opposite reaction” (Hyperphysics.phy-astr.gsu.edu, 2015)

Therefore:

Force A= -Force B // Force A + Force B= 0

For instance, when shooting a projectile with a slingshot, the force of gravity will pull the projectile to the center of the Earth, nonetheless, the projectile will also attract the Earth towards it, however, the mass of the ground will be much greater than the one of the projectile and therefore the projectile will end up falling.

5.-Projectiles

5.1.-Definition:

“A projectile is an object upon which the only force acting is gravity” (Physicsclassroom.com, 2015) , and which is in the air and hence can be sometimes affected by air resistance. A projectile needs to be thrown by an external force in order to cause its change in motion. There are three types of falls a projectile can adopt according to its impulse source.

·         Vertically accelerated projectile: Object thrown to the ground. An example of this would be throwing something to the floor. Gravity acting upon it will cause it to fall downwards by causing an acceleration.

·         Vertical free fall

·         Parabolic fall which results from the combination of vertical acceleration and free fall.  

5.2.-Forces and Projectiles

As projectiles are objects which are only influenced by gravity; the vertical motion of the projectile will be influenced by gravity and therefore a vertical acceleration will be produced. The projectile would be thrown upwards and gravity would push it downwards, creating an acceleration in its fall. Gravity is a downward force and therefore it causes the projectile to increase its acceleration in the downward direction.

5.3.-Projectile parabolic motion

The parabolic fall of a projectile is produced by the combination of vertical acceleration and free fall. Gravity is a force which causes a constant acceleration of 10 m/s^2. . Therefore, “Gravity causes a projectile to move in a parabolic path that is symmetric about the apex (the highest point in the trajectory”. Hence, gravity will not affect the velocity of the projectile but deform its horizontal path.

*Figure 1: representation of the motion of a projectile

*the projectile will move at a constant velocity in the horizontal direction that will be influenced my a constant acceleration caused by gravity in the downward direction of 10 m/s squared.

(Projectile Motion, 2015)

5.4.-Factors that influence the flight of a projectile:

It must be clear that the vertical flight of a projectile is not affected by its mass; as stated by Gallilleo all objects will be attracted towards the Earth with an equal force of gravity, regardless of what its mass is. However we must consider mass when studying a parabolical flight. Moreover, there are three variables that affect the flight of a projectile: projection angle, projection speed and Relative height of projection which is the result of projection height – landing height. Dependent variables such as maximum height or trajectory will be determined by these factors (velocity being always constant). In this project I am going to study the projection angle of a ball. As the projection angle increases, the projection height will increase as well as the time taken in seconds for the ball to fall (with constant air resistance).

·         Angular projection: refers to the angle in which a projectile is projected at an initial velocity (u) and by forming an angle with the horizontal direction.

5.5. –Equations. In this project I am going to change the angle of projection and measure the maximum height reached which is given by the following equation.

 where:

·         H is maximum height

·         Sin 0 is the component along the y axis

·         U: initial velocity

·         G: acceleration caused by gravity

 (Projectile Motion, 2015)

Variables:

·         Independent variable: in this experiment I am going to change the angular projection of my projectile measured in degrees by a protractor. In order to do this I will change the angle at which a ball-gun shoots.

·         Dependent variable: As a result of this variation I will measure the change in maximum height in meters by using a camera to film the parabolic flight of the projectile in order to analyze it afterwards and use the formula explained in the background. I will later watch the video and measure the maximum height of the required projectile by using a ruler in centimeters. I will use a centimeter scale to measure all heights which I will later convert into meters.

·         Constant variable: in order to perform a nice accurate experiment, air resistance must be taken into account. And therefore, all projectiles must be projected in the same place and at the same day with the aim of avoiding any variations. Moreover, mass of the projectile as well as projection velocity must be kept constant. The projectile must be always the same shape and size (one sheet of paper a4 size and 40 cm of cello tape). Initial velocity should always be constant and therefore the elastic band should always be pushed backwards 20 cm.

List of materials

·         A projectile (paper + cello tape)

·         a slingshot

·         2 iron stands

·         Cello tape

·         An elastic band

·         7 different balls of  the same size, shape, and mass

·         A big-sized protractor

·         A filming camera

·         A ruler

·         Logger pro

Method

First of all make your projectile by using a sheet of paper. Fold it until it is tightly held together in a rectangular shape and cover it  in cello tape to ensure that it lasts the whole experiment.

1.-In order to make your slingshot buy a 15 cm elastic band and wrap it around two iron stands of the same size.

2.-Get the filming prepared by placing a video camara in front of your slingshot.

3.-Hold the slingshot tightly by supporting yourself with a chair.

4.-With a protector, ensure that the slingshot projection draws a 10º angle with the chair.

5.-Ask for someone to start filming once you perform number 6.

6.-Take a projectile, pull the elastic backwards 20 cm and let it go.

7.-Repeat this procedure with increasing proportional angles of 10º 20 º 30º 40º 50º 60º 70º and 90º and make sure that you film each of them. Repeat each one 5 times

8.-Analyze the films in your computer by using a special program named Logger Pro.

Hypothesis

Based on my background, according to the formula that defines the maximum height of a projectile its angular projection will influence the magnitude of the sin.

Regarding that as angular projection increases the sin also increases, at constant velocity achieved at x cm of the elastic band and constant acceleration by gravity 10 m/ s², as the angle is greater, the maximum height will increase, until an optimum point is reached at 90 º degrees, where the projectile will reach its maximum height and beyond that, any angles greater than 90º will make the height dip again due to their inclination. (sin of 90º is 1, however sin of 100º is 0,98, sin of 110 0,93 and the relationship  between angle and sin keeps decreasing from aprox. 91º on).

RESULTS

Table

ANGLE OF RELEASE VS MAXIMUM HEIGHT OF PROJECTILE TABLE

Angle of release	sin	sin^2	g= acceleration by gravity m/s^2	maximum height (cm)
0º	0	0	10	4,6
10º	0,17	0,0302	10	11
20º	0,34	0,117	10	11,6
30º	0,5	0,25	10	12,1
40º	0,64	0,4096	10	12,5
50º	0,77	0,5929	10	13,8
60º	0,87	0,7569	10	15
70º	0,94	0,8836	10	19
80º	0,98	0,9604	10	20,5
90º	1	1	10	22

  

VISUAL DIAGRAM OF EXPERIMENT

GRAPH

CONCLUSION

As far as my graph is concerned, I am able to prove that my hypothesis was correct. This graph conveys a directly proportional relationship between the angle of release of a projectile and the maximum height it can reach. As stated in my previous hypothesis, the greater the angle of release is according to the line of the projection, the higher the projectile will go. This occurs due to the following equation:

 (Projectile Motion, 2015)

As the angle increases, its sin does it too and consequently the maximum height rises. Thereupon, keeping the acceleration by gravity constant at 10, as well as the constant initial velocity, the maximum height a projectile can reach with regard to its angle of projection. We have been able to conclude that the optimum angle of projection is 90º with sin 1, as the projectile has had the greatest maximum height, 22 centimeters. The least effective angle is 0º with only 4,6 cm of maximum height. Therefore, our conclusion is that as the angle increases and consequently its sin, the maximum height increases too being 90º the angle by which the projectile is able to travel the highest. This is proven with the results and the graph, as 4,6 < 11< 11,6< 12,1< 12,5< 13,8 <15< 19< 20,5 <22.

EVALUATION OF RESULTS

As a whole the results are concurrent and the expected ones after researching the topic and formulating a hypothesis. As explained in the conclusion, the results increase in number in relation with its increasing sin of the angle.
However, with the line of best fit we are able to conclude that some results are slightly anomalous, as they do not fit exatcly with the line. This might have been caused by errors in the method, which will be specified below. 
All in all, the results were coherent and accurate, in spite of the few times we carried out the experiment.

EVALUATION OF METHOD

After doing the experiment we have noticed some problems with the method; the first being the changes in angular projection. Angular projections were difficult to determine although a protractor was used. Hence, this altered the accuracy of results which were not set at exact, but approximate successive angles. In order to avoid this I would recommend the use of a machine that throws the projectile at a certain angle and thus avoiding any human errors.

Secondly, in spite of using logger pro to analyze all videos recorded, a device more accurate than a mobile camera should be used in order to be able to film the projection properly. Having done the experiment I would suggest recording it with a professional camera and doing it in a background where the projectile is easy to distinguish.

Moreover, all experiments should be done three times each in order to obtain accurate results, especially when dealing with physics. Therefore I would recommend doing the experiment three times in order to obtain an accurate average. 

REFERENCES

-Britannica.es,. (2015). Britannica Digital Learning. Retrieved 10 June 2015, from http://www.britannica.es/

-Hyperphysics.phy-astr.gsu.edu,. (2015). Newton's Laws. Retrieved 28 May 2015, from http://hyperphysics.phy-astr.gsu.edu/hbase/newt.html

-Khan Academy,. (2015). Forces and Newton's Laws of Motion. Retrieved 13 April 2015, from https://www.khanacademy.org/science/physics/forces-newtons-laws

-Oxforddictionaries.com,. (2015). Oxford Dictionaries - Dictionary, Thesaurus, & Grammar. Retrieved 10 June 2015, from http://www.oxforddictionaries.com/

-Physics.org,. (2014). physics.org | Home. Retrieved 11 June 2015, from http://www.physics.org/

-Physicsclassroom.com,. (2015). Acceleration. Retrieved 28 May 2015, from http://www.physicsclassroom.com/class/1DKin/Lesson-1/Acceleration

-Projectile Motion. (2015) (1st ed.). Retrieved from http://oregonstate.edu/instruct/exss323/06_Projectile_Motion.pdf

-Teachertech.rice.edu,. (2015). Newton's 3 Laws of Motion. Retrieved 28 May 2015, from http://teachertech.rice.edu/Participants/louviere/Newton/law2.html

PD: We decided after doing the experiment that calculating the initial velocity was too difficult considering the fact that we only had two lessons to finish the experiment and that the method had some errors mentioned in the evaluation of method. Therefore, we have reduced the objective of the experiment to the study the effect of angular projection in a parabolic projection.

Furthermore, we have taken into account the formative work's feedback and corrected the report. However, the evaluation of the line of best fit has been mentioned in the evaluation of method, rather than in the conclusion, as we thought that it should be there.