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# The Effect of Air Resistance with Relationship to the Area of the Paper in Free Fall Motion

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I-INTRODUCTION

A. Background of the Study

When an object is dropped, the force of gravity will cause it to speed up as it falls. But friction with the air, called drag, will tend to cause it to slow down. How much drag there is depends mostly on two factors: speed and shape. The faster an object moves through air the more drag there is. A compact object experiences less drag than an object of the same mass that is spread out. As a falling object speeds up, drag increases until it is equal to gravity. At that point, the object continues to fall at a constant speed, called terminal velocity. The tightly folded piece of paper experiences less drag than the loosely crumpled piece. The balance between gravity and drag occurs at a lower speed, a lower terminal velocity, for the crumpled paper. The study was conducted to know the effect of air resistance with relationship to the area of the paper in free fall motion. The specific objective of the study was to determine the factors that affect the air resistance and to determine the effect of size and shape of the area in relation to the speed of fall of the paper on the ground. The crumpled paper would fall faster because it meets less air resistance over its smaller exposed surface. In addition to that the researcher wanted to determine how this research would be applied and useful to daily activities like skydiving, motorbike racing and other sports.

B. Statement of the Problem

This study aims to prove that size and shape of the paper will affect the air resistance it experienced. Specifically, this experimentation aims to answer the following questions: 1. What are the factors that affect air resistance?

2. What type of paper to be used?

Significance of the Study

This study will be conducted in order to prove that the shape of the paper will change the speed of their fall on the design. This would be use in the concept of designing parachute, glides or even the paper plane or kite racing. The study was also important to know the factors that affect air resistance in everyday life, students would be aware why do bicycle and motorcycle racers were wearing streamlined helmet to reduce drag for safety purposes.

C. Scope and Limitations.

This study was concerned primarily on the effect of air resistance in relation to the area of the paper in free fall motion. The speed of the fall of the paper on the ground was measured using the same weight and kind of paper. The scope of the study will be limited to the use of four (4) papers of the same size and kind, one was crumpled, the second one was folded once horizontally and once vertically to make it one fourth of its original size. Paper three and four were left unaltered, but they were held differently when we dropped them. The third was held parallel to the ground, while the fourth one was held vertical and perpendicular to the ground with the bottom of the paper and the same level as the third. Papers were lined up to make sure their bottom was in the same level. The research was done for almost two months and the study made use of the descriptive qualitative and quantitative method of research.

II- REVIEW OF RELATED LITERATURE

This chapter deals and reviews studies and reliable resources and references on problems, topics and subjects closely related to the present study, as follows:

Related Literature:
Air resistance
As mentioned in http://en.wikipedia.org/wiki/drag(Physics), air resistance is the amount of drag or resistance an object comes across when falling. The resistance is the equal and opposite force that acts on the object due to Newtonâ€™s Second Law of Motion. The velocity of the object falling experiences an equal force in the opposite direction as it passes through the air particles. It has been further discussed in http://www.ehow.com/info_8568104_two-air-resistance-falling-objects.html#ixzz2Dc8xOVfU that size and shape are the two factors that affect air resistance. Air resistance works with surface area, so the more surface area, the more air resistance. The greater the size of the falling objects, the greater the amount of air resistance the object will encounter. This is due to the larger amount of surface area on the object that air particles act upon as the object travels. The more aerodynamic the shape of the falling object, the lower the amount of air resistance the object will receive. An aerodynamic shape means there is less exposed surface area on the object that the air particles can act upon. The shape can also alter the ease with which the object passes through the air particles.

A way to model air resistance is an object having to push the air molecules out of the way. Shape is just as important, some times more important, than size. Even how an object is rotating can affect air resistance. He even mentioned that probably the two most important things are called cross-sectional area and shape. A wider object has to push more air out of the way for every meter it falls. An object provided with a pointed bottom has to push less hard to do this than the same object with a flat bottom. This is why the front end of a missile is pointed. Also, an object falling faster has to push more air more quickly that the same object falling slowly. As for falling slower, this also depends on how the air resistance compares to weight.

When objects are hardly moving, such as when they are first released, there is no air resistance. As objects speed up, air resistance increases. High resistance objects will eventually reach a speed where air resistance pushing up is just as big as gravity pulling down: the object has reached its greatest speed. It keeps falling without continuing to get faster. Low resistance objects may be able to reach higher speeds, but not always. A big hollow ball that weighs twice as much as a pencil will not fall faster than a pencil because a pencil has to push so little air out of the way to make room for it. On the other hand, a steel pencil will fall faster than a wood pencil because it takes a higher speed for the air resistance to build up to the weight of the very heavy

III-METHODOLOGY

Materials

|Materials |Description |Number of items | |Paper |Letter size paper of the same |4 | | |size and kind | | |Stop watch |Small but convenient to use |1 | |Meter stick |Wooden 1 meter well calibrated |1 | | |meter stick | |

Paper 3 and 4 were compared the speed of the fall on the ground. In this experiment we used paper to demonstrate the effects of air resistance. The first one was crumpled up in a ball. The second one was folded once horizontally and once vertically to make it one fourth of its original size. Paper three and four were left unaltered, but they were held differently when we dropped them. The third was held parallel to the ground, while the fourth one was held vertical and perpendicular to the ground with the bottom of the paper and the same level as the third. We compared all of the pieces of paper by timing how long it took for them to hit the ground from the same height.

IV.RESULTS/FINDINGS

Observations of Falling Paper

|Paper |Observations | |1 vs. 3 |Paper # 1 fell first | | 2 vs. 3 |Paper #2 fell first | |1 vs. 4 |Paper # 1 fell first | |2 vs. 4 |Paper # 2 fell first | |1 vs. 2 |Paper # 2 fell first | |3 vs. 4 |Paper #4 fell first |

The table had shown that crumpled paper fell first on the ground as compared to paper unaltered an held parallel to the ground. Paper folded vertical and horizontally fell first as compared to unaltered paper held parallel to the ground. Crumpled paper and folded paper were also fell first as compared to unaltered paper held vertical and perpendicular to the ground. . It has been also observed that the folded paper hit first, and the crumpled paper hit afterwards. The crumpled paper had more drag, so it fell at a slower speed, even though the two paper objects had the same weight. Unaltered paper held vertical and perpendicular to the ground fell first as compared to unaltered paper held parallel to the ground.

V-ANALYSIS OF DATA

The results and finding of the experiments had been shown that the crumpled paper fall faster than unaltered paper or flat paper because it meets less air resistance over its smaller exposed surface. The rate at which the paper fall depends on the shape of the object and the resistance it offers the air as they drop. This is seen by dropping a flat sheet of paper and a crumpled piece of paper. The normal sheet of paper has a surface that offers more air resistance to make it fall slower. It supported my hypothesis that one of the factor that affects air resistance is shape of the paper. Since air resistance works with surface area, so the more surface area, the more air resistance. In addition to that the crumpled paper had more drag because it was wider and had more cross-sectional area. This meant that the air had farther to travel sideways to get out of the way. The paper could not travel downward until the air moved out of the way.

Moreover, the position of the paper when it was launch had also effect of the air resistance as in the case of the flat paper held horizontal and paper held vertical. The flat paper held vertical and perpendicular to the ground fell first because when the paper is perpendicular to the direction of motion, it is pushed back harder than when it is parallel. This was the reason why a rocket ship was designed pointed than rounded.

The experiments had done repeatedly because there was a case in a lower height of about 1 meter where the paper were launched the speed of the fall were almost the same with the papers. It has been observed that the distance of the paper from the ground where they were launched should be at least more than one meter.

The findings of this experiment had supported my hypothesis that crumpled paper would hit first the ground than the flat paper.
On the other hand, this experiment worked out really well besides for one thing. In last trial with paper three and four the results were inconsistent so we had to redo it several times. Sometimes the papers would both hit the ground at the same time, and others paper four would land first. It was Interesting to see how object of the same weight can fall at different times with different heights because of air resistance.

VI-GENERALIZATION

A. CONCLUSION
The findings and analysis had concluded and proved that when paper is dropped, the force of gravity will cause it to speed up as it falls. But friction with the air, called drag or air resistance, will tend to cause it to slow down. The drag depends mostly on two factors: 1. Speed: The faster paper moves through air the more drag there is. 2. Shape: A compact paper ( crumpled paper) experiences less drag than a paper of the same mass that is spread out ( flat paper or unaltered paper) The rate at which the paper fall depends on the shape of the object and the resistance it offers the air as they drop.

This is seen by dropping a flat sheet of paper and a crumpled piece of paper. The normal sheet of paper has a surface that offers more air resistance to make it fall slower. The greater the size of the falling objects, the greater the amount of air resistance the object will encounter. This is due to the larger amount of surface area on the object that air particles act upon as the object travels. The paper with a lot of drag will fall more slowly than an object with little drag. If the paper is wide, it will have more drag than a paper with the same weight that is narrow or more compact. Since air resistance works with surface area, so the more surface area, the more air resistance, the crumpled paper had more drag because it was wider and had more cross-sectional area. This meant that the air had farther to travel sideways to get out of the way. The paper could not travel downward until the air moved out of the way.

Analyzing all of these, it has been concluded that the shape of the paper will change the speed of their fall on the ground. A fast-moving paper or any object encounters more drag than a slow-moving paper or any object. This is because the fast-moving object has to push harder to get the air molecules out of the way in time for the object to move through them. An object with a large cross-sectional area encounters more drag than an object with a small cross-sectional area. This is because the air molecules have to travel farther to get out of the way of a large object. A falling object with a lot of drag will travel at a slower speed than a falling object of the same weight (or mass) with little drag. This is because the drag opposes the falling objectâ€™s motion.

B. RECOMMENDATION

After the experiment has been performed, the researcher would recommend trying another experiment by comparing the speed of the fall on the ground of loosely crumpled paper and crumple it a bit more tightly. How does this affect the speed with which it fall? For the most consistent results, researcher should line up the two pieces of paper so that the bottom edges are at the same level before releasing them. The experiments should be repeated with different height of the paper where they would launched and it should be higher than 1 meter in order to hear them hitting the floor at different times.

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