e103 Projectile

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ABSTRACT. Launch angles of projectiles greatly affect the range and maximum vertical distance of a launched projectile. Greater angles have shorter range and higher maximum vertical distance while smaller angles achieve reverse results. INTRODUCTION Projectile Motion is a different kind of motion because it still moves along a straight line but because of gravity it falls back again to earth after being released into air. Projectile Motion usually travels along a parabolic path or trajectory. There are many applications of projectile motion including the release of canons, throwing objects and even long jump from one place to another. The experiment will try to explain principles regarding projectile motion like the range of projectile, the angle of projectile and the highest point of projectile. This experiment aims to explain relationship of angle, range, and maximum height to the projectile being released. THEORY Projectiles are bodies that are released in the air, affected by gravity and always travel a parabolic path. The motion of projectiles is called projectile motion. There are 3 kinds of projectile motion which is ground to ground, air to ground and ground to air. Projectiles are usually affected by the velocity of the body while it’s been released, the angle of launch, and the gravity sometimes it is also affected by the wind. Regardless of the air resistance, velocity of a ground to ground projectile motion is still can be determined using the general formula of velocity which is distance over time. The formula is represented below: V o = x t where V o is the initial velocity of the projectile and x is the horizontal distance and t is the time. The time of travel of the projectile is usually affected by the vertical distance of the projectile to the ground over the gravity. This relationship can be represented by the formula: t= 2 y g where y is the vertical distance of the projectile to the ground and g is the gravity constant which is 9.8m/s 2 . The range of the projectile is affected by the square of the initial velocity of the projectile multiplied by the angle and divided by gravity. It can be represented by the formula: R= V o 2 sin 2 Ө g where R is the representation of range, V o is the initial velocity of the projectile sin2Ө is the angle of launch and that g is the gravity constant which is 9.8m/s 2 . To determine the maximum height of the projectile, you must again consider the initial velocity, the angle of launch and the gravity. The formula is represented below: y max = ( V o sin Ө ) 2 2 g where y max is the representation of the maximum height of the projectile, sinӨ is the angle of launch, and that g is the gravity constant which is 9.8m/s 2 . Since projectile motion experiment gathers 2 different experimental values. It is

Transcript of e103 Projectile

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ABSTRACT. Launch angles of projectiles greatly affect the range and maximum vertical distance of a launched projectile. Greater angles have shorter range and higher maximum vertical distance while smaller angles achieve reverse results.

INTRODUCTION

Projectile Motion is a different kind of motion because it still moves along a straight line but because of gravity it falls back again to earth after being released into air. Projectile Motion usually travels along a parabolic path or trajectory. There are many applications of projectile motion including the release of canons, throwing objects and even long jump from one place to another.

The experiment will try to explain principles regarding projectile motion like the range of projectile, the angle of projectile and the highest point of projectile. This experiment aims to explain relationship of angle, range, and maximum height to the projectile being released.

THEORYProjectiles are bodies that are released in the air, affected by gravity and always travel a parabolic path. The motion of projectiles is called projectile motion. There are 3 kinds of projectile motion which is ground to ground, air to ground and ground to air. Projectiles are usually affected by the velocity of the body while it’s been released, the angle of launch, and the gravity sometimes it is also affected by the wind.

Regardless of the air resistance, velocity of a ground to ground projectile motion is still can be determined using the general formula of velocity which is distance over time. The formula is represented below:

V o=xt

where Vo is the initial velocity of the

projectile and x is the horizontal distance and t is the time.

The time of travel of the projectile is usually affected by the vertical distance of the projectile to the ground over the gravity. This relationship can be represented by the formula:

t=√ 2 yg where y is the vertical distance of the

projectile to the ground and g is the gravity constant which is 9.8m/s2.

The range of the projectile is affected by the square of the initial velocity of the projectile multiplied by the angle and divided by gravity. It can be represented by the formula:

R=V o

2sin 2Өg

where R is the representation of

range, Vo is the initial velocity of the projectile sin2Ө is the angle of launch and that g is the gravity constant which is 9.8m/s2.

To determine the maximum height of the projectile, you must again consider the initial velocity, the angle of launch and the gravity. The formula is represented below:

ymax=(V o sinӨ )2

2g where ymax is the representation

of the maximum height of the projectile, sinӨ is the angle of launch, and that g is the gravity constant which is 9.8m/s2.

Since projectile motion experiment gathers 2 different experimental values. It is necessary to use the percentage difference formula which is represented below:

%dif=|EV 1−EV 2|

( EV 1+EV22 )x100%

where EV1 and EV2 are

2 experimental values gathered.

The formula must be used to determine accuracy of the results. It is different to the usual percentage error formula which has 1 experimental value and 1 actual value.

The formulas for the range, time and ymax are all derived using the relations of physical quantities in ground to ground motion. In ground to ground projectile motion, we can see from the formulas of range and ymax that it is really affected by gravity. The force of gravity allows the projectiles to back to ground after being released. If there are no gravity, bodies released in air will travel a straight line and will no longer come back. But because of gravity, bodies’ comeback and it now doesn’t only travel a straight line but it travels

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now 2 dimensional path because of the force of gravity.

MATERIALS AND METHOD

We borrowed first all the necessary equipments in this experiment, we borrowed 1pc projectile launcher, 1 pc metal ball, 1pc meter stick, 1pc plumb line, 1pc ram rod, 1pc iron stand with clamp and 1pc target board. We also bought carbon paper to measure the range of the projectile.

We can see from Figure1 (left) the materials that we borrowed.

Figure1

Take note that the experiment that we performed was really risky if improper handling of the equipment was done. The metal ball is really solid and it can hurt anybody. So, the projectile launcher and the metal ball must be properly handled when conducting the experiment. In our case, we didn’t have had any problem handling all the equipments.

After borrowing the equipments, we read the manual and we found out that the experiment again has 3 parts. We performed first the first part which is the determination of the initial velocity of the projectile. First we measure the y or the vertical distance of the projectile to the ground using the plumb line, then we set-upped the projectile launcher to short range using the ram rod and set-upped the angle to 0o. Simultaneously, while some of us are solving the time of travel of the projectile, some of us had put bond paper and carbon paper at the possible places where the projectile should land. After which we carefully fired the projectile to avoid accident. It then landed to the bond paper with carbon paper. We performed 5 trials to ensure that we got accurate results.

After performing the 5 trials, we measured the horizontal distance(x) after which some of my group mates solved the initial velocity.

The first part of the experiment was important because the initial velocity was an important factor in determining the range and the maximum height of the projectile. Then we get the average of the 5 trials and the data is the one that we used in the succeeding experiments.

After solving we gathered all the necessary data and recorded it. After which we then proceeded to the 2nd part of the experiment which is the determination of the range of the projectile. The 2nd part has 2 parts. It differs only on the angle of launch but the procedure was still the same. When we performed the first part, we set-upped the projectile launcher to an angle of 30o and we set it upped near the edge of the laboratory table. We again placed bond paper and carbon paper to measure the 1st experimental value of the range using the meter stick. Then we set-upped again the projectile launcher to short range using ram rod and carefully fired the metal ball again. We did again 5 trials to ensure accuracy and after which we recorded the results. To determine another experimental value of the range we solved it using the velocity we got from part 1. Then we computed the percentage difference. We repeated the procedure using 60o

angle of launch and we recorded again the results and solved the 2nd experimental value of range using the formula.

Figure2

We can see from Figure2 the actual performance of the determination of the range. After we gathered all the results we performed the last part of the experiment which is the determination of the maximum height of the projectile or ymax. We set-upped again the projectile launcher to 30o

and place it again near the edge of the laboratory table. Then we placed the target board to the middle of the computed range. We placed the

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bond paper and carbon paper to the target board because the ball now must hit the target board. Using the ram rod we set-upped the projectile launcher to short range and carefully fired again the metal ball to the target board. We did again 5 trials to ensure accuracy and after which we solved the 2nd experimental value of the ymax

using formula. We also measured the other experimental value ymax by using meter stick and measuring it from the ground to the point where the ball had hit the target board. After which we recorded all the results.

RESULTS & DISCUSSION

All the data gathered from the first part of the experiment are summarized below:

Trial Horizontal Distance(x)

Initial Velocity

1 0.53m 2.3m/s2 0.52m 2.26m/s3 0.53m 2.3m/s4 0.54m 2.34m/s5 0.52m 2.m/s

Table1

We can see from Table1 the experimental values of the horizontal distance of the projectile launched at 0o. We can also see the computed initial velocity from each trial. The average of the computed initial velocity is 2.30m/s. From the formula in theory section time is computed by the vertical distance and gravity. The vertical distance that we got from the experiment is 0.26m and the time is 0.23s. We can also see from Table1 that values of the horizontal distance are closer to each other which means that they are somehow accurate.

The data we gathered and solved in determining the range of the projectile is summarized below:

Trial Range(experimenta

l value)Percentage Difference

1 0.52m 11.55%2 0.52m 11.55%3 0.52m 11.55%4 0.523m 11.75%5 0.524m 11.93%

Table2

We can see from Table2 the data gathered using 30o launch angle of the projectile. We can see that the experimental value of range which is determined by measuring using meter stick is also close to each other. The percentage difference is computed using the other experimental value of the range from the formula in the theory section. The computed value of

range is 0.465m. We can see that the percentage difference is quite large but it is still accurate because two experimental values are tested for accuracy. Using the 60o angle the values gathered are summarized below:

Trial Range(experimental value)

Percentage Difference

1 0.515m 10.2%2 0.517m 10.59%3 0.513m 9.82%4 0.513m 9.82%5 0.513m 9.82%

Table3

We can see from Table3 the data gathered using 60o launch angle of the projectile. We can see that the experimental value of range is still close to each other. Again the computed value of range is 0.465m. We can also see that the percentage difference quite become lower in terms of values. But the values are somehow still closer to the 30o

launch angle results.

The data gathered from part 3 which is the determination of the maximum height of the projectile are summarized below:

Trial Maximum height (experimental value)

Percentage Difference

1 0.06m 11.02%2 0.06m 11.02%3 0.06m 11.02%4 0.065m 3.03%5 0.065m 3.03%

Table4

We can see from Table4 the data gathered from part3 using 30o launch angle. We can see again that the experimental values of the height are closer to each other. The experimental values of the maximum height are determined by manually measuring it using meter stick. The other experimental value is computed using the formula from the theory section. The value we computed is 0.067m. We can see that the percentage difference is also quite large but we can see from trial 4 and 5 that it has lesser percentage difference.

Using 60o angle the values gathered are summarized below:

Trial Maximum height (experimental value)

PercentageDifference

1 0.185m 7.8%2 0.185m 7.8%3 0.19m 5.13%

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4 0.195m 5.13%5 0.195m 5.13%

Table5

We can see from Table5 the data gathered using 60o launch angle of the projectile. We can see that the experimental value of the height is still close to each other. The computed value of the maximum height is different this time. We computed 0.20m this time. We can also see that the percentage difference quite become lower in terms of values. But the values are somehow still closer to the 30o launch angle results.

Upon comparing the 30o and 60o results we can see that in determining the maximum height, we produce lesser percentage difference and that in determining the range we produce higher percentage difference.

CONCLUSION The experiment shows that larger launch angles have shorter range while having higher maximum distance. The percentage difference is calculated from the initial velocity where the angle is 0o. The data also shows that larger angles produce lesser percentage difference which means that they approach closer to quadrantal angles where angles form a line. The bottom line is in ground to ground projectile motion; one thing that must be consider to successfully fire the projectile to the target, is the angle of launch because as what the experiment had shown greater launch angles have higher maximum distance and shorter range.ACKNOWLEDGMENT & REFERENCE I would like to thank some of my group mates who bought the carbon paper for us to use in this experiment. I would like also to thank the Institute for allowing us to borrow the necessary materials in this experiment. I would like also to thank the 2 laboratory assistants who assist us in using the equipments and carefully guide us on the risks that we might encounter during improper handling of the experiment.

[1] http://www.physicsclassroom.com/Class/vectors/U3L2a.cfm

[2] http://en.wikipedia.org/wiki/Projectile_motion

[3] Young, Hugh D. ,Freedman, Roger A., Ford Lewis A., University Physics with Modern Physics, 12th Edition, 2008