I. Introduction

In this lab the main focus was projectile motion. A projectile is an object flying through the air that is only under the force of gravity (neglecting air resistance). A projectile moves both horizontally and vertically, which creates a parabolic flight path. In vertical projectile motion there is a constant velocity since there are no forces in the horizontal direction (neglecting drag due to air resistance). Consequently, there is no acceleration in horizontal projectile motion. In vertical projectile motion gravity is acting on the projectile, which means that the acceleration in vertical projectile motion is equal to gravitys acceleration (9.8m/s2).

Some equations for projectile motion are the three kinematic equations, the equation for Vx (Vx = âˆ†x/âˆ†t), and the equation for time (âˆ†t = 2âˆ†y/g). The purpose of this lab was to get a projectile falling off a ramp on a table to land in a cup by using equations that are related to projectile motion. The hypothesis was that if all the calculations were correct (based on the horizontal and vertical speed of the projectile, the height of the table, the height of the cup, the time for the projectile to pass through the time gates, and the overall range of the projectile) the projectile would fall into the cup.

II. Procedure

Materials

* A ramp

* Clamp

* Marble

* String

* Washers

* Light probes with computerized recorder

* Styrofoam cup

Procedure

1. Place the ramp on the edge of a table not to close to a wall or anything that the marble might hit. Secure the ramp down with a clamp. Tie a string and attach one watcher to it so that it is just above the ground. 2. Set up the light probes by placing them over the ramp where it becomes horizontal. Make sure they are working right by testing if something goes threw it, than the light on the probe turns red and that the light is green when nothing is moving threw it. 3. Drop the marble from the top of the ramp making sure that you drop it before the screw at the top. The marble will go threw and the computerize stopwatch will record the time. Do this test two more times being careful of the screw and making sure you catch the marble before it hits the ground. 4. Proceed in making the necessary calculations to find the range 5. Once the range is found, you may test to see it your marble lands in the cup given to you. (Make sure to take the cups height into consideration) Safety Precautions

* Electrical safety with wires

III. Results

Many calculations were used to predict the exact spot where to put the cup for the ball to land in it. To find the velocity we used the time found by the light probes, .0251s, and the horizontal distance (Î”x) between the probes, .03m. The equation for horizontal velocity is Vx=Î”x/Î”t and if you plug in the numbers you get 1.19 m/s. From there, the distance from the ramp to the floor was measure. The vertical distance (Î”y) was .93m, but taking the height of the cup into consideration, the vertical distance was .83m. The equation to find time is the square root of 2(Î”y)/-9.8. When putting the vertical distance in the equation, you get the square root of 2(.83)/-9.8 = .41s. Using the calculation Î”x=V/t to find the range, the cup can be placed at .48m horizontally away from the ramp. Unfortunately, the marble didnt go into the cup the first time because of recording issues, but did go in the cup the second time using all of these calculations and equations correctly.

IV. Conclusion

While the events of the experiment support the initial hypothesis of the horizontal velocity and height of the table being crucial to the placement of the cup, the experiment provided unfavorable results. Due to miscalculations the ball struck the far lip of the cup and bounced off. This initial failure can be attributed to miscalculations of the horizontal velocity of the ball, meaning that a photo gate may have been placed on a curved area of the ramp. This resulted in a flawed time variable and potentially a flawed distance variable as well because the distance between the photo gates was estimated using a ruler.

During the second trial, more precision was put into measuring the horizontal velocity. Improvements included placing the photo gates closer to the edge of the ramp (A flat area) and putting the photo gates as close together as possible which provided a much more accurate measurement of distance (0.03m). After subtracting the height of the cup from the vertical displacement, the experiment was conducted again with the center of the cup placed at 0.48 meters. After dropping the ball onto the ramp at a point located directly below a screw (the point used during the time trials) the ball landed in the center of the cup.

V. Discussion

#3

There are two main reasons why the marble might miss the cup. If the height of the cup is not taken into consideration then the ball will fall short. Also, if the light probes are not being placed on the part of the ramp that is parallel to the table, then the ball will still be accelerating when it passes through the lasers. Therefore, the time it takes for the marble to travel will not be accurate and will cause the marble to miss the cup.

#4

Air resistance had a minor effect on the motion of the projectile. The first reason is that the formula for drag ( {Drag = Drag coefficient x Gas density x Velocity2 x Frontal Area)/2} ) explains how drag is directly proportionate to velocity squared. Thus, if the velocity is increased by an increment the drag equation squares that increment, making velocity a huge factor in deciding drag. But since the velocity was low during our experiment only using a small marble, a small ramp, and gravity, huge amounts of drag would not occur.

In the equation, drag is also directly proportionate to the frontal area. The marble has a very low frontal area that would be affected by air resistance. Furthermore, the drag coefficient is lower for spheres than in comparison to prisms and flat objects, according to grc.nasa.gov. This reaches the conclusion that due to the shape of a sphere, or in the labs case, a marble, would have less air resistance in comparison to many other shapes. With these proofs in mind, it ultimately leads to the conclusion that air resistance would not have had drastic effect in this lab.

How Projectile motion relates to real life

Projectile motion occurs in everyday life. In sports, projectile motion is used naturally in calculating how to make a certain object land in a certain area. Examples would be like basketball, in which the player, which wants a basketball to get into a hoop, angles, and then judges the mount of power after choosing the angle. This concept could be used when playing soccer and kicking a goal, in tennis when hitting over the net, in golf when taking the first shot, in archery when shooting an arrow at a target, in baseball when hitting a home run, etc.

Projectile motion is also used in simple devices, such as water fountains or leisure activities such as roller coasters. Many times in roller coasters, after taking the riders up the first hill, they are then free to move by gravity, thus becoming a projectile. The list goes on in how projectiles are used in everyday life, and the following are just a few out of the many useful examples of projectiles.

In this lab the main focus was projectile motion. A projectile is an object flying through the air that is only under the force of gravity (neglecting air resistance). A projectile moves both horizontally and vertically, which creates a parabolic flight path. In vertical projectile motion there is a constant velocity since there are no forces in the horizontal direction (neglecting drag due to air resistance). Consequently, there is no acceleration in horizontal projectile motion. In vertical projectile motion gravity is acting on the projectile, which means that the acceleration in vertical projectile motion is equal to gravitys acceleration (9.8m/s2).

Some equations for projectile motion are the three kinematic equations, the equation for Vx (Vx = âˆ†x/âˆ†t), and the equation for time (âˆ†t = 2âˆ†y/g). The purpose of this lab was to get a projectile falling off a ramp on a table to land in a cup by using equations that are related to projectile motion. The hypothesis was that if all the calculations were correct (based on the horizontal and vertical speed of the projectile, the height of the table, the height of the cup, the time for the projectile to pass through the time gates, and the overall range of the projectile) the projectile would fall into the cup.

II. Procedure

Materials

* A ramp

* Clamp

* Marble

* String

* Washers

* Light probes with computerized recorder

* Styrofoam cup

Procedure

1. Place the ramp on the edge of a table not to close to a wall or anything that the marble might hit. Secure the ramp down with a clamp. Tie a string and attach one watcher to it so that it is just above the ground. 2. Set up the light probes by placing them over the ramp where it becomes horizontal. Make sure they are working right by testing if something goes threw it, than the light on the probe turns red and that the light is green when nothing is moving threw it. 3. Drop the marble from the top of the ramp making sure that you drop it before the screw at the top. The marble will go threw and the computerize stopwatch will record the time. Do this test two more times being careful of the screw and making sure you catch the marble before it hits the ground. 4. Proceed in making the necessary calculations to find the range 5. Once the range is found, you may test to see it your marble lands in the cup given to you. (Make sure to take the cups height into consideration) Safety Precautions

* Electrical safety with wires

III. Results

Many calculations were used to predict the exact spot where to put the cup for the ball to land in it. To find the velocity we used the time found by the light probes, .0251s, and the horizontal distance (Î”x) between the probes, .03m. The equation for horizontal velocity is Vx=Î”x/Î”t and if you plug in the numbers you get 1.19 m/s. From there, the distance from the ramp to the floor was measure. The vertical distance (Î”y) was .93m, but taking the height of the cup into consideration, the vertical distance was .83m. The equation to find time is the square root of 2(Î”y)/-9.8. When putting the vertical distance in the equation, you get the square root of 2(.83)/-9.8 = .41s. Using the calculation Î”x=V/t to find the range, the cup can be placed at .48m horizontally away from the ramp. Unfortunately, the marble didnt go into the cup the first time because of recording issues, but did go in the cup the second time using all of these calculations and equations correctly.

IV. Conclusion

While the events of the experiment support the initial hypothesis of the horizontal velocity and height of the table being crucial to the placement of the cup, the experiment provided unfavorable results. Due to miscalculations the ball struck the far lip of the cup and bounced off. This initial failure can be attributed to miscalculations of the horizontal velocity of the ball, meaning that a photo gate may have been placed on a curved area of the ramp. This resulted in a flawed time variable and potentially a flawed distance variable as well because the distance between the photo gates was estimated using a ruler.

During the second trial, more precision was put into measuring the horizontal velocity. Improvements included placing the photo gates closer to the edge of the ramp (A flat area) and putting the photo gates as close together as possible which provided a much more accurate measurement of distance (0.03m). After subtracting the height of the cup from the vertical displacement, the experiment was conducted again with the center of the cup placed at 0.48 meters. After dropping the ball onto the ramp at a point located directly below a screw (the point used during the time trials) the ball landed in the center of the cup.

V. Discussion

#3

There are two main reasons why the marble might miss the cup. If the height of the cup is not taken into consideration then the ball will fall short. Also, if the light probes are not being placed on the part of the ramp that is parallel to the table, then the ball will still be accelerating when it passes through the lasers. Therefore, the time it takes for the marble to travel will not be accurate and will cause the marble to miss the cup.

#4

Air resistance had a minor effect on the motion of the projectile. The first reason is that the formula for drag ( {Drag = Drag coefficient x Gas density x Velocity2 x Frontal Area)/2} ) explains how drag is directly proportionate to velocity squared. Thus, if the velocity is increased by an increment the drag equation squares that increment, making velocity a huge factor in deciding drag. But since the velocity was low during our experiment only using a small marble, a small ramp, and gravity, huge amounts of drag would not occur.

In the equation, drag is also directly proportionate to the frontal area. The marble has a very low frontal area that would be affected by air resistance. Furthermore, the drag coefficient is lower for spheres than in comparison to prisms and flat objects, according to grc.nasa.gov. This reaches the conclusion that due to the shape of a sphere, or in the labs case, a marble, would have less air resistance in comparison to many other shapes. With these proofs in mind, it ultimately leads to the conclusion that air resistance would not have had drastic effect in this lab.

How Projectile motion relates to real life

Projectile motion occurs in everyday life. In sports, projectile motion is used naturally in calculating how to make a certain object land in a certain area. Examples would be like basketball, in which the player, which wants a basketball to get into a hoop, angles, and then judges the mount of power after choosing the angle. This concept could be used when playing soccer and kicking a goal, in tennis when hitting over the net, in golf when taking the first shot, in archery when shooting an arrow at a target, in baseball when hitting a home run, etc.

Projectile motion is also used in simple devices, such as water fountains or leisure activities such as roller coasters. Many times in roller coasters, after taking the riders up the first hill, they are then free to move by gravity, thus becoming a projectile. The list goes on in how projectiles are used in everyday life, and the following are just a few out of the many useful examples of projectiles.