Ch3_HallR

=Lesson 1: Vectors - Fundamentals and Operations= toc

10/12/11 - A and B Summary
__Vectors and Directions__ __Vector Addition__



10/13/11 - C and D Summary




10/18/11 - Lab: Vector Displacement
__Disuccision:__ The different answers and percent errors could be do to many things. Firstly, we could have followed the other group's instructions incorrectly, or the other group themselves may have faulted in writing out their directions. We might have not walked far enough (or too far), or traveled at a different angle. Also, my diagram could be mismeasured, thus resulting in wrong results. To eliminate these errors for next time, I would be more careful in creating my diagram, and also use a large-scale protractor to make sure that we walk in the right direction in the cafeteria. I would be more precise in measuring our distance with the tape measure as well.

=Lesson 2: Projectile Motion=

'What is a Projectile?' Summary:
__Questions:__ 1. What is a projectile? 2. What are the different types of projectiles? 3. Can a projectile have more than one force acting upon it? 4. Is a force required to keep an object in motion? 5. What is inertia?

__Central Idea:__ A projectile, which moves in 2 dimensions, is any object that once //projected// or dropped continues in motion by its own inertia and is influenced only by the downward force of gravity; perpendicular components have no affect on one another.

__Answers:__ 1. A projectile is any object that once //projected// or dropped continues in motion by its own inertia and is influenced only by the downward force of gravity. 2. Types of projectiles are objects dropped from rest, objects that are thrown vertically upward, and objects which are thrown upward at an angle to the horizontal (provided that the influence of air resistance is negligible). 3. No, since by definition, a projectile only has a single force that acting on it, which is gravity. 4. No, a force is not required to keep an object in motion, it is only required to maintain an acceleration. 5. Inertia is the idea that an object will remain in motion (and in the same direction) or at rest unless acted upon by an unbalanced force.

'Projectile Motion' Summary:
__Questions:__ 1. Does the force of gravity affect an object's inertia? 2. Does an object being shot horizontally maintain or increase its horizontal acceleration? 3. While falling, does an object maintain or increase its downwards acceleration? 4. When does a projectile begin free fall? 5. How does the force of gravity affect a projectile being launched non-horizontally?

__Central Idea:__ Projectiles travel with a parabolic trajectory since gravity accelerates them downward from an otherwise straight, gravity-free trajectory., and the downward force and acceleration causes a downward displacement from where the object would be if there were no gravity.



__Answers:__ 1. No, since perpendicular components of motion are independent of each other. 2. Neither, because a projectile is only acted upon by one force, which is gravity, and which does not affect the horizontal component. An addition force would be needed in order for a projectile to maintain or increase its horizontal acceleration. 3. While falling, an projectile increases its downward acceleration, because the force of gravity, which is the one force that is acting upon a projectile, constant increases an object's acceleration at a rate of -9.8 meters per second. 4. An projectile enters free fall once the force of gravity pulls the projectile out of its straight, inertial path. 5. The projectile will travel in a parabolic trajectory due to the fact that the downward force of gravity accelerates it downward from its otherwise straight-line, gravity-free trajectory. The cannonball falls the same amount of distance in every second as it did when it was merely dropped from rest.

Describing Projectiles With Numbers (Horizontal and Vertical Velocity) Summary:
__Questions:__ 1. In a horizontal launch, do a projectile's horizontal and vertical velocities change while in motion? 2. In an angled launch, do a projectile's horizontal and vertical velocities change while in motion? 3. Does a projectile's vertical velocity change at a different rate depending on if it is launched horizontally or at an angle? 4. Where is a projectile's motion symmetrical around? 5. Is there a point where a projectile's vertical velocity is 0?

__Central Idea:__ No matter what angle a projectile starts at, its horizontal velocity will always remain constant, and its vertical velocity will always change at a rate of -9.8 meters per second per second.   

__Answers:__ 1. In a horizontal launch, a projectile's horizontal velocity remains constant, while its velocity changes at a rate of -9.8 meters per second per second. 2. In an angled launch, a projectile's horizontal velocity remains constant, while its velocity changes at a rate of -9.8 meters per second per second. 3. No, a projectile's vertical velocity always changes at a rate of -9.8 meters per second per second, no matter what angle it is shot from. 4. A projectile's motion is symmetrical around its maximum height. 5. Yes, a projectile's vertical velocity is 0 at its maximum height.

Describing Projectiles With Numbers (Horizontal and Vertical Displacement) Summary:
__Questions:__ 1. What is the vertical displacement of a projectile dependent on? 2. How can one find the vertical displacement of a projectile launched horizontally? 3. What is the horizontal displacement of a projectile dependent on? 4. How can one find the horizontal displacement of a projectile? 5. How can one find the vertical displacement of a projectile launched at an angle?

__Central Idea:__ No matter what angle a projectile starts at, its horizontal displacement will always be equal tox = vix • t, while its vertical displacement will be y = 0.5 • g • t2 if fired horizontally, andy = viy • t + 0.5 • g • t2 if shot at an angle.



__Answers:__ 1. The vertical displacement of a projectile dependent on only the acceleration of gravity and not the horizontal velocity. 2. The vertical displacement of a projectile launched horizontally can be found byy = 0.5 • g • t2 3. The horizontal displacement of a projectile is dependent only on its horizontally velocity and the time it has been moving horizontally, not the force of gravity. 4. The horizontal displacement of a projectile can be found byx = vix • t 5. The vertical displacement of a projectile can be found byy = viy • t + 0.5 • g • t2

10/24/11 - Ball In Cup Acitivty


__Discussion of Results and Percent Error:__ Although our initial calculations stated that the ball would land 2.235 meters away from its starting position, we needed to take into account the height of the cup so that it would land inside of it. To do this, we knew that the cup would have to move closer to the launcher, because before, the ball was landing at the bottom of the side of the cup. Therefore, we moved the cup 0.031 meters closer to the launcher, at a position of 2.204 meters away from the launcher. Though this did in fact work and the ball did land inside, we then found where the cup should be analytically, which was 2.14 meters away from the launcher. Even though the ball got into the cup at both 2.204 and 2.14 meters, 2.204 meters was at the edge of where the ball would enter the cup, with the ball entering the center of the cup at 2.14 meters. Since the ball successfully got into the cup three times while it was 2.14 meters away from the launcher, which was also our theoretical answer, our percent error was 0%.

10/26/11 - Lab:Shoot for Your Grade
**__Objective:__** To launch a ball at a specified angle and speed, so that the ball passes through 5 rings in midair consecutively, and lands in a cup on the floor.

__**Purpose:**__ By finding the exact position of the ball after a specific time using its initial velocity, we will be able to locate where to put rings so that the ball will pass through them, and then place a cup so that the ball will land inside of it. The center of the ring/cup will be put at where the ball will be at that certain time, so that it will easily either pass through it or land inside of it.

__**Materials and Methods:**__ First, we found the initial velocity of our launcher. We did this by placing carbon paper on the ground in front of the launcher, which makes a dark dot on a piece of paper beneath it whenever the ball landed on it. By measuring all of the distances that the ball landed, we found the average launching distance of the ball at our assigned angle, which was 25 degrees. By using the average shooting distance, we then found the initial velocity of the ball being shot from the launcher at our angle, 4.84 meters per second. Next, as shown below, we found how long it would take for the ball to reach all of the 5 rings that we would hang. These 5 rings were simple tape rolls, which were hung from the ceiling by string, at 0.5 meter intervals. Once we found how long it would take the ball to reach each ring, we calculated at what height the ball would be at that time; we would hang the rings so that their centers were at these heights, so that the ball would pace through them. Finally, we found how long it would take for the ball to fall 0.7544 meters into the cup, and then how far away the ball would be at that time. At that position, we positioned the plastic cup, so that the ball would land in it.













[[image:ShootG16.jpg width="648" height="701"]]
media type="file" key="Shoot for Your Grade.mov" width="300" height="300" In the end, while we did get the ball to shoot threw 4 of the rings, we only accomplished that due to simple trial and error. Between our theoretical and experimental heights, we had between about a 10% to 15% error. Therefore, we were not completely successful in reaching our hypothesis, which was to shoot the ball through all 5 rings, as well as having it land in the cup. For our first ring, we had a 14.47% error, for our second ring, we had a 12.92% error, for our third ring, we had a 12.33% error, and for our fourth ring, we had a 10.42% error. Unfortunately, we were not able to have our ball go through the 5th ring nor land in the cup at all, resulting in 100% errors for each. The errors for the four rings that we did manage to shoot the ball through could have occured from erroneous calculations, the string holding up the rings slowing slipping from the ceiling, or the air conditioning in the room blowing the rings our of their correct position. If we were to redo this lab, our group would ensure to correct the possible sources of error. If the calculations were the problem, our group might have incorrectly performed a math operation, or simply wrote something incorrect by accident. Next time, we would double check our answers, and make sure they work when prior information is applied to them. If the problem laid in the A.C. or the string, we would more strongly secured the string to the ceiling, which would both prevent the string from falling, and from being blown by the wind. This concept is important to understand, because it can be applied to real-life projectiles. For example, if something was being shot at a specific target, you would want to make sure that whatever is being launched would accurately hit its target, and would have a clear path to reach it. For example, in the case of the military shooting/launching something at an enemy, they would want to know if the projectile would reach the enemy, if it would go to far, or not reach far enough. Furthermore, they would want to see if the projectile would hit anything else while on its path, which would alter its trajectory. If this was the case, they would want to change its path so that it wouldn't hit anything, or alter its initial velocity that it is being shot from.
 * __Conclusion:__**

11/9/11 - Project: Gourd-o-rama
__Pictures__ __Calculations:__ __Results:__ Total Distance traveled: 6.7 meters Total time: 3.01 seconds Total weight (with pumpkin): 1.15 kg Initial Velocity: 4.45 m/s Acceleration: -1.48 m/s2 __Discussion:__ To make it better, I would do a few things differently. Firstly, I would have used larger wheels on my cart, as well as actual axes instead of having each wheel independent of the others. Also, I would have used pins in the corners of the pumpkin to hold it in place, since the string did not stay on well and was too hard to manage. Lastly, I would have hollowed out part of my pumpkin, in order to lessen its weight and thus further reach the goal of achieving the lowest acceleration.