Ch3_CaspertS


 * __ VECTORS toc__**

**__Homework: Vectors - Lesson 1 (A+B): (Vectors - Fundamentals & Operations) - 10/12__** Vector quantity is quantity described by magnitude and direction. Scalar quantity is quantity described by magnitude. Vector quantities are represented by scaled vectors diagrams. Direction of vector is expressed as angle of rotation from east, west, north, & south or as a counterclockwise direction to due east. Magnitude of vector is depicted by length of arrow.
 * Vectors and Direction **
 * a scale
 * a vector arrow
 * magnitude and direction of the vector is labeled

Two vectors can be added together to determine the result. **The Pythagorean Theorem** Useful method for determining result of adding two vectors __that make a right angle__. Pythagorean theorem can be used to determine the resultant (hypotenuse of right triangle). Direction of //resultant// vector can be determined by trigonometric functions. Measure of angle is __not__ always the direction of the vector.
 * Vector Addition **

**Use of Scaled Vector Diagrams to Determine a Resultant** Magnitude and direction of sum of two or more vectors can be determined by **head-to-tail method**. Where head of first vector ends, tail of second begins. Draw resultant from tail of first to head of last and determine magnitude & direction.

**__Homework: Vectors - Lesson 1 (C+D): (Vectors - Fundamentals & Operations) - 10/13__** Resultant is vector sum of two or more vectors. If displacement vectors A, B, and C are added together, the result will be vector R. (A+B+C=R) When displacement vectors are added, result is //resultant displacement//. If two or more velocity vectors are added, result is //resultant velocity//. If two or more force vectors are added, result is r//esultant force//. 
 * Resultants **

Vector is a quantity that has magnitude and direction. Vector quantities are displacement, velocity, acceleration, and force. Each part of two-dimensional vector is known as **component**. Combined influence of two components is equivalent to the influence of the single two-dimensional vector.
 * Vector Components **

**__Homework: Vectors - Lesson 1 (E): (Vectors - Fundamentals & Operations) - 10/17__** Vectors directed at an angle can be thought of as having 2 parts (upward component, rightward component). Process of determining magnitude of a vector is known as **vector resolution**. Two methods are parallelogram method & trigonometric method.

**Parallelogram Method of Vector Resolution** Accurately draw vector to scale in indicated direction. Sketch parallelogram around vector. Components are //sides// of parallelogram. Measure length of the sides to determine magnitude.

**Trigonometric Method of Vector Resolution** Construct //rough// sketch of vector in indicated direction. Label magnitude and angle. Draw a rectangle about the vector. Components are the //sides// of rectangle. To determine length of the side **opposite** indicated angle, use **sine** function. To find side **adjacent** indicate angle, use **cosine** function.

**__Homework: Vectors - Lesson 1 (G+H): (Vectors - Fundamentals & Operations) - 10/17__** **Relative Velocity and Riverboat Problems** Magnitude of velocity of moving object with respect to the observer on land will not be the same as the speedometer reading of the vehicle.  Use the usual methods of vector addition. Magnitude of resultant velocity is determined using Pythagorean theorem. Direction of resulting velocity can be determined using a trigonometric function.

**Independence of Perpendicular Components of Motion** Force vector has two parts - an upward part and a rightward part. Component describes the affect of a single vector in a given direction. Any vector - force vector, displacement vector, velocity vector - directed at angle can be thought of as being composed of 2 perpendicular components.

=**__ Activity: Vector Mapping __**= **10/19**

**Experimental Displacement = 19 meters 8 centimeters**

**Find Results Analytically:**

**Find Results Graphically:**

**Percent Error (Analytically)**

**Percent Error (Graphing)**

**Conclusion:** Our group obtained a pretty high percent error of 7.56% graphing and 8.27% analytically. One reason for this was our way of measuring the vectors. There was a slight variation between the tail of one vector and the head of another due to human error. Also, when we measured our final displacement we just had 2 people pull the measuring tape in the air. This allowed from a little dip affecting the true displacement. To solve this problem, we could have used a more stiff measuring utensil.

**__Homework: Lesson 2 (A+B) - (Projectile Motion) - 10/19__**

__** Lesson A **__ **Central Idea:** A projectile is an object upon which the only force acting is gravity.

**Questions & Answers:**
 * 1) What is a projectile?
 * 2) A projectile is an object upon which the only force is gravity.
 * 3) What are the different types of projectile?
 * 4) It's not that there are different types of projectile, but an object in projectile can be moving up, down, left, or right. Any object where the only force is gravity, no matter what direction, is a projectile.
 * 5) What does Newtonan phsyics tells us about projectile motion?
 * 6) Newtonian's laws suggest that forces are only required to cause an acceleration?
 * 7) Gravity has a vertical effect on a projectile because it is a downward force. It has 0 effect on the horizontal distance.
 * 8) What is inertia?
 * 9) Inertia is that an object will continue in a straight line at constant speed unless it is acted upon by an unbalanced force.

**__Lesson B__** **Central Idea:** The force of gravity does not affect the horizontal component of motion, but rather it affects the vertical component of an object.

**Questions & Answers:**
 * 1) What is the projectile of horizontally launched projectiles?
 * 2) The projectile travels with a constant horizontal velocity and a downward vertical acceleration.
 * 3) Are there both horizontal and vertical forces on a projectile?
 * 4) No there is only vertical forces, which is gravity.
 * 5) What is a parabolic trajectory?
 * 6) This is when there is a non-horizontally launched projectile. The object starts off with a high, positive velocity, approaches a velocity of 0, and then accelerates with a faster, negative velocity. This motion forms a parabolic shape.]
 * 7) In a launched projectile, what happens if there is no gravity?
 * 8) The projectile would move at a constant speed in the direction it was launched. There would no unbalanced force acting up it to change its trajectory.
 * 9) Is the velocity of the horizontal component of a projectile changing?
 * 10) No the horizontal component is at a constant speed while the vertical component has a decreasing velocity.

**__Homework: Lesson 2 (C) - (Projectile Motion) - 10/20__** __** Lesson A **__ **Central Idea:** The horizontal and vertical components of the velocity vector change with time during the course of projectile's trajectory.

**Questions & Answers:**
 * 1) How does the velocity change in projectile?
 * 2) The horizontal components stays at a constant velocity and the vertical component has an increasing negative acceleration.
 * 3) Is there a force on a projectile?
 * 4) There is no horizontal force, but there is a vertical force downward.
 * 5) What does the equation "y=.5gt^2" mean?
 * 6) This is the equation for finding the vertical displacement of a horizontally launched projectile, which is "y". It is equals to (1/2) X gravity X time squared.
 * 7) What is the equation for a horizontally launched projectile?
 * 8) It is "x=(vx)t". This equation says that the horizontal displacement of a projectile is equal to the velocity of the horizontal component (which is constant) times the time it has been moving horizontally.
 * 9) What does the equation "y=(viy)(t)+(.5)(g)(t^2)" mean?
 * 10) This is the equation for the vertical displacement of a non-horizontally launched projectile. The equation takes into account both the "going up" and "going down" part in the parabolic trajectory that this kind of projectile makes.

=__** Class Activity: Ball in a Cup **__=

**Calculations:**
 * Finding the initial velocity of the ball at medium range.**
 * Guessing the range of the projectile whose only difference is the "change in Y"**

**Procedure:** media type="file" key="Ball in Cup Physics.m4v" width="270" height="270"

**Percent Error:**

We obtained a pretty high percent error of 10.98%. Although there should be some error to due the inconsistency in the ball launcher and the lack 100% efficiency in measuring, it shouldn't be this high. To decrease this we could have used a more stable launcher that didn't shift after each launch. But for the percent error to be almost 11% our group must have made a measuring mistake or did too much rounding along the way.

= __**Gourdorama Project**__ = with Andrew Chung

**Project:**

**Calculations:** Our project had an initial velocity of 2.27 m/s and an acceleration of -1.52 m/s^2. Our distance traveled by our cart of 1.7 meters was sub-par, clearly meaning there were changes that needed to be made to it to make it more efficient.

**Results:** Mass of Vehicle = 2.1 kg Distance Traveled = 1.7 m Time = 1.5 s Initial Velocity = 2.27 m/s Acceleration = -1.52 m/s^2

The two Skooter wheels attached by the piece of wood, which was our axel, was a good idea, but clearly was not efficient enough since our wheels fell off. What we needed was something on both sides of the wheel as well as the outside of the box that that would attach to the piece of wood to keep it stiffer and in use for longer. Also, although the cardboard was strong enough to hold the pumpkin, it did sag a little bit where the pumpkin was. Either we could have used another material for the body or we could have made it sturdier.
 * What to Change: **

= __**Lab: Shoot Your Grade**__ = with Michael Solimano, Nicole Kloorfain, George Souflis

**Purpose:** At a 15 degree angle, to shoot the ball off the counter, through five rings and into a cup. We will calculate the heights of the rings and the cup at equal intervals to predict how much we suspend them from the ceiling.

**Hypothesis** : With the ball shooter at a 15 degree angle on top of the counter, we will shoot the ball through five rings and a cup which display the parabolic trajectory of the ball.

**Find the Initial Velocity:** We did an initial test-shot of the ball. My finding its horizontal distance (4.66 m) we had enough information to solve for the initiial velocity of the ball. With now the initial velocity, acceleration, and change in distance of both they x-component & y-component, we have enough information to find the change in distance of the y-component at any time.

**Ring Predictions at Various Intervals** ** Interval 1 (0.78 m) **  The 1st ring will be .139 m above the ball's initial height. ** Interval 2 **** (1.56 m): ** The 2nd ring will be .138 m above the ball's initial height. ** Interval 3 (2.34 m): ** The 3rd ring will be .01 m below the ball's initial height. ** Interval 4 (3.12 m): ** The 4th ring will be 0.29 m below the ball's initial height. ** Interval 5 (3.9 m): ** THe fifth interval will be 0.714 m below the ball's initial height. ** Interval 6 (Cup) (4.66 m): ** **Procedure:**  By doing a test shot and measuring the horizontal distance traveled by the ball, we were able to have enough to data to find the vertical component of the ball at certain intervals (pictures above). After setting the rings to the correct height, we were able to get the ball through four of the rings. Here is a video of that. media type="file" key="Movie on 2011-11-09 at 09.26.mov" width="243" height="243" **Percent Error:** **1st Interval (Sample):** % Error = (l Theoretical - Experimental l)/(Theoretical) X 100 % Error = (l 1.359 - 1.28 l)/(1.359) X 100 % Error = (.079)/(1.359) X 100 % Error = 5.81 **Conclusion:** In the end, our group was only able to get the ball through four of the rings. We had an average precent error of 5.76% (not including the last ring and cup since we didn't get an experimental value). As you could see in our video, the ball went through the fourth ring; however, it hit the side of it, which is the reason for the inflated 12.9% error on the fourth interval. Other than that, our calculations were fairly accurate to what it came out to be. We were able to keep our horizontal distances fairly accurate with a 0.78 m interval, but we had to change up the vertical distances to fit the ball. There were multiple sources of error that accounted for this. For staters, the ball launcher had problems of its own. After each launch, the launcher shifted a little bit even though we had 2 clamps tied down it tightly. We tried to but the launcher back to its original location, parallel with the counter, but we could not to do it perfectly. We knew it would be up to the edge of the counter, but our group could have put a piece of tape or marker to indicate where to put the launcher. Another problem with it was that it didn't stay at the 15 degree angle after each launch. We kept putting it back, but of course there was inconsistency there. As for an error in the rings, it was almost impossible to get the correct horizontal components for each interval. Although we had the weigh toy, the rings were constantly moving whether it be the ball hitting it or another group lifting up the ceiling. We could come close but there were be a little inconsistency with the horizontal components. In conclusion, this lab was able to show us the parabolic trajectory of projectiles. You could really get the best understanding of that simply by looking at each group's rings when they were all done. It was pretty cool since those rings were showing us the path of the ball over time. This was a perfect example of many real life applications, like the path of a tennis ball off a racket or baseball thrown.