Ch3_Knapelr

Homework 1
10/12/11toc A vector quantity is described by magnitude and direction, while a scalar quantity is described by just its magnitude. Vectors can be show by a vector diagram, which uses arrows drawn to scale in a specific direction. For a vector diagram a scale must be listed, a vector arrow is drawn in a specified direction (has a tail and head), and the magnitude and direction of the vector is labeled. Vectors can go in all directions (north, south, east, west). Two conventions are that the direction of a vector is describe as an angle of rotation of the vector about its tail from east, west, north, or south. Second the direction of a vector is often expressed as a counterclockwise angle of rotation of the vector about its tail starting from Eat. Also, the magnitude of a vector in a scaled vector diagram is depicted by the length of the arrow.

Vectors can be added together to find the resultant, which is also known as the net force. There are two ways of doing this which is the analytical and graphical method. The Pythagorean theorem is used to find the result of two vectors that make a right angle. To then find the angle you use trigonometry. The other method id the head-to-tail method. This includes drawing a vector to scale. Draw the first line and then the second starting from the tail of the first. The draw the resultant and measure and convert back to units used in the problem.

Homework 2
10/13/11 The resultant is the sum of two or more vectors. A vector is a quantity that has both magnitude and direction(2 parts). Any vector directed in two dimensions can be thought of as having an influence in two different directions. The components of a vector depict the influence of that vector in a given direction. The combined influence of the two components is equivalent to the influence of the single two-dimensional vector. The single two-dimensional vector could be replaced by the two components.

Activity - orienteering


Percent error:

Our experimental measure for this experiment was 4.15m, while our theoretical measure for analytical was 4.25. When we calculated our percent error we got 2.0495 which meant that our analytical measurement and the experimental weren't that far off. When we graphed this our theoretical number came out to be 3.5m which was lower than when we did it analytically. Our experimental stayed the same and for this way we ended up getting 18.57%, which is much further away than when we did the analytical method. In conclusion, the analytical method was more accurate than the graphical method for this experiment.

Homework 3
10/17/11 Two types of vector resolution are the parallelogram and trigonometric method. The parallelogram method a drawn to scale diagram of the components. Start at the tail of the vector draw horizontal and vertical lines and then do the same for the head of the vector. Then draw the components (the sides of the parallelogram). Then find the length of a side by converting the units back. The trigonometric method is used to find the length of a side. First you roughly draw a sketch of the diagram, just for the directions. Draw a rectangle around the vector. Then draw the components of the rectangle (the sides). Since you have the angles, use the sine function and substitute the magnitude of the vector for the length of the hypotenuse.

Homework 4
10/18/11 Motion is relative to the observer. The observed speed of the boat must always be described relative to who the observer is. The resultant velocity of the plane (that is, the result of the wind velocity contributing to the velocity due to the plane's motor) is the vector sum of the velocity of the plane and the velocity of the wind. This resultant velocity is quite easily determined if the wind approaches the plane directly from behind. As shown in the diagram below, the plane travels with a resulting velocity of 125 km/hr relative to the ground. If the two vectors are at right angles than the Pythagorean theorem can be used. The magnitude can be found by using trigonometric function, by using the opposite tangent to find the angle. = =

Homework 5
10/19/11

A projectile is an object upon which the only force acting is gravity. 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. Free-body diagram of a projectile would show a single force acting downwards and labeled force of gravity (or simply Fgrav). Gravity acts to influence the vertical motion of the projectile, thus causing a vertical acceleration. The horizontal motion of the projectile is the result of the tendency of any object in motion to remain in motion at constant velocity. Due to the absence of horizontal forces, a projectile remains in motion with a constant horizontal velocity. Free-body diagrams are diagrams used to show the relative magnitude and direction of all forces acting upon an object in a given situation. The size of the arrow in a free-body diagram reflects the magnitude of the force. The direction of the arrow shows the direction that the force is acting. Each force arrow in the diagram is labeled to indicate the exact type of force. There is only one rule for drawing free-body diagrams is to depict all the forces that exist for that object in the given situation.


 * For this homework the website said that we were supposed to do method 3, but by accident i did lesson one and i asked you and you said that it was okay.

Homework 6
10/20/11

How can you describe projectiles? You can describe them using numbers and by creating graphs to show the motion and the horizontal and vertical motion.

In which directions do projectiles move? Projectiles can move in both vertical and horizontal motion.

What does gravity affect? Gravity affects vertical motion, but not horizontal motion. This is because gravity is a vertical force.

Main idea - You can describe the motion of vectors with numbers and that vertical motion would be 9.8m/s if their is no horizontal force acting upon it.

How do you find displacement of projectiles, horizontal and vertical? equation for vertical displacement - y=.5gt 2 Horizontal displacement is only influenced by the speed Horizontal displacement equation x=v ix T

What is inertia? Inertia is the resistance of change.

Main idea - the differences in equations and to look at vertical and horizontal projectiles and displacement.

What are the 8 characteristics of projectiles? 1. A projectile is any object upon which the only force is gravity 2. Projectiles travel with a parabolic trajectory due to the influence of gravity 3. There are no horizontal forces acting upon projectiles and thus no horizontal acceleration 4.The horizontal velocity of a projectile is constant (a never changing in value) 5. There is a vertical acceleration caused by gravity; its value is 9.8 m/s/s, down 6. The vertical velocity of a projectile changes by 9.8 m/s each second 7. The horizontal motion of a projectile is independent of its vertical motion. 8. the speed of a projectile is symmetrical around maximum height

Ball in cup
Lab

media type="file" key="My First Project - Medium.m4v" width="300" height="300" In conclusion, we were able to calculate the distance where the ball should land, but it was .74% off of where it actually landed.

Gourd-o-rama
We found that our initial velocity is 2.93 m/s and the acceleration is -.493s. Our pumpkin's furthest distance traveled was 8.7m in 5.93 seconds. Our project was able to travel a far distance and not fall apart while traveling down the ramp. Although this is true i would still make some changes if i were to do this again. We built our car to have the wheels able to slide through the hat, therefore during some runs the two sets of wheels were uneven causing it not to go as far.

Shoot your grade Lab
november 5th 2011 Lab partners: Andrea Aronsky and Jake Greenstein

The purpose of this lab was to be able to calculate the height of 5 hoops so that a ball would go through them when shot. Our ball was launched at 25 degrees, which caused us to have to readjust our velocity from the ball in cup lab part one. Also due to the angle, we knew that the distance the ball would travel would be different and the amount of time it would take to hit the ground would be different. We had to calculate all of this new data to be able to ensure that the ball would land in the cup at the right distance. We calculate both of the x and y components initial velocity and used those numbers and the x-distances of the hoops to find the y distances, so that the ball would go through the hoop.
 * Rationale:**

The ball will go successfully through the hoops and land in the cup if all our calculations were correct. The ball will have a parabolic trajectory.
 * Hypothesis:**

The materials we used were a ball, launcher, rolls of tape, string, and a tape measure. The angle that we set the launcher at was 25 degrees. We hung the rolls of tape to the ceiling with string. We then found the vertical heights of all the rolls of tape and then shot it through making adjustments to each roll to make sure that the ball would go through. Mostly, we just had to make small adjustments either moving it up, down, left, or right. In the end, we were able to get it through all 5 hoops.
 * Materials and methods:**

We launched the ball five time and then measured the distance from the launcher to the carbon paper to find the average ranger. We then used this number to calculate initial velocity and hang time.

These are the calculation that we used to find the time the ball would take to hit the ground at a 25 degree angle and also the inital velocity. We found the hang time to be 7.3s and the initial velocity to be 47.64 cms

Calculations for vertical distance of the rings: The calculations above are for the vertical distances where each ring should be. This is the calculation for how far the cup should be so that the ball being launched would land in the cup.

This is my sample calculations for percent error.

media type="file" key="New Project - Medium.m4v" width="330" height="330"

Data: This is a chart of the horizontal distances, the time the ball took to get to each hoop, the vertical distance we found mathematically, the vertical distance that we measured when doing the experiment and finally our percent error. We were not able to get the ball into the cup, but we still got it through 5 of the rings.

Conclusion: We found our hypothesis no to be entirely true. The first part of our hypothesis was correct. We thought that when you launched a ball the rings would start off by getting higher then decrease until it hits the floor. This is shown to be true through our calculations and the experimental height of the rings. You can see that it starts off high then gets higher until it hits its peak and then the heights get closer to the ground. Our calculations for the 4th and 5th rings showed to be negative numbers which just meant that the height of the rings would be lower than the height of the launcher. The part of our hypothesis that was off was where the rings should be placed so that the ball would go through them and land in the cup placed on the ground. It turned out that our calculations were a little off and so after setting up our rings we had to slightly adjust them so that the ball was able to go through all 5 rings. Our percent error for all the five rings ranges a lot, from 0.88% and 17.21%. Due to its parabolic trajectory and a vertical acceleration of -9.8 m/s the percent error for the rings further away from the peak could reasons to why the percent error is higher. There were many place for error in this experiment. Many other groups used our strings and the launcher and the strings would fall; therefore making us have to rehang them, which would make the horizontal distance a little off. Another source of error was the angle of the launcher. We set it to the correct angle, but sometimes it would shift and angle up or down. Another place for error was the launcher itself and how it was inconsistent. Depending on whether we hadn't used the launcher yet or if we had been launching the ball for 20 min would dictate where the ball would go. Because of this each launch would be different; therefore it was hard to get the ball through all the rings and the cup. One launch we would get it through 4 rings and then the next time it would go through the first one, but then hit the second. One last source of error was air resistance. Our calculations did not take air resistance into account, only the effects of gravity. The air vent was close by our strings and experiment so the air blowing would move the rings. We could fix these errors if each group had their own launcher and string and rings so that it would not be moved. Also, if we either shut off the air vents or used a launcher that wasn't near the vents would help in reducing the percent error. We could have also checked the angle and made sure that it was at 25 percent each time we launched the ball. We could have also made sure that the strings were secure that they didn't move. Also, something that would cool the springs would be good so that the springs would not heat up. We could have also waited a certain amount of time in between each launch to let the springs cool down.