Ch2marellal

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=toc Lab: A Crash Course Into Velocity (Part 1)= September 8th, 2011 Lindsay Marella and Magna Leffler


 * Objective: ** What is the speed of a Constant Motion Vehicle (CMV)?


 * Hypothesis: ** (Q) What is the speed of a CMV? (H) About 2mph

Constant Motion Vehicle, Tape measure and/or meter sticks, spark timer and spark tape
 * Available Materials ** :


 * Procedure: **

We taped spark tape to the CMV and put it through the spark timer. We turned the CMV on and let it go until all of the spark tape went through the timer. After, we located 10 marks on the tape, recorded their distance and time, and graphed the line to find the average speed of our CMV.


 * Data Points:**

1. Why is the slope of the position-time graph equivalent to average velocity?
 * Discussion questions **

The slope is equal to the rise over run, rise is the change in y, and run is the change in x. Y is position in this graph and x is time, so change in position divided by the change in time is equal to average velocity.

2. Why is it average velocity and not instantaneous velocity? What assumptions are we making?

It takes time to build up to speed, we are making the assumption that once it builds up to it’s peak, its speed will stay constant.

3. Why was it okay to set the y-intercept equal to zero?

It was okay to set the y-intercept to zero because, that was the point at which the line started, zero seconds and zero centimeters.

4. What is the meaning of the R2 value?

How close the line is to a perfect fit.

5. If you were to add the graph of another CMV that moved more slowly on the same axes as your current graph, how would you expect it to lie relative to yours?

I would expect the line of the slower moving CMV to lie below the line of the faster moving CMV because it will cover a smaller amount of space for the same amount of time and the points will be closer together.

The ending result was that our blue constant motion vehicle’s speed was 40.196 centimeters/second, as opposed to our hypothesis, 2mph, or 89.408 centimeters/second. The speed of the constant motion vehicle was actually closer to 1mph. There are countless sources or error in this particular lab and some ways to minimize these issues would be to put brand-new batteries in each one, find a flat floor area and use it for every experiment, make sure that all the CMVs go straight; no turning, and use a flatter meter-stick, or a tape measure for easier, more precise measuring. This affected our percent error, making our vehicle appear slower than the average speed for the "Bule Fast CMV".
 * Conclusion **

**Graph:**

= The Physics Classroom: Lesson 1-Describing Motion with Words=

Introduction to the Language of Kinematics
__M echanics __ - the study of the motion of objects __ Kinematics __ - the science of describing the motion of objects using words, diagrams, numbers, graphs, and equations -it is a branch of mechanics -the goal of any study of kinematics is to make mental models that serve to describe the motion of objects

Scalars and Vectors
__ Scalars __ - quantities that are fully described by a magnitude (or numerical value) alone __Vectors__ - quantities that are fully described by both a magnitude and a direction __Scalar Quantities__: distance, speed __Vector Quantities__: displacement, velocity, acceleration

Distance and Displacement
__ Distance __ - how much ground an object has covered during its motion __ Displacement __ - how far out of place an object is; it is the object's overall change in position. Person walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. Total distance of 12 meters, displacement is 0 meters

Speed and Velocity
__Speed__ - how fast an object is moving, rate at which an object covers distance __Velocity__ - the rate at which an object changes its position The __average speed__ during the course of a motion is often computed using the following formula: The __average velocity__ is often computed using this formula: Q: While on vacation, Lisa Carr traveled a total distance of 440 miles. Her trip took 8 hours. What was her average speed?

Acceleration
__ Acceleration __ - rate at which an object changes its velocity __ Constant acceleration __ - velocity is changing by a constant amount (m/s)/s unit can be mathematically simplified to m/s2 __Positive acceleration__ - object is speeding up __Negative acceleration__ - object is slowing down

=Notes 9/9- (Types of Motion)=

Average Speed
-total distance/total time, instantaneous speed can be different at any given time

Constant Speed
-same speed the entire time, instantaneous is the same

Instantaneous Speed
-a speed at any given time

Only 4 types of motion: at rest, constant speed, increasing, and decreasing Motion Diagram: Constant Speed (V) --> --> --> a=0 Speeding Up (increasing) (V) -> --> ---> a>0 (points in the same direction as velocity) Slowing Down (decreasing) (V) ---> --> -> a<0 (points in opposite direction from velocity)

Velocity/acceleration is positive if: --> or ^ Velocity/acceleration is negative if:<-- or v

= The Physics Classroom: Lesson 2: Describing Motion with Diagrams =

Introduction to Diagrams
-the use of words, graphs, numbers, equations, and diagrams

Ticker Tapes
__Ticker tape__- a long tape is attached to a moving object and threaded through a device that places a tick upon the tape at regular intervals of time - say every 0.10 second -as the object moves, it drags the tape through the "ticker," thus leaving a trail of dots, which provides a history of the object's motion -distance between dots on a ticker tape represents the object's position change during that time interval -large distance: object was moving fast during the time interval -small distance: object was moving slow during the time interval -reveal if object is moving with constant velocity or accelerating

Vector Diagram
__Vector diagrams__- diagrams that depict the direction and relative magnitude of a vector quantity by a vector arrow -vector quantity is represented by the size of the arrow -same size: constant -getting longer: accelerating -getting shorter: decelerating -can show acceleration, force, and momentum

** Activity: Graphical Representations of Equilibrium **

 * 1) How can you tell that there is no motion on a…
 * 2) position vs. time graph: horizontal line on 0
 * 3) velocity vs. time graph: horizontal line on 0
 * 4) acceleration vs. time graph: horizontal line on 0


 * 1) How can you tell that your motion is steady on a…
 * 2) position vs. time graph: straight line
 * 3) velocity vs. time graph: horizontal line on x speed
 * 4) acceleration vs. time graph: horizontal line on 0


 * 1) How can you tell that your motion is fast vs. slow on a…
 * 2) position vs. time graph: position changes quicker on fast, slower on slow
 * 3) velocity vs. time graph: horizontal line on an integer
 * 4) acceleration vs. time graph: horizontal line on 0


 * 1) How can you tell that you changed direction on a…
 * 2) position vs. time graph: position increased and decreased
 * 3) velocity vs. time graph: the same
 * 4) acceleration vs. time graph: the same


 * 1) What are the advantages of representing motion using a…
 * 2) position vs. time graph: find the distance and displacement
 * 3) velocity vs. time graph: find out speed and direction
 * 4) acceleration vs. time graph: find increases and decreases in speed


 * 1) What are the disadvantages of representing motion using a…
 * 2) position vs. time graph: difficult to record exact data
 * 3) velocity vs. time graph: tracks increase/decrease in speed when moving legs (though speed may be constant)
 * 4) acceleration vs. time graph: tracks increase/decrease in speed when moving legs (though speed may be constant)

At rest:
 * 1) Define the following:
 * 2) No motion: object is at rest
 * 3) Constant speed: object moving who have the same speed at all time

Fast:

Slow:

= Cart On An Incline Lab =

9/13/11

Magna Leffler and Lindsey Marella

**Objectives:** 1. What does a position-time graph for increasing speeds look like?


 * A upward, changing, non-strait line.

2. What information can be found from the graph?


 * You can find the place where the cart is as well as what the amount of time it took to get there.

**Available Materials:** Spark tape, spark timer, track, dynamics cart, ruler/meterstick/measuring tape

**Analysis:** a) Interpret the equation of the line (slope, y-intercept) and the R2 value.

Y=12.319x^2+1.3126x, R^2 = 0.99964

b) Find the instantaneous speed at halfway point and at the end. (You may find this easier to do on a printed copy of the graph. Just remember to take a snapshot of it and upload to wiki when you are done.)

c) Find the average speed for the entire trip.

add equations

13.47 cm/s

media type="file" key="Movie on 2011-09-13 at 12.49.mov" width="300" height="300"

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**Discussion Questions:**

1. What would your graph look like if the incline had been steeper?


 * The line would have an increased slope, and the curve would be steeper.

2.What would your graph look like if the cart had been decreasing up the incline?


 * It would be in a downward curve.

3.Compare the instantaneous speed at the halfway point with the average speed of the entire trip.


 * Average speed = 13.47 cm/s
 * Instantaneous speed = 12.5 cm/s
 * The average speed was greater because you reached a much higher speed at some points towards the end. Also the instantaneous speed was only halfway through the data and not at a particularly fast point.

4.Explain why the instantaneous speed is the slope of the tangent line. In other words, why does this make sense?


 * This makes sense because the slope of the line equals velocity, and if the line is strait the velocity is the same through the entire line.

5. Draw a v-t graph of the motion of the cart. Be as quantitative as possible.



= The Physics Classroom: Lesson 3/4 Position Time and Velocity Time Graphs = 1) -For a position-time graph, velocity is the slope -Acceleration means a curved line 2) -what the graph would look like if an object going at a constant speed of 5m/s would look like if it abruptly stopped for 5 seconds -going from a small slope --> big slope = positive acceleration and opposite for negative 3) -the concept of negative velocity 4) -negative velocity -v-t graphs, now I definitely understand them all

=Interpreting Position-Time Graphs=

[[image:Photo_on_2011-09-21_at_22.42.jpg width="560" height="424"]]
Questions 1, 2, 3: 4- V = 56/11, 5.1 m/s 5- V = 4/11, .36 m/s 6- 0 acceleration 7:
 * segment || describe || elapsed time (s) || Xi (m) || Xf (m) || d (Xf-Xi) || V (d/t) m/s ||
 * AB || at rest || 2 || 10 || 10 || 0 || 0 ||
 * BC || constant || 2 || 10 || 0 || -10 || -5 ||
 * CD || at rest || 1.5 || 0 || 0 || 0 || 0 ||
 * DE || constant || 0.5 || 0 || -16 || -16 || -32 ||
 * EF || at rest || 2 || -16 || -16 || 0 || 0 ||
 * FG || constant || 1 || -16 || 0 || 16 || 16 ||
 * GH || constant || 2 || 0 || 14 || 14 || 7 ||

[[image:Photo_on_2011-09-21_at_22.49.jpg width="598" height="454"]]
Questions 1, 2, 3: 4- V = 25/10, 2.5 m/s 5- V = 7.5/10, .75 m/s 6- 0 acceleration 7:
 * segment || describe || elapsed time (s) || Xi (m) || Xf (m) || d (Xf-Xi) || V (d/t) m/s ||
 * AB || constant || 1 || 0 || 0.5 || 0.5 || 0.5 ||
 * BC || constant || 1 || 0.5 || 3 || 2.5 || 2.5 ||
 * CD || constant || 2 || 3 || 0 || -3 || -1.5 ||
 * DE || constant || 1 || 0 || 3 || 3 || 3 ||
 * EF || constant || 2 || 3 || 13 || 10 || 5 ||
 * FG || constant || 1 || 13 || 13.25 || 0.25 || 0.25 ||
 * GH || constant || 2 || 13.25 || 7.5 || -5.75 || -2.875 ||

[[image:Photo_on_2011-09-21_at_22.49_#3.jpg]]
Questions 1, 2, 3: 4- V = 800/100, 8 m/s 5- V = 0/100, 0 m/s 6- 0 acceleration 7:
 * segment || describe || elapsed time (s) || Xi (m) || Xf (m) || d (Xf-Xi) || V (d/t) m/s ||
 * AB || constant || 40 || 0 || 400 || 400 || 10 ||
 * BC || at rest || 30 || 400 || 400 || 0 || 0 ||
 * CD || constant || 20 || 400 || 200 || -200 || -10 ||
 * DE || constant || 10 || 200 || 0 || -200 || -20 ||

(D,E)

F:
1- V = 6km/.25 hr, AB- 24 km/hr 2- at rest, BC- 0km/hr 3- V = 2km/(1/6)hr, CD- 12km/hr 4- V = 8km/.75hr, 10.7 km/hr (average speed and average velocity) 5- 0 km/hr 6:

G:
1- V = 60m/10s, 6m/s 2- V = 0m/5s (at rest), 0m/s 3- V = -100m/25s, -4m/s 4- V = 40m/20s, 2m/s 5- V = 160m/40s, 4m/s 6- V = 200m/6s, 3.33m/s 7- 0m/s 8:

= __Lab: A Crash Course In Velocity (Part II)__ =


 * Date:** 9/21/11
 * Partners:** Rachel Knapel, Molly Lambert, Maggie Leffler
 * Objectives:** Both algebraically and graphically, solve the following 2 problems. Then set up the situation and run trials to confirm your calculations.


 * Calculations for part A:**

According to these calculations, the blue, faster car should travel 135.416 cm or about 1.4 m before catching up and becoming parallel with the yellow, slower car. Below is a video demonstrating this situation.

The blue car placed one meter behind the yellow car and is catching up to it at certain point. We then marked the spot where they met and saw that our calculations from before were close to the experiments results.


 * Calculations for part B:**

Our calculations show that when the two cars meet, the blue should travel 475.375 cm and the yellow car should travel 124.626 cm. Below is a video of the actual situation of the two cars meeting up and crashing.

Here, the two cars crash at a certain point when separated 600 cm. We then marked the place where they crashed, and saw that our results were approximately correct.



The % error in our experiment was very high (88%) because during the trials the blue car would not stay on course which gave us inconsistent results and the yellow cars batteries continued to fall out. Because of these difficulties, it caused our experimental data to stray from the theoretical values we formulated.
 * Discussion Questions:**
 * 1. Where would the cars meet if their speeds were exactly equal?** The cars would meet at the exact halfway point, which would be 300 cm. This is so because they are going the same exact speed so they would travel the same amount of distance in the same amount of time, causing them to meet halfway.
 * 2. Sketch position-time graphs to represent the catching up and crashing situations. Show the points where they are at the same place at the same time.**
 * 3. Sketch velocity-time graphs to represent the catching up situation. Is there any way to find the points when they are at the same place at the same time?**

=Egg Drop Lab= Lindsay Marella and Remzi Tonuzi September 27th, 2011

Two sheets of computer paper taped together to make a cone, one sheet of shredded notebook paper on the inside.
 * Design:**

2 pieces of computer paper 1 piece of notebook paper Scotch tape
 * Materials:**

Prototype 1: This was our heaviest design, because at first we wanted to see how much shredded paper was needed to cushion the egg. We found that 2 sheets was plenty. Prototype 2: On our second test we took a single piece of paper and ripped it by hand which resulted in larger pieces and less absorption. The egg was unprotected, which resulted in a dry crack. Prototype 3: This was our final device, and we played it a safe, by using one sheet of heavily shredded notebook paper. It worked perfectly; the egg stayed intact, and (I believe) was the lightest in the class of the survivors. The only amendment that can be made to our design is possibly using less paper in the cone part to make it even lighter.
 * Results:**
 * || Prototype 1 || Prototype 2 || Prototype 3 ||
 * Egg weight (g) || 54.12 || 68.43 || 55.89 ||
 * Device || 34.99 || 13.80 || 18.49 ||
 * Device + egg || 89.11 || 82.23 || 74.30 ||


 * Acceleration:**

d- 8.5m Vi- 0 (egg was dropped) t- 1.57 (average of 1.97 and 1.16) a= ?

d=Vit + 1/2at 8.5m = (0m/s)(1.57s) + (1/2)(a)(1.57s^2) 8.5 = 1.23a a = 6.90m/s^2 This is less than g=9.80m/s^2.

= The Physics Classroom: ﻿ Lesson 5 Free Fall/Acceleration of Gravity =

Introduction to Free Fall
Free falling object: object that is falling under the sole influence of gravity

A ticker tape trace or dot diagram shows acceleration If an object travels downward and speeds up, then its acceleration is downward.
 * Free-falling objects do not encounter air resistance.
 * All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s



The Acceleration of Gravity
Acceleration of gravity: acceleration for any object moving under the sole influence of gravity. g: quantity of gravity

Representing Free Fall by Graphs
 A position versus time graph for a free-falling object:  Starts with a small velocity (slow) and finishes with a large velocity (fast) Negative slope of the line indicates a negative (i.e., downward) velocity

 A velocity versus time graph for a free-falling object is shown below:

=Freefall Lab= Lindsay Marella and Magna Leffler October 5th 2011

What is acceleration due to gravity? 9.8 m/s 2 What would a v/t graph look like? A diagonal line going away from the origin. How would you get acceleration due to gravity from making a v/t? Acceleration due to gravity is represented on a v/t graph by the slope. (slope = acceleration due to gravity)
 * Hypothesis: **

100 g weight, ticker tape, spark timer, masking tape, measuring tape
 * Materials: **

**Procedure:** We taped a piece of ticker tape to a 100g weight and dropped it from the balcony to the foyer to find the acceleration. Then, the dot were measured and made into graphs (position/time and another to find the acceleration).

**Data:** y = mx + b Vf = Vi + at slope-acceleration y-int- initial velocity



When we made the line of best fit for the P/T graph we used a quadratic line. The equation for our line is y=407.06x^2 - 45.123x, its formula is y=Ax^2 + Bx. We went on to explain that A is really one half of the acceleration and that B is the initial velocity. So the equation of the line is d=v(i)t+1/2at^2. Our acceleration (2A/100) is 8.1412m/s and our Initial velocity is (B/100) 0.44123 m/s.

When we made the line of best fit for the V/T graph we used a linear line. The equation for our line is y=804.55x - 41.792, its formula is y=Mx + B. We went on to explain that M is the slope of our line which is the acceleration and that B is the initial velocity. So the equation of the line is v(f)=v(i)t+at. Our acceleration (M) is 8.0455 m/s/s and our Initial velocity is (B/100) 0.41792 m/s.


 * Discussion Questions: **

1) Does the shape of your graph agree with the expected graph? Why or why not? Yes, it looks like the expected graph of an accelerating object 2) How do your results compare to that of the class? (Use Percent difference to discuss quantitatively.) Our results were very uniform to the rest of the class. Having on a .17% difference clearly shows that our lab was rather accurate. 3) Did the object accelerate uniformly? How do you know? Yes, because our line of best fit was extremely close to a straight line (r value of .99986).  4) What should the velocity-time graph of this object look like?

5) Write down the expected equation of the line from this v-t graph (use specific information from your x-t graph). y=804.55x-41.792  6) What factor(s) would cause acceleration due to gravity to be higher than it should be? Lower than it should be? (...again)

**Conclusion:** My hypothesis was correct. I could have been more specific in how the v/t graph is shaped, but it was correct nonetheless.Percent error and percent difference:



Error was caused by friction from the ticker tape going through the spark box. Also, obviously measurements were not absolutely precise, but quite accurate enough to formulate and almost straight line. If I could change this lab in any way, it would be to find a higher place to drop the weight (with obviously more ticker tape) to collect more data.

=Notes in Classwork Notebook= THE BIG FIVE: 1) d = 1/2(Vi + Vf) t 2) Vf = Vi + at 3) d = Vi(t) + 1/2(at^2) 4) Vf^2 = Vi^2 + 2ad 5) Vav = d/t (constant) Position/Velocity/Acceleration graphs Practice problems similar to Ch2 p40 #30