Ch3_TalasH

= = =Lesson 1: Fundamentals and Operations - a,b=

toc

=**Lesson 1 - c,d**=

= =

=__Vector addition notes:__ =  


 * 1) Draw a sketch of the vector head-to-tail. Draw vector 1. At the head of vector 1, start drawing vector 2
 * 2) Draw the resultant from tail of vector 1 to head of vector 2 (from beginning to end).
 * 3) Do Pythagorean theorem to find R.
 * 4) Do trig to find theta.

   = = __Estimating__


 * 1) Sign must be between minimum (subtracting) and maximum (adding).
 * 2) Angles must be between the angles and vectors given

Example)



=__Activity: Vector Mapping__ =

Given a start + end position, create a sequence of perpendicular paths to get from beginning to end.

__Parameters__
 * 1) minimum 5 legs
 * 2) measure final displacement
 * 3) hand in index card with requested info

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">__Data__

Measured Resultant: 2689 cm
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Legs <span style="color: #ffffff; font-family: 'Times New Roman',Times,serif; font-size: 110%;">jhnl || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Distance (cm) <span style="color: #ffffff; font-family: 'Times New Roman',Times,serif; font-size: 17.6px;">hn || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Direction ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">786.80 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">N ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">2 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">700.00 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">W ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">3 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">533.50 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">W ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">4 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">359.10 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">W ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">5 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">135.40 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">S ||
 * <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">6 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">1025.5 || <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">W ||

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">__Analysis__

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Draw to scale

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Find resultant magnitude by measuring and by calculating. (graphically and analytically)

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">% error between measured + actual and between calculated + actual

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Graphical Resultant**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Resultant = 2640 cm

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Analytical Resultant**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">786.80 N + 700.00 W + 533.50 W + 359.10 W + 135.40 S + 1025.50 W <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">= 651.4 N, 2618.10 W



R= 2697.92 NW

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">__% Error: for graphical resultant__ <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**( |** theoretical **-** Experimental **| /** theoretical **)** x 100 <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**( |** 2640 **-** 2689 **| /** 2640 **)** x 100 = **1.86%**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">__% Error: for analytical resultant__

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**( |** theoretical **-** Experimental **| /** theoretical **)** x 100 <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**( |** 2640 **-** 2697.92 **| /** 2640 **)** x 100 <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**= 2.19%**

=<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Lesson 1- e** =



=Lesson 1 - f=



=Lesson 1 - g,h=



=Lesson 2: Projectile Motion - a,b=

__Main idea:__ Applying both kinematic principles and Newton's laws of motion to understand and explain the motion of objects moving in two dimensions.

__Questions:__ What is a projectile?


 * when only gravity is acting on an object.

What are the types of projectiles?


 * an object dropped from rest, an object thrown vertically upward, and an object thrown upward at an angle.

What is Newton's law of inertia?


 * Gravity makes an object slow down and come to a stop. Without it, it would keep going.

What is Newton's law of motion?


 * An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

What do horizontally and non horizontally launched projectiles look like?

horizontal



non horizontal

Central idea:
 * A projectile is any object upon which the only force is gravity,
 * Projectiles travel with a parabolic trajectory due to the influence of gravity,
 * There are no horizontal forces acting upon projectiles and thus no horizontal acceleration,
 * The horizontal velocity of a projectile is constant (a never changing in value),
 * There is a vertical acceleration caused by gravity; its value is 9.8 m/s/s, down,
 * The vertical velocity of a projectile changes by 9.8 m/s each second,
 * The horizontal motion of a projectile is independent of its vertical motion.

=Lesson 2 - c=

Main idea: Describing motion of projectiles numerically. A projectile has a vertical acceleration of 9.8 m/s/s, downward and no horizontal acceleration.

How does a projectile only have a vertical force? Does the horizontal force stay the same?

Yes the horizontal force stays the same but when gravity acts on an object the vertical force changes by 9.8 m/s^2.

How do you find the vertical displacement of a projectile, the y component? use the equation y = 0.5 x g x t^2.

How do you find the horizontal displacement of a projectile? use the equation, x = ViX x t

What is the trajectory of a projectile? It is between the x component (constant horizontal motion) and the y component (changing vertical motion).

How will the presence of an initial vertical component of velocity affect the values for the displacement? With no gravity, a projectile would increase the vertical distance and would equal to the time multiplied by the initial velocity (viy• t). With gravity, it would fall a distance of 0.5 • g • t2

What would these two combined influences make? y = viy x t + 0.5 x g x t^2

Central idea: When the initial velocity of the y component is 0, the equation is y = viy x t + 0.5 x g x t^2, not 0.5 x g x t^2.

=Vector Mapping cont.= <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">Measured theoretical Resultant = 63.11 m = 6311 cm
 * Legs || Distance (m) || Direction ||
 * 1 || 30 || East ||
 * 2 || 30 || South ||
 * 3 || 15 || East ||
 * 4 || 15 || South ||
 * 5 || 9.60 || East ||
 * 6 || 2.76 || South ||

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Graphical Resultant**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**Analytical Resultant**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">__% Error: for graphical resultant__ <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**( |** theoretical **-** Experimental **| /** theoretical **)** x 100 <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**( |** 6311 **-** 7320 **| /** 6311 **)** x 100 = **16%**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">__% Error: for analytical resultant__

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**( |** theoretical **-** Experimental **| /** theoretical **)** x 100 <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**( |** 6311 **-** 7254 **| /** 6311 **)** x 100 <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**= 14.94%**

=Ball in Cup Lab= Lab Partner(s): Noah Pardes, Nicole Tomasofsky 10/24/11

How fast does the launcher shoot the ball at "medium range"? (be sure to launch horizontally.)

__Available Materials:__
 * Data Studio || meter stick or metric measuring tape ||
 * plumb bob || target ||
 * ramp || Carbon paper ||
 * masking tape || two right-angle clamps ||
 * Yellow Ball || newsprint ||
 * 1 Photogate Timer || Calipers ||

__Data:__
 * Trial<span style="color: #ffffff; font-family: 'Times New Roman',Times,serif; font-size: 17.6px;">nhjbnlk || Horizontal Distance (cm) ||
 * 1 || 317.56 ||
 * 2 || 323.26 ||
 * 3 || 322.36 ||
 * 4 || 315.61 ||
 * 5 || 318.96 ||
 * Average || 319.55 ||

__Procedure__

media type="file" key="Movie on 2011-10-25 at 10.53.mov" width="300" height="300" media type="file" key="Movie on 2011-10-25 at 10.57.mov" width="300" height="300"



__Finding Time Then **Initial Velocity**__



__Finding Horizontal **Distance**__

Actual = 262.5 cm theoretical = 319.55

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">__% Error:__ <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**( |** theoretical **-** Experimental **| /** theoretical **)** x 100 <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**( |** 319.55 **-** 262.5 **| /** 319.55 **)** x 100 = **17.85%**

=Gordo-rama!=

__Our Car:__

Finding Acceleration Then Initial Velocity d = 11 m t = 4.6 s Vf = 0 a =? Vo =?

Vf^2 = Vo^2 + 2ad lfkdmsbhvgbddddddjkfdshuvfbsdkzfbwlkshjn Vf = Vo + at

The car we created was light weighted, had creative decorations, and survived several trials. However, there is still room for improvement. I would definitely try to reinforce the wheels because they would bend in and out due to the pumpkin mass. We could have used screws to put through the hole in our wheels. This would make the wheels more consistent to go in one direction and would disable them from bending. Also, in order to enable it to have an even slower acceleration, we could have put line-like strips of hot glue around the wheels. It was important to keep the vehicle light, and so we would definitely not change the wheels. = =

=**Lab: Shooting the grade**= October 28 - November 8 2011 Lab Partner (s) : Noah Pardes, Nicole Tomasofsky


 * __Purpose__**

For this lab, we had to find the vertical heights for 5 hoops with a given angle. First, we would need to measure and find the average horizontal displacement and vertical displacement. This will enable us to find the initial velocity since we already have our given angle, 20°. We could then put up the first hoop and measure the displacement from the exact position the ball is launched to the bottom of the hoop. With this information we would be able to find the theoretical vertical height of the first hoop. We would repeat these steps for each hoop and then to find the actual vertical height, we would take the measurement from the center of the hoop to the floor.


 * __Materials and Methods__**

In order to calculate the initial velocity, we placed carbon paper over white paper on our predicted horizontal position. After we launched the ball at least 5 times, using a launcher, we measured what the horizontal distances using measuring tape and averaged them (the ball had left marks on the paper). Then we needed to measure the vertical height of the counter and launcher and calculate the initial velocity. Next we set up the hoops, which is the masking tape, by using tape, string, and paper clips. After we measured the horizontal distance between each hoop, which are to be approximately the same, we used them to calculate the y displacement. Then we set up the theoretical heights and started to do several trials. After much frustration, we realized we would have to change the vertical displacements slightly. In order to compare our theoretical Y, we measured our actual Y.


 * __Observations and Data from Initial Velocity__**

Y displacement = -1.27 m
 * Trials<span style="color: #ffffff; font-family: 'Times New Roman',Times,serif; font-size: 17.6px;">jknbhk,n || X displacement (cm) ||
 * 1 || 499.70 ||
 * 2 || 502.30 ||
 * 3 || 500.10 ||
 * 4 || 503.30 ||
 * 5 || 506.50 ||
 * average || 502.38 ||

The table shows the data used to find average horizontal displacement. This was needed to solve for initial velocity along with the angle, vertical height, and acceleration. Our velocity calculated, 6.72 m/s, was different from the previous activity which was 7.10 m/s. This is probably because of the 20° angle the launcher was set on. Although the angle of a projectile does not usually affect the initial velocity, it did here. This proves that finding initial velocity was an important step for this lab.




 * __Observations and Data from Performance__**

Best Performance media type="file" key="physics best trial.m4v" width="300" height="300"

Actual Displacement Our best trial shows that the ball launched did not go exactly through the center of the hoop. However, it is extremely difficult to this since the launchers are inconsistent.
 * || X (m) jnno || Y (m)<span style="color: #ffffff; font-family: 'Times New Roman',Times,serif; font-size: 17.6px;">mhn ||
 * Hoop 1<span style="color: #ffffff; font-family: 'Times New Roman',Times,serif; font-size: 17.6px;">bn || 0.88 || 1.40 ||
 * Hoop 2 || 1.45 || 1.46 ||
 * Hoop 3 || 2.17 || 1.345 ||
 * Hoop 4 || 2.86 || 1.26 ||


 * __Physics Calculations__**

__Hoop 1__ 6.31 || 6.72sin20 = 2.30 || X d = vit + (1/2)at^2 .88 = 6.31t t = .14 s
 * || x || y ||
 * vi at θ gijhh || 6.72cos20 = jklm
 * a || 0 || -9.8 ||
 * t ||  ||   ||
 * d || .88 || ? ||

Y d = vit + (1/2)at^2 d = 2.3(.14) - 4.9(.14)^2 d =.225 m .24 + 1.27 = //**1.49 m**//

__Hoop 2__

X d = vit + (1/2)at^2 1.45 = 6.31t t = .23 s

Y d = vit + (1/2)at^2 d = 2.3(.23) - 4.9(.23)^2 d = .269 m .269 + 1.27 = //**1.54 m**//

__Hoop 3__

X d = vit + (1/2)at^2 2.17 = 6.31t t = .34 s

Y d = vit + (1/2)at^2 d = 2.3(.34) - 4.9(.34)^2 d = .21556 .215 + 1.27 = //**1.48 m**//

__Hoop 4__

X d = vit + (1/2)at^2 2.86 = 6.31t t = .45 s

Y d = vit + (1/2)at^2 d = 2.3(.45) - 4.9(.45)^2 d = .052 .052 + 1.27 = //**1.32 m**//

__Theoretical__
 * Hoop hjjk || Time (s) hjnk || Y displacement (m) ||
 * 1 || 0.14 || 1.49 ||
 * 2 || 0.23 || 1.54 ||
 * 3 || 0.34 || 1.48 ||
 * 4 || 0.45 || 1.32 ||


 * __Error Analysis__**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">__% Error:__ <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">**( |** theoretical **-** Experimental **| /** theoretical **)** x 100 <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">( **|** 1.49 -1.4 **| /** 1.49) x 100 <span style="font-family: 'Times New Roman',Times,serif; font-size: 110%;">= 6%

My hypothesis was correct because we were able to find where the vertical height would approximately be by using the given angle and the actual horizontal displacement. However we were unable to get the ball through a total of five hoops and into a cup. Unfortunately, we had only gotten it though four hoops. Due to our precise calculations, all of our data matched our results. For example, our theoretical height for the first hoop was 1.49 m and our actual height was extremely close to this; 1.40 m. If the % error is under 10%, this means that the data is accurate. Our highest percent error was 8.78% and our lowest percent error was only 3.00%, meaning we had great results!
 * Hoops kjn || x jkn.kllk || t (s) hjbknm || Theoretical y (m) bhjn || Experimental y (m) hjnkm || % Error ||
 * 1 || 0.88 || 0.14 || 1.49 || 1.40 || 6.00% ||
 * 2 || 1.45 || 0.23 || 1.54 || 1.46 || 5.20% ||
 * 3 || 2.17 || 0.34 || 1.48 || 1.35 || 8.78% ||
 * 4 || 2.86 || 0.45 || 1.32 || 1.36 || 3.00% ||
 * __ Conclusion __**

These errors may have occurred through many misleading factors. For example, the spring in the launcher may have heated up after practicing many trials. This would lead the launcher to have a softer impact on the ball and so our results would slightly change. So as to avoid this, we would need to warm up the launcher before considering if the positions of the hoops should change or not. Also the launcher was extremely inconsistent; the trajectory of the ball would not be exactly the same every time. There were instances where the ball would hit the hoop and then go right through it. There is nothing specific one could do to fix the launcher so it will be exactly the same trajectory every time, unless one invests in a much more expensive launcher that is more consistent. In addition, we did not measure vertical acceleration; we had just assumed that it was -9.8 m/s^2. To receive more accurate results, we could have found a more precise measurement of acceleration.

A real life situation of projectile motion could be when a fireman is putting out a fire. The water shooting out of the hose does not come out straight; it has a parabolic curvature due to gravity. This means that it is important that a fireman takes this into consideration when saving a burning building. In football, projectile motion is also seen. When a football is thrown, it will have a downward acceleration, which will enable the catcher to approximate where to catch the ball. The ball will have a parabolic curve due to gravity and will not shoot straight across only (horizontal motion). Also, the football's trajectory will change if initial velocity, time, and distance change, just like when a ball is launched from a launcher. The same concept exists with a baseball, basketball, etc.