Home Cooking 11-25-14: Projectiles n' Stuff

This Home Cooking involves launching a ball off of a ramp and predicting the change in X 

X Velocity

Y Velocity

Screenshot of Video

Our Math:

Voy = 0.451 m/s
Vox = 1.675 m/s
Height of ramp: 0.21 m

Y = Vot + 1/2gt^2
-0.21= 0.451t+1/2(-9.8)t^2
0 = 4.9t^2 + 0.451 - 0.21

USING THE QUADRATIC FORMULA

(time equals -b plus or minus the square root of b^2 - [4ac] all over 2a)

t = 0.25809 seconds

THEN FIND CHANGE IN X

X = (0.25809) * (1.675) =

                                        = 43.23 centimeters or 0.4323 meters


Actual Distance/Error Analysis:

Distance: 58.25 centimeters or 0.5825 meters

When doing this mini-lab, a few errors could have caused our distance (calculations vs. actual) to be off about 15 centimeters. During the analysis of our lab on LoggerPro, our scale may not have been accurate (we used a roll of tape) which may have brought up error in our lab. The ball we used for this lab was also a bit blurry on LoggerPro and, even though we tried to put a point in the middle for each frame, it may also be in accurate. If the angle was pointed towards the right or left (rather than straight), the distance may also be shorter.

WE LOVE PROJECTILE MOTION!
(thank you Yusuf for the help!)

Projectile Motion Part 2 - Embrace the Struggle

Objectives:

• Measure the velocity of a ball using two Photogates and computer software for timing. 
• Apply concepts from two-dimensional kinematics to predict the impact point of a ball in projectile motion.
• Take into account trial-to-trial variations in the velocity measurement when calculating the impact point. 

Key Terms:

     Velocity

      Position 

      Acceleration 

      Displacement
      Accuracy
      Precision

Pre-Lab Discussion:

1. If you were to drop a ball, releasing it from rest, what information would be needed to predict how much time it would take for the ball to hit the floor? What assumptions must you make? Since you have acceleration (g = 9.8m/s^2) and Vo (0 m/s), you need to find final velocity. 
2. If the ball in Question 1 is traveling at a known horizontal velocity when it starts to fall, explain how you would calculate how far it will travel before it hits the ground. You must find the change in X. You know the initial velocity for both components. The vertical component is free fall and the time (t) up = time (t) down. 
3. A pair of computer-interfaced Photogates can be used to accurately measure the time interval for an object to break the beam of one Photogate and then another. If you wanted to know the velocity of the object, what addition information would you need? You would need to know the change in X and the time, which is measure by the Photogate. 

Procedure: 

Considering this section of the lab was a horizontal component, the ball had to roll on a horizontal surface after leaving the ramp. Our setup looked like this: 

Setup for Horizontal Component. Ramp was taped in place to reduce movement and error throughout the experiment. After five trials, we found five distances: 0.42 m, 0.428 m, 0.422 m, 0.425 m, 0.427 m. 

When measuring the distance of the impact point, the ruler was lined up with the EDGE of the table and the ruler of the floor was lined up with the tiles so it was straight

Rather than taping the floor where the impact point was, we used carbon paper. The carbon paper is placed over the white paper (Look, Physics on Physics!) and leaves a dark circle when the ball lands on it. 

                                                

1. Ramp was constructed
2. Photogates were place at end of ramp where the ball will be rolling on the book
3. Photogate distance was set and LabQuest data recorder was set to PULSE
4. Ball was rolled down ramp 9 times (9 trials)
5. Photogates recorded time and velocity 

Takeaways/Analysis: 

Data Table from recorded information/calculations






Time and Velocity graphs






Time and Velocity graphs, time analyzed







Time and Velocity graphs, both analyzed. The slope should be 0. 

1. Was your actual impact point between your minimum and maximum predictions? If so, your prediction was successful. Our prediction was not successful but very close to the range of data we recorded. The important aspect of the horizontal component of this lab is to take away the fact that the ball will always land (more or less) in the same spot. In the extension in this lab below, the impact point of the ball will change depending upon the angle it is 

EXTENSION

The extension portion of the lab turned out to be extremely rewarding, yes, even after three classes of struggling to find just the right lab set up. Using the same ruler and carbon paper system before, my lab group and I launched ourselves into a physics adventure. First I want to discuss two previous set ups we tried:

Set Up One - 

"it's not even clearing the book at 15 degrees, Sarah"

In this set up, we attempted to use a setup similar to the horizontal component. When a ramp (we used a book cover) is adjusted to meet the 30, 45, and 60 degree goals. We found that the ball was not able to roll over the ramp. We also tried to shoot it with a rubber band. That practically screamed "ERROR." We decided not to do that.

Set Up Two - 

"isn't 45 degrees suppose to go farther than 30 degrees Sarah?"

In this set up, Mr. Eschelbacher (shout out, probably spelled your name wrong) provided us with a heavenly Projectile Launcher. We originally had this set up on the edge of the table: 

Of course, this means we did not take into account of a LOT of things (such as change in X) and we had to ditch this idea. 

Set Up Three - SUCCESS

"no way - it works!"

Dont get me wrong, there was still a lot of struggle in this set up as well. We learned we had to pull the level back further for more power and adjusted the ruler for each angle, both of which were previous errors. Lets get talkin'

Here's How We Did It:

First, we started with 30 degrees. We used a protractor app on the iPad to measure the angle for the Projectile Launcher. Using the carbon paper, we lined it all up and started our trials. The ball was shot out of the launcher five times for each angle (30,45,60). Books of the same height were laid out in front of the launcher so the ball lands at the same 'ground level.'A few errors arose as we started this successful chapter of our lab, including position of the ruler, position of the black card we used to shoot the launcher, slight movement of Projectile Launcher every time a ball was shot, etc. We did what we could to reduce these errors and got some satisfying results later on. The position of each point of the paper was measured and the average was found. Here's what we came up with:

30 Degrees; shortest distance, average = 0.83 m

45 Degrees: farthest distance, average = 0.905 m

60 Degrees: (should be about the same as 30), average = 0.77 m 

These results were definitely what we were looking for, as it should have been like this:

Even though 30 degrees and 60 degrees were meant to be the same, the errors discussed previously in our lab were more than likely the cause of the shorter distance.

So why does this happen?

At a 60 degree angle, the ball would have the highest Y component before falling but would not go as far because it is angled more up than away. At a 30 degree angle, the ball reaches the ground first because it is closer but is launched more away rather than upward. This then produces similar results. At a 45 degree angle, it is a perfect balance of X component to Y component. This means it has the furthest distance in both directions.  

MY Takeaway:

Beyond the results and charts and graphs and explanations, this lab has truly helped me "embrace" physics more and learn to struggle with it. I am always a bit hesitant when approaching physics in general considering it is not my strongest area in my education. I thoroughly enjoyed the lab and honestly cannot wait to see what is ahead. 

Projectile Motion - How are we gonna kill that monkey?

Sarah Hits Mark on Anti-Hazing Form Day 

Objectives:

1. To determine the relationship between the horizontal and vertical components of projectile motion.

2. To interpret and discuss the graphs of both components of projectile motion.

Key Terms:

      Velocity 

      Position 

      Acceleration 

      Displacement

Pre-Lab Discussion:

What can you hypothesize about the interdependence of the horizontal and vertical components of projectile motion?

   These two components of projectile motion are independent from each other. This hypothesis can be tested by tossing a ball and using LoggerPro to analysis the horizontal (position and velocity graphs) and the vertical (position and velocity graphs) components individually. Also, this can be tested by throwing and dropping a ball from the same height and at the same time. If this is correct, the balls will hit the ground at the same time. 

What We Used:

• rubber ball
• two meter sticks
• Sarah and Yusuf and friends
• LoggerPro analysis
• hazing on anti-hazing day 

Procedure:

1. Set up laptop camera perpendicular to balls horizontal path

2. Placed two meters sticks on board behind us (led to an error)

3. Hit record

4. Tossed the ball - hit Mark, ruined friendships

5. Loaded it into LoggerPro for analysis

6. Analyzed graphs

Data Graphs/Video:

Vertical Velocity

Horizontal Position

Vertical Position

Takeaways/Analysis:

1. How should you stage your video to enable the most effective analysis?

     The majority of the errors that arise in this lab can occur in the video recording process. Without a careful approach in this step, hitting Mark would have been nothing. First, the camera of the laptop needed to be perpendicular to the horizontal motion of the ball that we were throwing. Second, we needed an object of which we could set a scale from. In our lab, we used a meter stick and the diameter of the ball. Finally, we needed to make sure that the scale is the same distance from the camera as the ball. This was an error we came across in our lab and caused inaccurate results in the slope of the overall data graph.

2. What do the position vs. time graphs for the horizontal component of the object's motion tell you about the nature of projectile motion?

     Based on the graphs from the lab analysis, it is evident that the horizontal component, or x, of an object's projectile motion, has a constant velocity. In a velocity vs. time graph, this shows a straight line because velocity remains constant over time. In a position vs. time graph, it will depict a linear fit increase because the ball will move the same distance over the same amount of time. The horizontal component is independent from the vertical component.

3. What do the position vs. time graphs for the vertical components of the objects's motion tell you about the nature of projectile motion?

     Based on the graphs from the lab analysis, it is evident that the vertical component, or y, of an object's projectile motion, is independent from the horizontal component. In the position vs. time graph, the graph depicts the path of the ball as analyzed in the video. In the velocity vs. time graph, the graph depicts constant acceleration due to gravity. The y component is free fall. 

5. What errors did we face during this lab?
The major error we faced in this lab was the misplacement of the meter stick. The meter stick was placed behind the ball and our video analysis did not scale properly.