PHYS 1 College of San Mateo Projectile Motion & Vector Analysis of Motion Questions

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gp0091

Science

PHYS 1

College of San Mateo

PHYS

Description

Video Analysis of 2D Motion

Our goal in this lab is to get a better understanding of the relationships between the position, displacement, velocity, and acceleration vectors in two dimensional motion. You will take home videos of a thrown object and an object moving in a circle and analyze the motion graphically.

Equipment

You will need the following equipment to complete the lab. If you do not have any of the equipment listed below, please let your instructor know.

  • Smartphone or computer with video recording capabilities. Cameras with slow motion capabilities are ideal.
  • A way to prop up your phone so that you can take videos of yourself doing things (or another person to help you take videos).
  • Computer that runs Vernier Video Analysis (Links to an external site.).
  • An object that can be thrown without damaging anything.
  • An object that spins and keeps spinning without external interference. The front wheel on a bicycle that is turned upside down is perfect. Other options might be a record on a record player, a salad spinner, or even a basketball spun on a finger, if you are good at it and have someone who can film it. As a last resort you could tie an object to a string and try to spin it around at constant speed, but this is not ideal since it's not really possible to keep the speed constant with this method.
  • Some tape to mark a point on your spinning object.

Taking the Videos

Your goal is to take videos of a number two-dimensional motion. For effective analysis these videos need to be taken carefully. For each video make sure you do the following:

  • Prior to each recording, measure a distance between two well-separated points that will be in your video that lie in or close to the plane of motion. For teh video of circular motion this might be the radius or diameter of the spinning object. Record the distance between these two points and mark the two points so that they will be visible in the video.
  • The motion of the object should be across the screen, not towards or away from the camera.
  • Do not move the camera while the video is being recorded. This is crucial! There is a tendency to try and “track” moving objects with the camera: try to avoid doing this! Propping up the camera rather than holding it is ideal, but you can take good videos by carefully holding the camera steady.
  • If possible, use slow-motion filming.
  • Use a background that is of a different color than moving object. If the object is dark, use a light background, and vice-versa.
  • Caution: with many phones there is a delay after you press the “record” button before filming begins. Hit the “record” button, wait until you see at least one second has elapsed in the recording, and then do the motion.
  • Note for iphone 11+ users: the software can't deal with the most recent movie formatting. Before taking you video go to settings/camera and switch your video format to "most compatable".

Videos to record:

  1. Record a video of an object tossed upwards and sideways flying through the air. (The motion should look like a parabola in the video). Be sure that you capture a good amount of upwards and downwards motion. You do not need to record falling all the way to the ground.
  2. Record a video of an object moving in a circle at a constant speed; the motion should look circular in the video. We want to track a single point on the object, so mark the point you want to track with a piece of tape. With a bike wheel, salad spinner, or basketball you can just give it a spin and let it spin by itself and if there isn't too much friction the motion should be close to constant speed. A record player should maintain a constant speed once it is running. If you are trying to use an object tied to a string, try and spin the object in a horizontal plane and have someone film from below or above; if you spin the object vertically the speed will likely vary because of gravity.
  3. Once you have taken your videos transfer them to your computer. (You can also use Video Analysis on your phone, but using a computer is much easier).
  4. Find and record the frame rate each video was taken at. This can be tricky; on some phones (like my old iphone 6), if you play a slow motion video file on your computer it will appear to be normal speed. In this case, locate the file and view its “Properties” and then click the “Details tab. The frame rate (in fps, or frames per second) should be displayed in the “Video” section. On other phones, like my Samsung Galaxy s10, a slow motion video taken at 240 fps will appear slowed down when played on a computer video player, and the file properties will say the video was taken at 30 fps. In this case, you can try and look up the frame rate your phone uses for slow motion. 240 fps is a good guess if you are not sure.

Video Analysis with Vernier Video Analysis

You can access Vernier Video Analysis using this link (Links to an external site.). More documentation (Links to an external site.) is available as well. Start by doing this tutorial (Links to an external site.) starting at the 1:26 mark. Follow along on your own device so you learn how to use the software. When analyzing your videos, consider the following things:

  1. Track the motion of the center of the object if the object is non-spherical; points on the outside of objects will likely rotate around the center, which complicates the motion in ways we don't want (yet).
  2. Only analyze motion where the object is moving by itself; omit any motion where the helper’s hand is touching the object, and after the object has come to rest.
  3. Experiment with the "advance frames" feature. You want about 15-20 data points for the entire motion.
  4. You can place the origin wherever makes sense: it does not necessarily need to be at the starting location of the object.
  5. Use meters for distance: if you measured your known distance in another system of units, convert it to meters.
  6. Make the movie as large as possible on your screen so that you can place points most accurately.
  7. We are focusing only on the x-motion here: for the first video, there should be no motion in the y direction and in the other videos we will ignore the y direction.

Data Analysis

Below, you will perform a series of actions and answer a series of questions. When needed, you can write equations using Canvas' equation editor. Here are instructions for using the equation editor (Links to an external site.).

Doing The Lab

Once you have read through the instructions above, start the lab by clicking "Start the Quiz" below. The questions will contain further instructions. Enter your answers but do not hit the "submit quiz" button until you are done with the entire lab. In theory Canvas should save anything you enter into the quiz even before you submit the quiz, though I recommend keeping a backup copy of your answers on your own computer. You should be able to enter and leave the quiz as much as you like until the due date.

Unformatted Attachment Preview

Question 1 Projectile Motion Video Analyze your projectile motion video following the instructions above. Be sure to only include times when the object is flying through he air not touching anything; exclude times when the object is in your hand or landing. Make the graphs bigger and choose the "two graphs" option. Make the upper graph display "x(m)" and the lower graph display "X Velocity (m/s)". Note that if there are any outliers this likely indicates you made a mistake while placing points: identify the source of the incorrect point and correct the error. Once you have done this, upload a screen capture (Google how to take a screen capture using your computer if you don't know how to do so) of your computer screen showing: 1. A still picture from your video that shows the points you have placed. 2. The X vs. Time graph, zoomed in on the data as much as possible. 3. The X-Velocity vs. Time graph, zoomed in on the data as much as possible. Question 2 Given the graphs above, how you would you describe the x-component of the motion: is it constant velocity, constant acceleration, or neither? If it is constant velocity or close to it, use a linear fit on the x vs. t graph to find the velocity. If it is constant acceleration (or close to it) is a linear fit on the x-velocity vs. t graph to find the acceleration. Report your result below. Question 3 Switch your graphs to Y(m) and and Y Velocity (m/s). Once you have done this, upload a screen capture of your computer screen showing: 1. A still picture from your video that shows the points you have placed. 2. The Y vs. Time graph, zoomed in on the data as much as possible. 3. The Y-Velocity vs. Time graph, zoomed in on the data as much as possible. Question 4 Given the graphs above, how you would you describe the y-component of the motion: is it constant velocity, constant acceleration, or neither? If it is constant velocity or close to it, use a linear fit on the y vs. t graph to find the velocity. If it is constant acceleration (or close to it) is a linear fit on the y-velocity vs. t graph to find the acceleration. Report your result below and comment on anything you notice. Question 5 Vector Analysis of Motion We'll now use your video analysis, along with Google Slides, to do some graphical vector analysis of the motion. Start by identifying three evenly spaced points in the projectile's motion as it is moving upwards. If you only have a few points on the way up, choose three consecutive points. If you have many points that are close together you may wish to choose points spaced further apart (for example the 2nd, 4th, and 6th points in the motion). Try and avoid using points that are outliers. Follow these instructions on how to do vector analysis on these three points: Instructions on vector analysis. (Links to an external site.) Minimize Video Be very careful as you place the vectors: accuracy is vital here! You first drew a vector that connected the first and second points. What physical quantity (displacement, average velocity, instantaneous velocity, average or instantaneous acceleration, etc.) does this vector literally represent? What other physical quantity is this vector proportional to? Question 6 What physical quantity (displacement, average velocity, instantaneous velocity, average or instantaneous acceleration, etc.) is the red vector proportional to? Question 7 Repeat the steps above with a second set of three points spanning the top of the projectile's motion (so that one point is before the top, a second is near the top, and a third is on its way down). Skip the same number of points between the points you chose as before (for example if you used points 2, 4, and 6 in your first analysis, you might use use points 10, 12, and 14, but not 11, 12, and 13 in your second analysis). Finally, repeat the analysis again with a third set of points that occur during the downward motion. Zoom out so that the results of the three vector analyses are visible and take a screen capture and upload it here. Question 8 Compare your red vectors. What does this tell you about the acceleration of the ball as it flies through the air? Question 9 Conduct video analysis of an object moving in circular motion with constant speed. As you place points in Video Analysis, place points for a full circle of motion, but no more. If a part of the circular motion is obscured try and start the tracking immediately after that part. Observe the position graphs for both x and y motion. Comment on what you see- does it make sense? Question 10 Choose three sets of three points in different parts of the circular motion and conduct vector analysis as you did for the projectile motion. Take a screenshot showing your results and upload it here. Question 11 Describe the direction of acceleration of the tape as it moves around the circle. Question 12 The object is supposed to be moving at constant speed as it rotates. How, then, is it possible that it is accelerating?
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Running Head: VIDEO ANALYSIS OF 2D MOTION

Video Analysis of 2D Motion
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VIDEO ANALYSIS OF 2D MOTION
Video Analysis of 2D Motion
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Anonymous
Just what I was looking for! Super helpful.

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