23 Two-Dimensional Motion
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Introduction
Except for a few limited cases, a motion detector is not useful to analyze motion in two dimensions. A better technique is video analysis, in which a video is made of an object’s motion and the position of the object is determined on a frame-by-frame basis. Once the movie is scaled, this position data can be used to determine the velocity and acceleration of the object during its motion. The LoggerPro software you have been using has integrated video analysis capabilities.
I. Motion on an Incline
The motion of a cart on an incline is a simple example of a two-dimensional motion; the cart moves in both the horizontal and vertical directions. Although this is an example in which a motion detector can be used to collect kinematic data (by rotating the coordinate system this motion can be modeled as a one-dimensional motion along the incline), we will use it as an introduction to video analysis techniques.
Open the file Movie and select Insert/Movie. Find the movie CartonIncline and open it. Play the movie. You will analyze the motion of the fan cart rolling down the incline. Return the movie to the first frame.
To extract data from a video:
- Click the icon in the lower right portion of the movie. The video analysis tools will appear.
- Enlarge the movie until it fills as much of the screen as possible. This will allow you to accurately select the pixel representing the cart’s position.
- Select and maneuver the cross-hair until it is directly over the white dot representing the center of the cart. Click on the white dot. The movie will automatically advance to the next frame. Click on the position of the cart in every frame of the movie. The software will automatically create a graph of x- and y-position vs. time.
- Currently, the position of the cart is measured in pixels. To convert from pixels to meters, you need to scale the movie using a known length included in the movie. To do this, select to open the scaling tool. Click and drag along the length of the meter stick near the bottom of the frame. When you release the mouse, the dialogue box requests the length of the object used for scaling. Type and enter the appropriate length. The position data will immediately change to meters.
- Select a coordinate system. (The default system is the lower left corner of the video frame.) To move the coordinate system, select and then click where you would like the coordinate axis to appear. For this activity, choose the initial position of the cart.
Arrange a graph of x- and y-position vs. time and a separate graph (Insert/Graph) of x- and y-velocity vs. time on the screen. Print these graphs (on the same page) and attach the graphs to the end of this activity.
Question: Describe the relationship between the x- and y-components of motion. Which direction inv