Collisions and the Center of Mass

Overview

We will use VideoLab to investigate a 2-Dimensional collision. In particular we will be interested in learning about the Center of Mass of the system and to illustrate how, in a sense, it can be considered as a point that carries both energy and momentum.

 

PreLab:

Please complete this PreLab and hand it in prior to next week's lab.

Optional PreLab: MAP Tutorials

If you are having trouble with the concept of centre of mass or motion of the CM you may find the following tutorials provide you with valuable insight into the concept of Center of Mass. If so, it would be a good idea to work through one or more of these tutorials either on your own or with a partner.

  1. Center of Mass:
  2. Motion of the Center of Mass

VideoLab - the Data

Please download the following two video files to your local documents folder. You will need to access these with LoggerPro..

File #1
 1 big mass, 1 small mass
File #2
 1 big mass, 1 small mass

Big Puck mass = 1.0 kg; Small Puck mass = 0.50 kg; movie clip frame width = 1.00 m

Special Considerations Using LoggerPro-VideoLab

In this use of VideoLab you are measuring the spatial position of two objects with respect to time. To run VideoLab you need to click on each object before the applet advances to the next data frame. This will generate all the data that you need. Be sure to select the appropriate graphing options to see your data. You may, for example wish to look at x vs y for each puck.

How to Load a Movie

Choose insert/movie and browse to where you have copied the movie files.

 

 

Figure1: Inserting a movie

How to Work with the Movie File

  • Click the bottom, right icon (open tool kit) to see the various options.
  • Set origin lets you define where the origin should be - choose the white dot in the middle of the frame.
  • Set scale assigns actual dimensions to your measurements - click on this and then with the L-mouse drag from the mouse across the video frame - this is 1.00 m
  • Add data point makes a measurement of the puck position and stores this in VideoLab. It also advances the movie by 1 frame.
  • Do 1 puck at a time - when you want to record the data for the other puck rewind the movie and click on the select object button to add tell VideoLab you have another object
  • use the add data point button again to collect the position time data for the second puck.

 

 

 

 

Figure2: How to interact with the movie
   

 

How to Export Your Data

WARNING!!!! Make sure that you know which puck is which! It is easy to get them mixed up. Look at the left-hand column i LoggerPro - it displays the data table that you just produced. Cut and paste this into EXCEL. You may wish to download sample.xls and use this as an example of how I analyzed the data.

 

What to Do With the Data:

MOMENTUM and ENERGY

  1. determine the (x,y) location for the CM of the system for each data point measured.
  2. from the velocity data determine the velocity of each puck before and after the collision. You can average a number of values before and after the collision - make sure to avoid values immediately before and after the collision!
  3. Add these velocity components to get the velocity of each puck before and after the collision. You will need this for the Kinetic Energy determination.
  4. Determine the total x and y momentum before and after the collision and add these (vectorally) to get the initial momentum and final momentum of the system.
  5. Determine the velocity of the CM (again add x and y components) and from this determine the momentum of the CM.

MOTION OF THE CM

  1. Prepare a graph showing the X-Y locations for each puck as well as the CM. To do this just plot the x and y locations. Since the time is the same for each puck and pair of points you should be able to reproduce the path that the pucks took on the video. What do you notice about the path of the CM? Explain why you would expect this.
  2. For one of the data sets in each group, the CM line will not be straight. Explain why you think this is and try to fit a curve to the CM line.
  3. Discuss whether or not you have evidence that an external impulse is acting on the CM. If there is evidence, explain where the impulse comes from and provide a quantitative analysis of the impulse.

 

What to Hand In...

The most important thing to hand in is a detailed conclusion in which you discuss each of the sections listed above. Be sure to include tables and graphs (properly labeled and numbered) where appropriate. On the basis of your experiment you should be able to explain why the CM travels in the path it does and how much energy is available to perform work during a collision.

Due Date: Next Week