PHYS111Q : Labs
Subsections


6 Collisions in One Dimension

Introduction

Figure 4: A ``bouncy'' collision in one dimension.
\includegraphics{coll-fig1.eps}

Figure 4 shows a diagram of a ``bouncy'' collision in one dimension between two objects of masses $m_A$ and $m_B$ initially moving with velocities $v_{A1}$ and $v_{B1}$. The law of conservation of translational momentum for this collision is expressed

\begin{displaymath} m_A v_{A1} + m_B v_{B1} = m_A v_{A2} + m_B v_{B2} \end{displaymath} (21)

where $v_{A2}$ and $v_{B2}$ are the velocities of the objects after the collision.

Figure 5: A ``sticky'' collision in one dimension.
\includegraphics{coll-fig2.eps}

Figure 5 shows a ``sticky'' collision in one dimension in which two objects collide and stick together. In this case, Eq. 21 simplifies to

\begin{displaymath} m_A v_{A1} + m_B v_{B1} = (m_A + m_B) v_2 \end{displaymath} (22)

You will study one dimensional collisions involving two carts of the kind used in Labs 3. You will test the law of conservation of momentum (Eq. 21) quantitatively and get a feel for the qualitative behavior of colliding carts.

Experiments

Setup

This week, you will use the white Universal Lab Interface (ULI) instead of the blue LabPro interface.
  1. Plug the serial cable from the ULI into the serial port (the 9-pin port on the back labeled ``10101'') of your laptop, and run Logger Pro.

  2. A Setup Interface window should appear. Make sure the Port box is set to COM1, and click the Scan button. An icon that looks roughly like the front panel of the ULI should appear in the Logger Pro menu bar. If it doesn't, ask for help.

  3. Click on File -> Open, double click on the _Physics with Computers folder and on the Exp 19 Momentum Energy Coll subfolder. Open the file called Exp 19 Motion Detector.mbl.

  4. Place the two motion detectors at opposite ends of the track, facing inward so that each detector tracks one of the two carts.

  5. Note : It's a good idea to put your data into the spreadsheet provided (described in the Analysis section below), and determine whether or not the results make sense to you as you go along.

``Bouncy'' Collisions

  1. Orient the two carts with their magnetic sides inward. (The spring cart has magnets under the Velcro on the side opposite the spring bar.)

  2. Measure five collisions with a stationary ``target''

    Make sure you collect ``good'' measurements. That is, look carefully at your data to make sure that you have enough velocity data from each cart both before and after each collision. Read the Analysis section below so that you have a sense of what ``enough data'' means.

    Also avoid ``violent'' collisions. Gentle collisions transfer less momentum to the track and therefore conform more closely to the assumption that the two carts are an isolated system.

  3. Measure five collisions in which both carts are initially moving.

``Sticky'' Collisions

  1. Orient the two carts with their Velcro sides inward.

  2. Measure five collisions with a stationary ``target.''

  3. Measure five collisions in which both carts are initially moving.

Analysis

For each collision, use Analyze -> Statistics on the velocity vs. time graph to find the average velocity of each cart before and after the collision. Be sure to select time frames (a) as close to the collision as possible and (b) in which the velocities are approximately constant. When recording your results, keep in mind that the sign of each velocity carries direction information and must be kept. Record the standard deviation reported by the statistics function as the uncertainty.

You have been given a spreadsheet (Collisions.xls) programmed to calculate the total translational momentum of the system before and after each collision. All you need to do is measure and enter the masses and velocities of the carts. Each (horizontal) row corresponds to one collision. Your mass and velocity measurements and their uncertainties go into columns B-M. Column A (``Label'') is included so that you can identify the type of collision considered.

Group Assignment

Show your spreadsheet to your instructor and discuss preliminary answers to the questions below.

Individual Assignment

Hand in a hardcopy of your spreadsheet and answers to the following questions.
  1. For what percentage of the 20 collisions you studied are your observations consistent with the law of conservation of translational momentum? Mark each of these collisions with an asterisk (*) in your spreadsheet before you print it out or by hand on the printout.

  2. (a) Under what circumstances in one dimensional collisions between two objects is one of the objects stationary after the collision? (b) How about both objects?

  3. Sketch qualitatively correct distance vs. time graphs corresponding to the following collisions.


Copyright © 2003-2007, Lewis A. Riley Updated Tue Nov 30 13:48:34 2004

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