PHYS111Q : Labs

6 Collisions in One Dimension

Introduction

**Figure 5:** A ``bouncy'' collision in one dimension.
$\includegraphics{coll-fig1.eps}$

Figure 5 shows a diagram of a ``bouncy'' (elastic) collision in one dimension between two objects of masses and 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 6:** A ``sticky'' collision in one dimension.
$\includegraphics{coll-fig2.eps}$

Figure 6 shows a ``sticky'' (perfectly inelastic) 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 Lab 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

Connect the LabPro interface to the USB port of your laptop with the cable provided.
Click on File -> Open, double click on the _Physics with Computers folder and on 19 Momentum Energy Coll.
Place the two motion detectors at opposite ends of the track, facing inward so that each detector tracks one of the two carts.
Place the carts in contact with each other at the center of the track. Make sure there are no obstructions between the motion detectors and the carts, and press the Zero $\scalebox{0.7}{\includegraphics{LoggerPro3-zero.eps}}$ button (to the left of the Collect button on the toolbar).
Check the boxes next to LabPro:1 DIG1:Motion Detector and LabPro:1 DIG2:Motion Detector, and click OK.
Wait a few seconds for the motion detectors to stop clicking.
You may find that the 10 second collection time is inconveniently long for the measurements you'll be making. If so, click the Data Collection button $\scalebox{0.7}{\includegraphics{LoggerPro3-data.eps}}$ to adjust the length of the measurement.

Note : It's important to put your data into the spreadsheet provided (described in the Analysis section below) as you go along so that you can determine whether or not the results make sense to you.

``Bouncy'' Collisions

Orient the two carts with their magnetic sides inward. (The spring cart has magnets under the Velcro on the side opposite the spring bar.)
Measure five collisions with a stationary ``target''
- Measure two collisions between carts of equal mass and three with different mass combinations.
- Be sure to investigate the behavior of the system with a large mass difference.
- Try to discover if it is possible for one or both of the carts to be stationary after this kind of collision.
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.
Measure five collisions in which both carts are initially moving.
- Measure two collisions between carts of equal mass and three with different mass combinations.
- Be sure to investigate the behavior of the system with a large mass difference.
- Try to discover if it is possible for one or both of the carts to be stationary after this kind of collision.

``Sticky'' Collisions

Orient the two carts with their Velcro sides inward.
Measure five collisions with a stationary ``target.''
- Measure two collisions between carts of equal mass and three with different mass combinations.
- Be sure to investigate the behavior of the system with a large mass difference.
- Try to discover if it is possible for the system to be stationary after this kind of collision.
Measure five collisions in which both carts are initially moving.
- Measure two collisions between carts of equal mass and three with different mass combinations.
- Be sure to investigate the behavior of the system with a large mass difference.
- Try to discover if it is possible for the system to be stationary after this kind of collision.

Analysis

For each collision, use the Statistics button $\scalebox{0.7}{\includegraphics{LoggerPro3-statistics.eps}}$ on the toolbar with the velocity vs. time graph to find the average velocity of each cart before and after the impact. 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.

Before You Leave Lab

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

Group Assignment

Hand in your spreadsheet and answers to the following questions.

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.
(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?
Sketch qualitatively correct position vs. time graphs corresponding to the following collisions.
- A ``bouncy'' collision between two objects with equal masses initially moving toward each other with equal speeds.
- A ``bouncy'' collision between two objects with a large mass difference initially moving toward each other with equal speeds. (Label the trajectory of the larger mass.)
- A ``sticky'' collision between two objects with a large mass difference initially moving toward each other with equal speeds. (Label the trajectory of the larger mass.)