MC-14b  Air Track Collisions

OBJECTIVE: To study conservation of energy and momentum in collision.

APPARATUS:

Air track, assorted slotted masses, air supply, hose, gliders; photogates & support stands and PASCO interface and computer.

Pre-lab Quiz

You should be able to complete this brief quiz before proceeding.

• Expt. M14 Quiz

SUGGESTIONS:

1. Use the large gliders whenever possible. Small ones often tilt upon impact and hence give excessive friction.
2. Turn on the air supply and experiment with the gliders. Adjust the leveling screw so that the nominal cart acceleration is minimized. Adjust the air flow so the gliders move freely without rocking side to side.
3. Make sure that the photogates are plugged into the first two phone jack inputs in the PASCO interface module. Also set the two photogates approximately 40 to 50 cm apart and so that they track the 10 cm long plate atop the glider.
4. Click on the telescope icon below to launch the PASCO data acquisition software. It should already be configured to display a two column table which will display the speed of the glider as it passes through the infrared photogate. (It already assumes that the plate is exactly 10 cm long and actually measures the time.)
   To start the data acquisition CLICK on the REC icon. To stop it, CLICK on the STOP icon (the upper left window is configured like a tape player). Each time a glider passes the photogate an entry will appear in the appropriate table column. NOTE: The photogates measure the speed but do NOT sense the direction of motion. You are responsible for the latter.
5. The results of this experiment are very technique sensitive. Take a single glider and practice sending it through both photogates until you are able to get reasonably equivalent speed readings from both photogates. Check the behavior by launching the glider from both ends and record, in your lab book, the speed measured in four or five satisfactory trials. Estimate the precision associated with a pair of velocity measurements and show how this will impact your momentum and kinetic energy measurements.

EXPERIMENT I:

1. Choose gliders of equal mass (or make them approximately the same by fastening weights on one). Qualitatively predict the expected outcome of the next step (i.e., item 2) before attempting the experiment.
2. With glider #1 at the end of track and glider #2 at rest near the center, give #1 a push toward glider #2.
   To help prevent confusion, stop glider #2 before it bounces back.
   As before you should perform multiple trials until you achieve consistent results and record a few of them.

   Check conservation of momentum and energy in the impact. In equation,
   

   $$m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2,$$
   
   
   call velocities to the right positive, those to the left negative.
3. Comment on how well these two quantities are conserved and, if your results seem poorer than expected, suggest possible sources of error.

4. Devise a method for determining how elastic is a rubber band collision and record your results.

Figure 1: Sketch of the air track configuration for elastic collisions.

Suggested tabulations:

Glider: #1 #2 Velocity Readings: #1 #2

mass Before impact (u)

length After impact (v)

Before Impact After Impact

$$_1 _2 _1 _2$$

$$_1 _1 _2 _2 _1 _1 _2 _2$$

$$\frac{1}{2} _1 _1^2 \frac{1}{2} _2 _2^2 \frac{1}{2} _1 _1^2 \frac{1}{2} _2 _2^2$$

change in momentum = ; % change in momentum = .

change in energy = ; % change in energy = .

EXPERIMENT II:

Perform the same procedure as Exp. I (steps 1, 2 and 3) except start both gliders from opposite ends of the air track and with considerably different velocities.

EXPERIMENT III:

Repeat Exp. II but for inelastic collisions by attaching cylinders with needle and wax inserts. Note that the needle must lines up exactly with the insert or there will be significant sideways motion when the two gliders strike.

Figure 2: Sketch of the air track configuration for inelastic collisions.

EXPERIMENT IV:

Increase m$_1$ by adding masses a nd repeat EXP. I.

MEASUREMENT OF FRICTION:

Estimate the frictional force between the glider and track by using the velocity data recorded before Exp. I. From any net decrease in velocity you should be able to obtain the frictional force. Does this information help you understand the experimental data?

JAVA APPLET:

If time permits and you are interested the HTML version of the lab has a link to an applet which animates elastic collisions of two point masses.

Interesting resources on the web

Mark Sutherland's excellent Java Applet gallery. Here you will find applets for Projectile Motion, The Damped Harmonic Oscillator, Elastic Collision, Coupled Oscillations, Coriolis and Centrifugal Forces, The Kepler Problem, The Simple Plane Pendulum, Chaos in the Driven Pendulum, and Motion in an electro-magnetic Field.

This site also offers lectures in dynamics (mechanics), a picture gallery and much more.

Elastic collisions Conservation of energy and momentum This applet animates elastic collisions of two point masses. The user enters the ratio of the target mass to the projectile mass and the ratio of the projectile's final speed to its initial speed, and the applet animates the collision in the target rest frame and in the center of mass frame.