INTRODUCTION

    In class we have concentrated on studying the behavior of orbital systems in which one of the two objects in the system is much more massive than the other, so that the center of mass (CM) of the system is essentially fixed. In this lab you will look at the behavior of a system in which the two orbiting objects have the same mass. In the reference frame of the laboratory their motion is fairly complicated, but if you analyze the motion from the reference frame of the (moving) CM, it is much simpler.

    According to Newton's Second Law for a system of particles coupled together and isolated from all external forces, the CM of the system should move in a straight line with constant velocity; it is not difficult to subtract this motion from the motion of the objects in the laboratory frame (see Moore, Ch. N10.3). For this same system, angular momentum L = r x p should be conserved. In this lab you will first simplify a complicated motion by looking at it in the CM reference frame, and then test whether or not L is conserved.

EXPERIMENT

    The experimental apparatus is an air table with a spark-timer. The two pucks, which are coupled to each other by a string, ride on a cushion of air so that they have very low friction. The timer records the position of each puck on a sheet of newsprint at specific intervals.

1. Turn on the air supply to the table and practice several times releasing the two pucks and giving one of them a small horizontal motion. Be very careful that you do not push down on the pucks, as the carbon paper underneath is very easily torn, and holes in the carbon paper will stop the puck's frictionless motion. Mark the edge of the paper where you're starting the pucks.

   When you have practiced several times, have your partner run the spark timer for you. The timer should be set to StandBy and the rate to 15 cps; just as you release the pucks, your partner should switch the timer to Spark On and stop it before the pucks come to a stop.

   CAUTION: Keep your hands away from the edges of the air table and the pucks while the spark timer is on. You could get a shock from the apparatus.

2. Remove the sheet of newsprint. The paths of the pucks will be marked on its underside. Mark the starting point and final point on your spark trace, and label the two pucks A and B (since they have the same mass – 550 g – the designation doesn't matter). Record the setting of the spark timer.

ANALYSIS

3. Starting at the final point on each trace, use a pencil to carefully circle every 2^nd point.

4. Number corresponding pairs of circled points, starting with number 1 for the first clearly distinguishable circled pair at the beginning of the trace.

5. Construct the line linking each numbered pair of points, and find the CM for each successive time. Draw the best-fit line for the CMs.

6. Using a transparency grid, find the coordinates of each pair of points. Move the grid along so that the origin is at the CM for each time, and the x-axis falls along the line formed by the CMs. This effectively subtracts the motion of the CM from the recorded motion of the pucks in the laboratory frame. Tabulate your results in the following way:

   Time, t

   xA

   yA

   xB

   yB

7. When you have recorded positions for at least 8 points, make a graph of the motion of A about the CM. Draw a line from each point to the center of mass; this is the radius r of the puck's orbit. Do the same on a separate graph for B (to speed things along, one partner should plot the motion of A, the other B).

8. Align the transparency grid along a line r on one of your graphs. Measure the distance of r directly from the grid.

9. Again use the transparency grid to measure the "vertical" height between two points. Use these measurements to calculate the area swept out in a particular time interval (assume that the area is a right triangle – a reasonable estimate here).

   If angular momentum is conserved, then the areas of these triangles will be the same!

DISCUSSION

• Referring to your original record of the motion of the pucks, how well do the CM's fall along a straight line? If they do not, what do you think might account for the deviation from the behavior predicted by Newton's Second Law?

• Was angular momentum conserved by the system? Again, if not, what do you think would account for this deviation from expected behavior? Did you notice any pattern in the pucks motion?

Return to Physics 151

©	St. Lawrence University	Department of Physics

Revised: 25 Aug 2021

Canton, NY 13617