Experiment 6
1D COLLISIONS
PROCEDURE
For each collision, determine the
momentum and kinetic energy of each glider before and after the collision,
then check to see if these quantities are conserved by comparing total
values. Because of the uncertainty associated with timing measurements
and other factors such as rebound elasticity, leveling, etc., numerical
accuracy of 15% or less will be considered adequate for this experiment.
Ask your lab instructor if you have questions about the validity of any
specific measurement.
Preliminary SetUp
Figure 61.Schematic of glider
and photogate setup
♦♦♦NOTE:
DO NOT slide gliders on the track without turning on the air supply.♦♦♦
Refer to Figure 61 for
proper arrangement of the apparatus. Complete the following items before
taking data. All data will be entered on an accompanying Worksheet.
This Worksheet also contains the necessary tables and equations
to test for momentum and energy conservation.
BE CAREFUL
TO USE ONLY THE CELLS SPECIFIED FOR DATA ENTRY, AND DO NOT CHANGE CELL
FORMATS OR LOCATIONS.

Turn on the air supply and check
the leveling of your air track by observing whether your gliders have a
tendency to move without assistance. Adjust the leveling as necessary
by placing or removing shims under the single support foot. Ask your
lab assistant for help if necessary. NOTE: Proper
leveling is very important for this experiment!!

Position the photogates approximately
70 cm from each end of the track. The distance between photogates
should be as small as possible but with sufficient separation to allow
two gliders (with bumpers) to be totally within the gates without triggering
the timing light.

Adjust the vertical position
of each photogate so that the top part of the glider blocks the light beam
as it passes the gate, but not so low as to obstruct free passage of the
glider.

Turn on power to the
DataLogger interface and check to see that the photogate and computer connections
are secure. The two photogates should have their signal cables connected
to the DIG/SONIC 1 and DIG/SONIC 2 inputs of the interface.

Configure the LoggerPro
software by opening the DoubleGate
link.

Check the action of the photogates
by passing your hand in front of each one to see that the lights activate
and deactivate as expected and that the corresponding time increments appear
on the computer screen. Note which column on the screen applies to
which gate.

Practice timing measurements
by launching a glider through the photogates to see that the times of passage
are properly recorded on the computer screen. Note that clicking
the Collect button on the LoggerPro window erases previous
data and "arms" the timer. Timing begins only when the photogate
is first blocked, and stops when it is unblocked.

Measure the length of each glider
to the nearest millimeter. Repeat three times and enter these data in cells
C11:C13
and
E11:E13 of the Worksheet.

Attach one bumper to each glider
and weigh the gliders (including the bumper) to the nearest 0.1 gram.
Repeat three times and enter these data, expressed in grams, in cells D11:D13
and
F11:F13 on the Worksheet.
Procedure
1  Elastic Collision between Equal Masses; One Mass Initially at Rest.
1. Place
one glider (A) near one end of the track and a second
(B)
in the middle between the two photogates. (Both gliders should have bumpers
pointing in the same direction  specifically in the direction of motion.)
2. Arm the photogates
by clicking the Collect button on the LoggerPro window.
3. Launch glider
A gently but firmly such that, after the collision, glider
B
is displaced completely from its stationary position between the photogates.
If m_{A} and m_{B} are
approximately equal, the first glider should essentially come to rest between
the photogates while glider B moves off with the same speed as A
prior to the collision. In practice, the velocities will not be exactly
equal because the collision is not perfectly elastic.
4. Copy
the transit times Δt_{A}
(before the collision) and Δt_{B}
(after the collision) from the Table Window, and enter these values
in cells B22 and E29 respectively on the Worksheet.
5. Repeat
this process two more times, and enter the resulting transit times in cells
B23:24
and E30:31 of the Worksheet.
Procedure
2  Elastic Collision between Unequal Masses; One Mass Initially at Rest.
1. For
this experiment, add two weights (50 g each; 100 g total) to Glider
B.
Again, weigh the glider (including weights and bumper) and enter the data
in cell C52 of the Worksheet.
2. Using
the lighter glider as the projectile and heavier as the target, repeat
the steps in Procedure 1 to obtain three different sets of timing data
for this system. In this case, you will need to record Δt_{A}
both before and after the collision as well as Δt_{B}
after.
NOTE:
In this situation, glider A should rebound and pass through Photogate
1 a second time (but in the opposite direction). The velocity and
momentum for this glider after the collision therefore is negative. This
is accounted for in the equations built into the Worksheet.
3. Enter
your timing data for this procedure where called for in cells B59:B61;
B66:B68;
and E66:E68 of the Worksheet.
Procedure
3  Inelastic Collision between Equal Masses; One Mass Initially at Rest.
1. For
this experiment and the next, you will need to replace the rubber bumpers
with devices that stick together when the gliders collide. This
is accomplished with a needle and cork system that your lab assistant can
show you. Add these items to each glider, and measure and record
the revised masses in cells C94 and C96 of the Worksheet.
2. Repeat
steps 1  4 from Procedure 1 three times, and record your
new data in cells B101:B103, B108:B110, and E108:E110
of the Worksheet.
NOTE:
In this situation gliders A and B have the same velocity after the collision
because they are connected together, so the times in cells B108:B110,
and
E108:E110
of the Worksheet should be nearly identical. In addition, Photogate
#2 will give double readings for the transit time because the coupled
masses have a gap in the middle which triggers the photogate. In
any case, just copy one set of numbers into the Worksheet.
Procedure
4  Inelastic Collision between Unequal Masses; One Mass Initially at Rest.
1. Add
two 50 gram weights to glider A. Recheck the mass of each
glider (including weights and cork or needle) on the pan balance,
and enter the revised masses in cells C144 and C146 of the
Worksheet.
2.
Using the heavier glider as the projectile and the lighter as the target,
repeat Steps 1  4 of Procedure 1 three times to collect
timing data for this situation.
3. Enter
your resulting data in cells B151:B153, B158:160, and E158:E160
of the Worksheet.