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                                                                                             Collision Lab
Up to now we have been describing the motion of one object. Now we start to consider two objects colliding
with each other. We want to be able to describe the motion of the two objects after the collision if we know
their motions before the collision. We are trying to make predictions. For now, we will limit ourselves to
straight-line (one-dimensional) motion and “inelastic” collisions, where the two objects stick to each other and
travel together after the collision.

In this lab, you will be given a number of collision situations. You will first make predictions about what you
think the results of the collision will be. Then, you will use the tracks and carts, along with the photogates, to
test your predictions.



PART I: PREDICTIONS

(a) Both moving, stopping after colliding
For each of the situations listed in the table below, a blue cart will be moving at speed v. You will push a red cart
in the opposite direction at just the right speed so that the two carts stick together and come to a complete
stop. (It will obviously take some practice.) In some of the situations the carts are identical; in others, the carts
have different masses. In the charts below, write down your predictions for the speed with which the red cart
will have to be moving in order to have both carts come to a stop. Your predictions should be written in terms
of the initial speed v; that is, if you think the red cart will have to be going three times the speed of the blue cart,
you would write down 3v. (Leave the “Actual Results” part blank until you perform the experiments, in Part II.)



                                   Your prediction                                 Actual results
         Blue Cart                      Red Cart                       Blue Cart                     Red Cart
   mass           speed           mass          speed           mass           speed           mass           speed

     m               v             m                              m                              m

     m               v             2m                             m                             2m

     m               v             3m                             m                             3m

    2m               v             m                              2m                             m

    3m               v             m                              3m                             m




                                                                                                                      1
(b) Initially at rest, pushing off each other
What about a collision in reverse? Called an “explosion”, you’ll start two carts at rest right next to each other,
then release the spring-loaded plunger on the red cart so that carts push off of each other in opposite directions.
In the chart below, write down your predictions for the same five mass combinations listed above. (Again, write
down your predictions in terms of v, the speed of one of the carts.)



                                       Your prediction                              Actual results
          Blue Cart                         Red Cart                    Blue Cart                       Red Cart
   mass            speed            mass             speed      mass             speed         mass             speed

      m               v                m                            m                              m

      m               v                2m                           m                              2m

      m               v                3m                           m                              3m

    2m                v                m                         2m                                m

    3m                v                m                         3m                                m



(c) One cart moving, the other at rest
Now let’s consider a different question. For the same five mass combinations listed above, a blue cart will be
moving at speed v toward a red cart at rest. The two carts will stick together after the collision. In the chart
below, write down your predictions for the speed of the carts after they collide and stick together. As before,
your prediction should be written in terms of v.

                      Your prediction                                               Actual results
           Before Collision                  After Collision             Before Collision                After Collision
                                                Both Carts                                                 Both Carts
   Blue Cart               Red Cart                             Blue Cart             Red Cart
                                                 Together                                                   Together
mass       speed      mass      speed        mass      speed   mass      speed      mass    speed        mass      speed

  m           v           m        0            2m              m                    m         0          2m

  m           v           2m       0            3m              m                   2m         0          3m

  m           v           3m       0            4m              m                   3m         0          4m

  2m          v           m        0            3m             2m                    m         0          3m

  3m          v           m        0            4m             3m                    m         0          4m




                                                                                                                        2
PART II: TESTING YOUR PREDICTIONS
You should have predictions written down for fifteen different situations. Now you will use the carts and tracks
to test each of your predictions. Each cart by itself is 250 g; you also have two extra 250 g masses that you can
add to the cart(s) to vary their mass.

Set up your tracks and photogates as shown in class. Follow the instructions shown below to set up the
LabQuests. Using the photogates to measure speeds, perform the collisions listed above and record the speeds
of the two carts. Compare the experimental results to your predictions.

Using a Photogate with LabQuest
1. Connect the cables from the photogates to DIG1 and DIG2 on the right side of the LabQuest.
2. Turn on the LabQuest.
3. Select the “Sensors” menu, then “Sensor Setup”. For DIG1 and DIG2, choose “Photogate” from the pull
   down menus. Click OK.
4. Click the box labeled “Mode” on the right side of the screen. For Photogate Mode, choose “Gate” from the
   pull down menu.
5. In the box labeled “Length of object”, enter the width of the flag on top of your cart, in meters. (These
   brackets have a width of 1.6 cm = 0.016 m.) Click OK.
6. To start collecting data, click the green arrow in the bottom left of the screen.
7. You should ignore everything on the data collection screen EXCEPT the boxes labeled “velocity” on the right
   side of the screen. Do not pay any attention to the graphs, or to the “Gate Time” or “Time” boxes.
8. You can (and should) run multiple trials. To see the velocities for all your trials, click on the Table tab at the
   top of the screen.
9. When you have collected all the data you want, click the red square in the bottom left of the screen to stop
   collecting data.


PART III: ANALYSIS
Analysis for this lab is very different than the other labs we have done. There is nothing to graph, only masses
and speeds to compare. To help you come up with a general rule, we’re going to draw diagrams with carts and
velocity vectors. You’ll be drawing vectors for situations that you tested, and also for other combinations that
you did not test.

      Do the diagrams on pages 4, 5, and 6 before going on to Part IV on this page.

PART IV: DRAWING CONCLUSIONS
Our goal in this lab is to be able to make predictions about the motion of two objects after they collide if we
know their motion before they collide. What we want is to be able to make one general statement that will
cover all the cases you tested in Part II (and more). This should be in the form of a rule or formula: if the carts
are doing X, then Y will happen.

Your rule should be specific enough to answer the following questions:
        o A 1-kg cart is moving at 4 m/s. How fast would a 0.5-kg cart have to move in the other direction for
            them to hit each other and both come to a stop?
        o A 1-kg cart is moving at 6 m/s. It hits a 2-kg cart moving the other direction at 1 m/s and sticks to it.
            How fast and in what direction does the combined cart move after the collision?

                                                                                                                      3
(a) Both moving, stopping after colliding
                                                                            For each of the situations shown here,
                                                                            draw a vector on the red cart to
                                                                            indicate how fast it would have to be
                                                                            going in order to stop the blue cart.
                                                                            Remember that the length of your
                                                                            arrow should indicate the speed of the
                                                                            cart.




                                                                            The situations shown here are not the
                                                                            ones you tested in your experiment. If
                                                                            you can figure out the speeds for the
                                                                            red cart in order to stop the blue cart,
                                                                            you have generalized your rule to make
                                                                            predictions about other collisions.




What about the two carts has to be the same in order for them to stop when they collide? (Look at your
pictures above.)



Describe your rule for part (a) in “If-then” format (“If [something], then the carts will stop when they collide.”):




                                                                                                                       4
(b) Initially at rest, pushing off each other
                                                                           For each of the situations shown here,
                                                                           draw a vector on the red cart to
                                                                           indicate how fast it would be going
                                                                           after the two carts have pushed off of
                                                                           each other. Remember that the length
                                                                           of your arrow should indicate the speed
                                                                           of the cart.




                                                                           The situations shown here are not the
                                                                           ones you tested in your experiment. If
                                                                           you can figure out the speeds for the
                                                                           red cart after pushing off the blue cart,
                                                                           you have generalized your rule to make
                                                                           predictions about other explosions.




What about the two carts is the same after they push off of each other from rest? (Look at your pictures above.)



Describe your rule for part (a) in “If-then” format (“If the two carts are at rest and push off of each other, then
[something].”):




                                                                                                                      5
(c) One cart moving, the other at rest
           Before collision                       After collision              For each of the situations shown
                                                                               here, draw a vector on the combined
                                                                               cart to indicate how fast it would be
                                                                               going after the collision. Remember
                                                                               that the length of your arrow should
                                                                               indicate the speed of the cart.




This is a more difficult rule to figure out. Let’s try to go back to parts (a) and (b) and redraw those situations in
the same “Before/After” table like we have here.

                                  Before                                              After

 from
part (a)

 from
part (a)

 from
part (b)

 from
part (b)


How can you make a rule about the number of arrows before and after the collision (or explosion) for each of
these cases? Does that help you make a rule for before and after the collisions in part (c)?




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posted:3/6/2012
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