Electrical Equivalent of Heat plunger

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					Experiment #7: Conservation of Momentum                                                Page 1 of 6



Conservation of Momentum

Equipment Required                                                         Part Number
Xplorer GLX                                                                PS-2002
PASport Motion Sensors (2)                                                 PS-2103
2.2 m PAScar Dynamics Track System                                         ME-6956
Mass Scale                                                                 SE-8723


Purpose
Elastic and inelastic collisions are performed with two dynamics carts of different masses.
Magnetic bumpers are used in the elastic collision and Velcro® bumpers are used in the
completely inelastic collision. In both cases, momentum is conserved.

Theory
The momentum of a cart depends on its mass and velocity.

    Momentum  p  mv                                                (1)

The direction of the momentum is the same as the direction of the velocity. During a collision,
the total momentum of the system of both carts is conserved because the net force on the system
is zero. This means that the total momentum just before the collision is equal to the total
momentum just after the collision. If the momentum of one cart decreases, the momentum of the
other cart increases by the same amount. This is true regardless of the type of collision, and even
in cases where kinetic energy is not conserved. The law of conservation of momentum is stated
as
     p TotalBeforeCollision  pTotal AfterCollision                  (2)

The kinetic energy of a cart also depends on its mass and velocity but kinetic energy is a scalar.
              1
        KE  mv 2                                                   (3)
              2
The total kinetic energy of the system of two carts is found by adding the kinetic energies of the
individual carts.




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                                       Physics Lab Manual        PS-2817
Experiment #7: Conservation of Momentum                                                Page 2 of 6

Pre-lab Questions
1.   When two carts at rest push off from each other, they speed away in opposite directions.
     Initially, there is no momentum for the two-cart system. How is momentum conserved in
     this situation?

2.   When two carts at rest push off from each other, they speed away in opposite directions.
     Why is kinetic energy not conserved for the two-cart system? Where does the excess kinetic
     energy come from?

Setup
1.   Level the track using the leveling screws on the track feet. When you place a cart at rest on
     the track, it should not move.

2.   Use the setup shown in Figure 1. Use one red and one blue cart so it is easy to distinguish
     between the carts. Slide a Motion Sensor onto each end of the track. Set the switch on tope
     of each Motion Sensor to the cart position.

3.   Open the GLX file called "momentum.glx" or configure the GLX using the instructions in
     the appendix at the end of this experiment. Plug the Motion Sensors into Ports #1 and #2 on
     the GLX.

Procedure
I. Explosions
A. Equal Mass Carts




                                   RED              BLUE


                                  Figure 1: Setup for Explosions

1.   Use the balance to find the mass of each cart. They should have the same mass, but if they
     don't, just keep track of which mass is which.

2.   Fully depress the plunger on one cart. Does it matter which cart has its plunger depressed?
     Place the two carts on the track so that they are in contact with each other.



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                                       Physics Lab Manual        PS-2817
Experiment #7: Conservation of Momentum                                                   Page 3 of 6


3.   Start recording on the GLX and tap the trigger release to launch the carts. Then stop
     recording on the GLX before the carts hit the Motion Sensors.

4.   Using the velocity vs. time graph, use the Smart Cursor to find the velocity of the red cart
     just after the explosion. It may be helpful to re-scale the graph, to see just that area you are
     interested in.

5.   Repeat step 4 to find the velocity of the blue cart after the collision.

6.   Calculate the momentum of each cart after the explosion.

7.   The total momentum of the two cart system is zero before the collision because they are
     both stopped. How can the total momentum of the two cart system still be zero after the
     collision if they are both moving? Hint: Momentum is a vector.

8.   How does the total momentum before and after the explosion compare? Since it is difficult
     to compare a number to zero, compare the red cart's momentum to the blue cart's momentum
     after the explosion: They should be equal and opposite to each other. Calculate the percent
     difference.

B. Unequal Mass Carts




                                     RED             BLUE



1.   Use the balance to find the mass of two mass bars, and then place them both in the blue cart.
     Repeat steps 2 through 8 of part A.

2.   For the unequal mass carts, calculate the kinetic energy of each cart after the explosion.

3.   Do the two carts have the same kinetic energy after the explosion? Should they?

4.   Where did the kinetic energy of the carts come from? Who pushed in the plunger? Did they
     do work? How much?

5.   The momentum for a gun and its bullet are the same, but their energies are not. Which has
     more energy, the bullet or the recoiling gun?




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                                       Physics Lab Manual        PS-2817
Experiment #7: Conservation of Momentum                                              Page 4 of 6

II. Qualitative Collisions
For each of the following collisions, make a "Before" diagram and an "After" diagram. Show
each cart with a velocity arrow to indicate its direction of motion. Also draw a momentum arrow
for each of the carts indicating the direction and approximate value of the momentum. An
example is shown below. It may be useful to use the GLX to determine approximate speeds, but
you do not need to record any measurements, or do any calculations.

A. Use the same mass carts with the Velcro sides toward each other so the carts will stick
   together. This is a totally inelastic collision. You will need to have the plunger depressed
   (see Figure 2).




                           Figure 2: Velcro Bumpers for Inelastic Collisions

    1.   Blue cart at rest, Red cart has velocity toward blue cart.




    2.   Red cart and Blue cart are moving toward each other with about the same speed.

         Question: If the two carts are thrown with about the same speed, the final speed of the
         two will be zero, and thus the final Kinetic Energy will be zero. Where does the
         Energy go?

    3.   Red cart and Blue cart are both moving toward the right. Red cart has a greater velocity
         than Blue cart.



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                                       Physics Lab Manual        PS-2817
Experiment #7: Conservation of Momentum                                                Page 5 of 6


B. Place a mass bar in Blue cart and repeat the collisions from part 1 to 3 above.

C. Use the same mass carts with the magnetic bumpers toward each other so the carts will
   bounce off each other and the collision will be elastic (see Figure 6). Repeat the collisions
   from part 1 to 3 above.




                      Figure 6: Magnetic Bumpers for Elastic Collisions

D. Place a mass bar in Blue cart and repeat the collisions from part 1 to 3 above.

III. Quantitative Collisions
A. Perform collision #1 from Part II for equal mass carts. Start recording on the GLX, perform
   the collision, and stop recording.

B. Using the velocity vs. time graph, find the velocity of the Red cart just before and after the
   collision.

C. What are the initial and final velocities of the Blue cart? On the Graphs menu (F4), open
   Graph 2 to analyze Velocity2.

D. Measure the mass of each cart. Don’t forget which cart is which! Calculate the total
   momentum of the two-cart system before and after the collision.

E. Compare these two by calculating the percent difference.
                      p      pafter
      %difference before            x100%
                          pbefore
F. Calculate the kinetic energy of the carts before and after the collision. Where did the energy
   go?

G. Repeat steps A through F for the unequal mass carts of collision #1 from Part II for
   magnetic bumpers.
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                                       Physics Lab Manual        PS-2817
Experiment #7: Conservation of Momentum                                           Page 6 of 6




Appendix: Xplorer GLX Configuration
1.   After plugging the Motion Sensors into Ports #1 and #2 on the GLX, go to the Sensors menu
     on the GLX and change the Sample Rate for each Motion Sensor to 20 Hz. For each Motion
     Sensor, make the Position Not Visible and the Velocity Visible.

2.   Open the Graph window and select Two Graphs (5) on the Graphs menu (F4). The top graph
     should be Velocity (from Motion Sensor #1) vs. Time and the bottom graph should be
     Velocity (from Motion Sensor #2) vs. Time. On the Graphs menu (F4), select New Graph
     Page (6) and select Velocity2 for the vertical axis. Return to Graph 1.

3.   Open the Data Files window on the main menu and name the file "momentum" and save it.
     Return to the Graph window. The GLX is now ready to record data.




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                                       Physics Lab Manual        PS-2817