Momentum and Energy in a Collision

Today you will investigate the behavior of linear momentum and kinetic energy for two different types of one-dimensional collisions.  This experiment uses low friction tracks to provide an approximately frictionless surface on which two carts can collide with each other or with other objects.  You will investigate how linear momentum and kinetic energy change (or don't change) throughout various interactions.  It will be necessary to observe the motion very carefully in order to interpret your results correctly.  Remember that momentum is vector quantity and energy is a scalar.  In both experiments the sonic rangers have been set up so that they are using the same origin (i.e. x=0 at one of the sonic rangers, but not both). 

Part One:  Elastic collisions

• Measure the mass of each cart.  (One of them should have one of the black blocks  added.) Start the Collisons2 Lab experiment by double clicking its icon. Play around with the system so that you know what the "active" area of the motion detectors is.  This is the area in which both detectors see the cart well.  You will need to be sure the collisions occur in this region.
• The Pasco carts have magnets in them that cause the carts to repel one another.  Have the less massive cart at rest initially and roll the other one toward it (without taking data).  Describe the "collision".
• Now repeat the collision while taking data with the sonic rangers.  When you have recorded a good collision and are happy with your data, print your x(t) and v(t) graphs.
• Create calculated columns for the momentum and kinetic energy of each cart as well as the total momentum and total kinetic energy.  Make one graph with all three momentums on it and another with all three kinetic energies on it.   Print these graphs as well.
• Did the collision change the kinetic energy of the less massive cart significantly?  If so, did its kinetic energy increase or decrease?
• Did the collision change the kinetic energy of the more massive cart significantly?  If so, did its kinetic energy increase or decrease? 
• Did the total kinetic energy change significantly?  If so, did it increase or decrease?
• During the actual collision there is a dip in the total KE.   By the end of the collision this KE (or at least most of it) has returned.   Where did the energy go during the dip?
• Which cart had the bigger momentum change as a result of the collision or was the momentum change the same (in magnitude) for both carts?
• Was total momentum conserved in the collision?

Part Two:  Inelastic collisions

• First adjust your air track to be as level as possible. If the end with the single fixed leg is too low, try inserting a thin slotted mass under that leg, so that you can adjust the track to be level.
• Measure the mass of each cart.  (One of them should have some extra mass added.)
• Start the Collisons1 Lab experiment by double clicking its icon. Play around with the system so that you know what the "active" area of the motion detectors is.  This is the area in which both detectors see the cart well.  You will need to be sure the collisions occur in this region.
• Place the less massive cart in the approximate center of the active area. The cart should remain almost stationary for a few seconds. If not, recheck your level.
• You will be pushing the less massive cart so that it collides with the stationary one. Note that one of the carts has a needle on the end and the other a cylinder of wax. Thus, when they collide, the needle enters the wax and they stick together.  The needle should be on the less massive cart.
• First try the experiment without taking data. Describe what happened qualitatively.  Considering the system consisting of the two carts, will the collision of the carts change the total momentum of the system?  If so, what will happen to the total momentum? 
• Now repeat the experiment and take position data. When you hear the detector begin operation, give the less massive cart a push. (Keep trying until you get a graph with no anomalous spikes.)
• Change the time axis so that the graph ends just before the carts hit the end of the track. Print graphs of position and velocity versus time. On each graph label the part of the graph where the collision is taking place. 
• Create calculated columns for the momentum and kinetic energy of each cart and for the total momentum and total kinetic energy.  Use the same vertical for all graphs of the same type.  Print these graphs.
• Based on your experimental results, is the total momentum of the system conserved during the collision?  Does the total kinetic energy stay the same during the collision?  If not, where did the energy go?

In your conclusions, compare your results for the two experiments.