# A Momentum Conservation Experiment for an Inelastic Collision Between Two Carts

Do you have two PocketLab Maker Kit carts, and do you have the free VelocityLab app?  Then you are all set to do some experiments in conservation of momentum with PocketLab!  This lab discusses how to setup and perform an inelastic collision in which one cart (A) is moving toward another cart (B) that is at rest.  When cart A hits cart B, they stick and move off together.  The photo below shows the two carts shortly before the collision would occur.  PocketLab is mounted on a front wheel of cart A.  Small pieces of wood are stuck to the carts and protrude further than the wheels.  Some thick double-stick mounting tape is attached to the ends of the wood that overhang the wheels.  When the carts collide, the tapes stick together, providing an inelastic collision.  In such a collision some of the kinetic energy of the carts is converted into other forms of energy, including heat and sound.

The figure below shows the setup used by the author to study conservation of momentum.  A pair of rails, with inside separation just a little larger than the axle of the carts, was constructed with thin balsa wood sticks.  This is optional but does help to keep the carts on "the straight and narrow".  Cart A is given an initial push at the far left end of the track, while cart B is at rest near the middle of the track.  After sticking together, the carts hit the white Styrofoam bumper at the right end, recoil some and then stop.

The figure below shows position, velocity, and acceleration vs. time graphs that were constructed from data obtained from a .csv file created by the VelocityLab app.  The graphs are marked up in red, noting how the motion of the carts applies to the graphical interpretation of the data.

The two most important pieces of information needed to verify the law of conservation of momentum are identified with stars in the velocity graph: (1) the speed of cart A just before colliding and sticking to cart B, and (2) the speed of the combined carts just after sticking together.  (Note that the mass of cart A is 0.159 kg and the mass of cart B is 0.102 kg.)

With all of the above information, it is quite easy to compute the momentum of the system right before the collision [p = mv = 0.159 kg x 0.802 m/s = 0.128 kg-m/s], and right after the collision [p = mv = (0.159 kg + 0.102 kg) x 0.453 m/s = 0.118 kg-m/s].  The momnetum before and after agree within about 8%.  Calculations of the kinetic energy of translation reveal that about half of this kinetic energy is lost:  0.051 J just before the collision, and 0.027 J just after the collision.

The VelocityLab.csv file has been attached for those that may be interested in it.  The video below is a combined video and data, showing graphs of position, velocity, and acceleration in sync with the motion of the carts.

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