Con of Linear Momentum Data Sheets

							                                                                     Conservation of Linear Momentum



DATA ANALYSIS
Mass Measurements:

                                            M (kg)              uM (kg)          uM/M
                          Mass 1
                          Mass 2

Speed Before collision:

                                            v (m/s)         uv (m/s)             uv/v
                          Mass 1
                          Mass 2

Angle Before Collision:

                                                      θ (deg)         uθ (rad)
                                   Mass 1
                                   Mass 2

Speed After Collision:

                                                      v (m/s)         uv (m/s)
                                   Mass 1
                                   Mass 2

Angles After Collision:

                                                      θ (deg)         uθ (rad)
                                   Mass 1
                                   Mass 2

Sample Calculation: (Mass 1 before collision)

              π
       uθ =         uθ (deg) = _______________________________________________
              180




                                                                                                 65
Department of Physics and Astronomy
Conservation of Linear Momentum

Components of Momentum Before Collision:


                               Px (kg m/s)          uPx (kg m/s)            Py (kg m/s)   uPy (kg m/s)

            Mass 1

            Mass 2

            System



Components of Momentum After Collision:


                               Px (kg m/s)          uPx (kg m/s)            Py (kg m/s)   uPy (kg m/s)

            Mass 1

            Mass 2

            System



Sample Calculation: (Px and uPx of Mass 1 before the collision)

       Px = mv cos θ = _______________________________________________________


       u Px =   (v cos θ ⋅ u m )2 + (m cos θ ⋅ u v )2 + (mv sin θ ⋅ uθ )2
           =________________________________________________________________


Sample Calculation: (Px and uPx of the System before the collision)

       Px = Px , mass1 + Px , mass 2 = _________________________________________________


       u Px = u Px, mass1 + u Px, mass2 = _______________________________________________
                2             2




66
                                                                                 University of North Carolina
                                                                                   Conservation of Linear Momentum

Total Momentum of the System:


                                                 P (kg m/s)         uP (kg m/s)       θ (deg)        uθ (deg)

                 BEFORE

                  AFTER



Sample Calculation: (Before the collision. Note: Px and Py below are Px,system and Py,system)


        P = Px2 + Py2 = _______________________________________________________

                            2                         2
               P  2  Py  2
        u P =  x  u Px +   u Py
                            P
               P          

              = ________________________________________________________________

       θ = tan −1 (Py Px ) = _____________________________________________________

                                                  2             2
                          Py           u Px     u Py   
        u  Py          =                      +       
                        P            P        P       
          
                Px 
                         x            x        y      


                        = _____________________________________________________________

                                          −1
               P              
                                    2
                                        
        u θ = 1 +  Y                  u        (where uθ is in radians)
                PX                     Py P 
                                             
                                          x


              =________________________________________________________________

                                                                     180
       convert uθ from rad to deg. : uθ (deg) =                            uθ (rad) = _________________________
                                                                      π




                                                                                                                  67
Department of Physics and Astronomy
Conservation of Linear Momentum

Kinetic Energy Before Collision:


                                                          K(J )                uK (J )
                                     Mass 1
                                     Mass 2
                                     System



Kinetic Energy After Collision:


                                                          K(J )                uK (J )
                                     Mass 1
                                     Mass 2
                                     System



Sample Calculation: (Mass 1 Before Collision)

             1
       K=      Mv 2 = ______________________________________________________
             2

                      2
             v2      2
       uK = 
             2       u m + (Mv ) 2 u v2
                     
                    

           = ____________________________________________________________

Sample Calculation: (System Before Collision)

       K = K mass1 + K mass 2 = _______________________________________________


       u k = u K , mass1 + u K , mass 2 = ___________________________________________
               2             2




                                                  2                    2
                                      u M , mass1   u v , mass1 
       where u K , mass1 = K mass1   
                                     M             + 2
                                                                 
                                                                          and similarly for Kmass2
                                      mass1   v mass1 


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                                                                                    University of North Carolina