5.4 Conservation of Momentum in Two Dimensions

Transcription

1 Phyic Tool bo 5.4 Coneration of Moentu in Two Dienion Law of coneration of Moentu The total oentu before a colliion i equal to the total oentu after a colliion. Thi i written a Tinitial Tfinal If the net force acting on a yte of interacting object i zero, then the linear oentu of the yte before the interaction equal the linear oentu of the yte after the interaction For any colliion inoling a yte on which the total net force i zero, the total oentu before the colliion equal the total oentu after the colliion. Colliion in two dienion are analyzed uing the ae rincile a colliion in one dienion: coneration of oentu for all colliion for which the net force on the yte i zero, and both coneration of oentu and coneration of kinetic energy i the colliion i elatic. The are four oible outcoe in a colliion between two object The object collide and rebound The object collide and oe in the ae direction The object collide, tick together, and continue oing in the ae direction One of the object to after colliion. Elatic Colliion: two billiard ball colliding E Ki i The force between the bodie are alo coneratie, o that no echanical energy i lot or gained in the colliion. E K Inelatic Colliion: two tenni ball colliding E Ki i E K Coletely Inelatic Colliion: two illy utty ball colliding E Ki i E Note: It i a coon iconcetion that the only inelatic colliion are thoe in which the colliding bodie tick together. If two car collide and bouce off each other in a fender-bender, the work done to defor the fender cannot be recoered a kinetic K

2 energy of the car, o the colliion i inelatic. Proble Soling Strategy The firt te i to ditinguih between elatic; inelatic, and coletely inelatic colliion. In any colliion in which eternal force can be neglected (net force i zero), oentu i conered and the total oentu before equal the total oentu after; in elatic colliion only, the total kinetic energy before equal the total kinetic energy after. Eale The figure below how an elatic colliion of two ball on a frictionle table. Ball a ha. Ball A ha an initial elocity of a 0.500kg and ball B ha a 0.300kg A B 4.00 in the oitie -direction and a final elocity of.00 in an unknown direction. Ball B i initially at ret. Deterine the final eed B and in the figure. of ball B and the angle Solution: Becaue the colliion i elatic, the initial and final kinetic energie are equal AA 1 AA B A A1 A A B B B kg kg kg 4.47 B

3 Becaue of the elatic colliion, we need to aly the coneration of oentu Coneration of the -coonent of total oentu: A A1 A A B B 0.500kg kg.00 co 0.300kg 4.47 co Coneration of the y-coonent of total oentu: 0 A Ay B By kg.00 in 0.300kg 4.47 in Soling thee two equation for and co in 0.300kg kg kg kg.00 co 0.500kg.00 in Squaring, adding and alying 36.9 and 6.6 in co 1, then oling, we find that Eale A 1000 kg a oing at 30 E 0 W 30 N elocity of the joined a. Solution: hit another a 100 kg oing at, If the two ae tick together after the colliion, find the final Since the ae tuck together, thi i a totally inelatic colliion and thu ue the law of coneration of oentu. In the -direction

4 1 1i i 1 1f f kg kg kg kg f co In the y-direction 1 1iy iy 1 1y fy kg kg kg kg fy in fy f f f fy tan E The final elocity of the a i N Eale The figure below how a ballitic endulu, the yte for eauring the eed of a bullet. A bullet of 5.00g i fired into a block of wood with a M.00kg, uended like a endulu, and ake a coletely inelatic colliion with it. After the iact of the bullet, the block wing u to a aiu height 3.00 c. deterine the initial elocity of the bullet?

5 Solution: Thi quetion can be broken down into two tage The firt tage when the bullet jut ebed itelf into the block. The econd tage i when the block and the ibedded bullet oe a a unit. We need to find the eed, V of the bullet block cobination. We will ue the to oentu coneration in the firt tage to relate M V M V At the beginning of the econd tage, the block-bullet unit ha kinetic energy: V 1 M V Now, ince the colliion i inelatic, the alue i le that the kinetic energy before the colliion. The block-bullet unit wing u to a height y, where the kinetic energy i zero and it otential energy (gh) i M gy

6 1 Therefore M V M gy V Therefore M gy gy Now, lugging in the alue for the ariable M gy.00kg kg kg kg J Note: the kinetic energy before the iact i The kinetic energy after the of the block-bullet i kg The kinetic energy i lot a linter and heat and ound J