Ch 8 : Conservation of Linear Momentum 1.Linear momentum and conservation 2.Kinetic Energy 3.Collision 1 dim inelastic and elastic nut for 2 dim only inellastic 4.Collision in CM frame 5.Rocket motion (varying mass)

Definition of Linear Momentum and Conservation To derive the basic result of this chapter Impulse=  p we integrate the A. energy equation (W=  K) A time A. Time with respect to: B. Newton’s 2 nd law B. Space Which of the following is required to get the momentum to be conserved: A. F net =0 B. F net external =0 C. F net internal =0 D. A or B is ok b/c they are equivalent Which of the following is true for a system of 2 particles m 1 and m 2 if the net force on the system is zero? A. v 1 and v 2 are constant B. m 1 v 1 and m 2 v 2 are constant C. m 1 v 1 + m 2 v 2 is constant As a result of the above we are led to define the momentum of a system of 2 particles m 1 and m 2 as: A. p= (m 1 v 1 + m 2 v 2 ) B. p= (m 1 + m 2 )(v 1 +v 2 ) C. p= (m 1 + m 2 )(v Average )

Momentum and Averages The fact that p system = p CM is a consequence of : A. The definition of the CM of a system B. The conservation of momentum C. The internal forces cancelling 2 by 2 D. The equality is not always true Written in terms of the momentum N2 reads for a system of 2 particles: A. F net =  p B. F net =p 1 +p 2 C. F net =dp 1 /dt + dp 2 /dt D. F net =dp 1 /dt - dp 2 /dt To average a quantity Q(x,t) between 2 position A and B which of the following should you compute? A. B. C. D.

Collisions: General What is the definition of a perfectly inelastic collision between 2 objects? A. All speeds remain unchanged B. All final velocities are equal C. The vector sum of the 2 velocities remains unchanged D. Kinetic energy is conserved During a collision we assume: A.Internal forces are zero B. External forces are zero C. Both A and B If initial velocities and masses are known, which of the following can be determined exactly after any collision? A.All final velocities B. Final velocity of the CM C. Both A and B What is the definition of a perfectly elastic collision between 2 objects? A. All speeds remain unchanged B. All final velocities are equal C. The vector sum of the 2 velocities remains unchanged D. Kinetic energy is conserved

Collisions: General In 2 dimensions the conservation of momentum during a collision gives how many component equations? In addition, if the collision is perfectly inelastic. this assumption give how many more equations in 2 dimensions? For a collision between 2 particles in 2 dimensions, if the masses and initial velocities are known we must solve for the final velocities. How many unknowns do we have to solve for? 1, 2, 3, 4 Or, if the collision is perfectly elastic. this assumption gives how many more equations in 2 dimensions? So in 2 D we have 4 unknowns to solve for: v’ 1x, v’ 1y, v’ 2x, v’ 2y With momentum conservation we get : 2 equations p 1x + p 2x = p’ 1x + p’ 1x p 1y + p 2y = p’ 1y + p’ 1y In addition: If perfectly inelastic : 2 extra equations: v’ 1x = v’ 2x v’ 1y = v’ 2y ( => solution determined) If perfectly elastic : only 1 extra equation: K 1 + K 2 = K’ 1 + K’ 2 ( => 1 undetermined parameter e.g angle between the velocities the 2 outgoing particle)

Example space repair Examples: space repair and rr car with grain

Example space repair Example: crash test

Example space repair Example: ballistic pendulum

Example space repair Other examples Other examples: elastic collision of 2 blocks, inelastic car and truck and CM frame and rocket lift off are studied in the ch8 notes

Ch8 Click. Problems