Law of Conservation of Momentum The total momentum

Law of Conservation of Momentum

• The total momentum of all objects interacting with one another is the same before and after the interaction in the absence of external forces (ie: friction, applied forces)

• Do not confuse this with the momentum of one object. When an outside force interacts with only the one object then the momentum changes as seen in the impulsemomentum theorem.

total initial momentum = total final momentum m 1 v 1 i + m 2 v 2 i = m 1 v 1 f + m 2 v 2 f

Types of Interactions • Momentum is conserved when objects push away from each other –Recoil – think Newton’s 3 rd law –explosions –initially both objects move at same speed (sometimes at rest)

Rocket Cart - Recoil

Spud Gun - Recoil

Collisions • Momentum is conserved during collisions –perfectly inelastic • objects stick together and move at same final speed –Ex: Baseball lands in catchers glove • kinetic energy is not conserved due to deformation • energy converts to sound, heat, etc.

Collisions • Inelastic –objects bounce off each other and move separately –kinetic energy is not conserved due to deformation

Collisions • elastic –objects bounce off each other and move separately • Ex: 2 pool balls collide –Kinetic energy is conserved • Objects maintain original shape

All of the above were considered head -on collisions… here is a glancing collision

Example 1: A 70. 9 -kg boy and a 43. 2 -kg girl, both wearing skates face each other at rest on a skating rink. The boy pushes the girl, sending her eastward with a speed of 4. 64 m/s. Neglecting friction, determine the subsequent velocity of the boy. Ans: -2. 83 m/s

Example 2: Anna Litical and Noah Formula are doing The Cart and the Brick Lab. They drop a 2. 07 kg brick on a 2. 6 kg cart moving at 28. 2 cm/s. After the collision, what is the velocity of the dropped brick and cart, which are moving together? Ans: 15. 7 cm/s

Example 3: A 10. 0 g object moving to the right at 25. 0 cm/s makes an head-on collision with a 15. 0 g object moving in the opposite direction at 33. 0 cm/s. After the collision the 10. 0 g object moves at 44. 6 cm/s left. a) What is the velocity of the 15. 0 g object? Ans: 13. 4 cm/s b) Determine if this is an elastic or inelastic collision using conservation of energy. Does Kei = Kef? 0. 00113 J = 0. 00113 J Yes, therefore it is elastic.