6.2 Conservation of Momentum pp Mr. Richter

Agenda  Warm-Up  Check HW  Return Lab Notebooks  Intro to Conservation of Momentum  Notes:  N3L and Conservation of Momentum  Conservation of Momentum  Recoil  Lab Wednesday

Objectives: We Will Be Able To…  Describe the interaction between two objects in terms of the change in momentum of each object.  Compare the total momentum of two objects before and after they interact.  State the law of conservation of momentum.  Predict the final velocities of objects after collisions, given the initial velocities.

Warm-Up:  A man and an elephant standing on skateboards push off of each other.  Which, if either, pushes with more force?  Which, if either, pushes for a longer amount of time?

Newton’s Third Law and Conservation of Momentum

N3L and Conservation of Momentum  When two objects collide they push off of each other.  According to Newton’s Third Law, they push with equal and opposite forces.  Also, they must push for the same amount of time. One cannot push the other without being pushed as well.  This means that their impulses (F Δ t) are equal and opposite, which means their change in momentum must be equal and opposite as well.

N3L and Conservation of Momentum  Algebraically:

The Law of Conservation of Momentum  In words: the total momentum of all objects interacting with one another remains constant, regardless of the nature of the forces between the objects.  Momentum is conserved whenever two or more objects collide (more on specific types of collisions in the next section)  This is only true in the absence of friction.

Momentum Conservation Example Before the CollisionAfter the Collision

Conservation of Momentum: Problem Solving  A 20 kg Object A traveling to the right at 5.0 m/s collides with a stationary 15 kg Object B initially at rest. After the collision, object A continues moving to the right at 4.0 m/s. What is Object B’s velocity after the collision?  1.3 m/s to the right

Recoil When objects push off of each other.

Recoil  Recoil scenarios are special types of collisions when two objects push off of each other when both are initially at rest.  Some examples (all are assumed frictionless):  Our warm up, with the man and the elephant.  Shooting a rifle  Two ice skaters pushing away

Recoil  The conservation of momentum equation changes when both initial velocities are zero.  The momentum of one object is equal and opposite the momentum of the other object in recoil scenarios.

Recoil Problem Solving  An 80.0 kg man and a 400 kg elephant stand next to each other on skateboards. If they pushed off of each other, the man would move to the left at 12.0 m/s. What would the elephant’s velocity be?  2.40 m/s to the right

Wrap-Up: Did we meet our objectives?  Describe the interaction between two objects in terms of the change in momentum of each object.  Compare the total momentum of two objects before and after they interact.  State the law of conservation of momentum.  Predict the final velocities of objects after collisions, given the initial velocities.

Homework  Due Thursday  p. 219 #1, 2, and 4  p. 221 #1-3