1. Conservation of Momentum
It’s Not Just a Good Idea, It’s the Law
Standards:
2e Students know momentum is a separately conserved quantity from energy.
2f Students know an unbalanced force on an object produces a change in momentum.
2g Students know how to solve problems involving elastic and inelastic collisions in one dimension by using principals of conservation of momentum and energy.

2. Law of Conservation of Momentum
Momentum is conserved for a system if there are no outside forces.
Conserved means stays the same
System a group of objects that interact
Outside force is a force that does not come from the objects in the system interacting
True for elastic collisions, inelastic collisions and explosions
Not true for falling bodies, simple pendulums and objects sliding or rolling down inclined plane
Question: State the law of conservation of momentum. What does it mean to say some quantity is conserved? What is a system? Distinguish between an internal and outside force for a system. List three cases where momentum is conserved. List three cases where it is not conserved.
Activities:
Write the law of conservation of linear momentum on the board.
Discuss what it means for a quantity to be conserved, what a system is and the difference between external and internal forces. Use example of trying to push a car by sitting inside it and punching the dashboard vs. pushing off the ground for the difference between internal and external forces.
List examples where momentum is conserved and where it is not on slide. Remind students what an elastic and inelastic collision are using the happy and sad balls again.
Point out that today we are talking about the situation which is opposite to yesterday’s lecture. Namely no outside forces will be acting in the direction of motion and therefore momentum will stay the same.

3. Cases where Momentum is Not Conserved
Falling body
Outside force of Earth’s gravity
Conserved if include Earth
The Simple Pendulum
Outside forces of gravity and tension on bob
Sliding or rolling down inclined plane
Outside forces of gravity and friction
Questions: List some examples of objects moving for which momentum is NOT conserved. What outside forces act in each case?
Activities:
Talk about a falling body and how momentum is not conserved because of outside force of gravity. Talk about how you can make a closed system by including the Earth but the velocity the planet moves towards the ball is so small it would be next to impossible to measure.
Draw a simple pendulum and point out that bob changes velocity during path. Gravity again is acting as an outside force here and thus momentum is Not conserved.
Draw inclined plane and ask whether ball rolls down with constant or changing speed. Once this is established again point out that gravity acts as an outside force . Momentum is thus not conserved in this system.

4. Collisions Elastic Collisions Inelastic Collisions
Collisions involving bouncing
Momentum is conserved
Objects have different velocities after collision
Equation will not have parenthesis
Collisions involving sticking
Momentum is conserved
Objects have same velocity after collision
Equation will have parentheses on momentum after side
Questions: Distinguish between an elastic and inelastic collision. For which type of collision is momentum conserved? Which type of collision results in two objects having the same velocity after the collision? For which type of collision is momentum conserved in 2 and 3 dimensions?
Activities:
State that momentum is conserved in all collisions. Point out that all forces are between objects in system if define system as all interacting objects in the collision. Thus no outside forces.
Review difference between elastic and inelastic collisions using happy and unhappy balls if necessary.
Use transparency to show how to derive equations for momentum conservation for both elastic and inelastic collisions for similar massed objects. Make a chart showing the equation for momentum before and after each collision.
Demonstrate collisions of different massed objects using air track. Derive formulas before going to the back and seeing if they are true.
Point out patterns in equations namely when same massed objects collide then bodies simply exchange momentums. Elastic equations do not have parenthesis while inelastic do have parenthesis.
Finish with the constrained elastic collision. Discuss how momentum is given to system when large ball hits ground. After this discuss how entire momentum of large ball is transferred to smaller ball resulting in large velocity.

5. Explosions Momentum before = momentum after = 0
There is motion of objects in system. Momenta are equal and in opposite directions for different parts of system
Examples
Gun and Bullet
Rocket and Fuel
Question: Is momentum conserved in an explosion? What is the momentum before, during and after an explosion? If the momentum is always zero then how can there be any movement during an explosion? Do all pieces blown out during an explosion have to have the same mass and velocity?
Activities:
1) Show 1 dimensional explosion using dynamics carts. Discuss how momentum before, during and after explosion is zero and how momenta from one cart is equal and opposite that of another cart.
2) Refer to Physical Science Video Disk pictures side 1 and comment on symmetry of explosion.
3) Conclude that momentum is conserved in an explosion
4) Demonstrate with cart and masses
4) Parallel 3rd law discussion with rifle and bullet and rocket and fuel. Use size of variable to indicate size of quantity for each object and point out that momentum remains zero.

6. Check Question
You find yourself in the middle of a frozen lake with perfectly frictionless ice. This means that you cannot push off horizontally on the ice. How can you propel yourself to the side of the lake?

7. Momentum in 2D and 3D
Momentum is conserved in all directions and as a total amount in 2 and 3 D collisions and explosions
Pbefore = Pafter
Pxbefore = Pxafter
Pybefore = Pyafter
Pzbefore = Pzafter
Question: How is momentum conserved during 2 and 3 dimensional collisions and explosions?
Activities:
Show picture of firecracker exploding and show that momentum is conserved in each perpendicular direction.
Show picture of off axis elastic collision and again show that momentum is conserved in each perpendicular direction.
Show Physical Science video disc pictures of of atomic explosion and comment on symmetry of explosion.
Draw 4 masses in square and talk about how momentum is a vector sum of each.

8. Solving Momentum Problems
Draw before and after picture.
Write conservation of momentum equation
Solve equation for unknown
Substitute