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# Momentum

## So this conserved quantity is a powerful tool for analyzing any kind of physical phenomenon.

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# Σ m·v (before) = Σ m·v (after)

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### Momentum – Chapter from alternate text, “Light and Matter”

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# Impulses change momentum

### Relate the two: ## ### Ball bouncing on a billiards table ### If  Δp  occurs over a long period time then the force of impact is small. ### very large Δp  in a small Δt # Bouncing (rebounding)

### Her hand bounces back, yielding as much as twice the impulse to the bricks. ### Let’s look at this in slow motion: ### Bouncing (rebounding) PhysicsClassroom.com

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# Conservation of momentum

### “p before firing is zero. After firing, net p is still zero,

because the of the cannon is equal and opposite to the p of the cannonball.”

# Does p disappear?

### “At first glance this looks impossible. In physics terms, a system (in this case a canoe + two occupants) cannot change its own overall momentum because all internal forces ultimately cancel out. In other words, where is the newfound linear momentum coming from that gets them out of this predicament?” # Collisions

## Something else besides momentum is conserved

### Some principle must be restricting the real-world outcomes – we infer that some other conservation principle exists.

The following image is from HyperPhysics, by Carl R. Nave

## Videos

“A Tale of Momentum & Inertia” (House Special CGI animators, Director Kameron Gates)

A Tale of Momentum & Inertia (House Special CGI animators)

Cartoon laws of physics.  Intuitive ideas about motion – that are totally wrong. Inspired by classic Warner Brothers cartoons.  Cartoon laws of physics

Videos showing the cartoon laws of physics

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## Momentum Lab

Goal: Study conservation of momentum, in 1-dimension, in collisions of two bodies.

Use air-carts floating on an aluminum track, suspended by a cushion of air so as to be nearly frictionless.

Momentum Lab : Word file that you can print out

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## How was conservation of momentum discovered?

https://kaiserscience.wordpress.com/2016/10/13/discovery-of-conservation-of-momentum/

## Videos

Articles

Practical problem solving: When we do use conservation of momentum to solve a problem? When do we use Newton’s laws of motions?

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Learning Standards
2016 Massachusetts Science and Technology/Engineering Curriculum Framework

HS-PS2-2. Use mathematical representations to show that the total momentum of a system of interacting objects is conserved when there is no net force on the system. Emphasis is on the qualitative meaning of the conservation of momentum and the quantitative understanding of the conservation of linear momentum in
interactions involving elastic and inelastic collisions between two objects in one
dimension.
HS-PS2-3. Apply scientific principles of motion and momentum to design, evaluate, and refine a device that minimizes the force on a macroscopic object during a collision. Clarification Statement: Both qualitative evaluations and algebraic manipulations may be used.

### Common Core Math

• CCSS.MATH.CONTENT.7.EE.B.4  Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
• CCSS.MATH.CONTENT.8.EE.C.7  Solve linear equations in one variable
• CCSS.MATH.CONTENT.HSA.SSE.B.3  Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. (including isolating a variable)
• CCSS.MATH.CONTENT.HSA.CED.A.4  Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
• http://www.corestandards.org/Math/