- In my opinion, the conservation of a scalar quantity (like energy) is simpler than conservation of a vector quantity (like momentum).
- Collisions are an easy way to “break” the energy model, i.e., it’s not useful for analyzing collisions. There are several collisions which all start with the same amount of kinetic energy, but have different outcomes.

So yesterday we analyzed the energy transfers in various collisions:

- Red & Blue Pasco carts and tracks
- Logger Pro with Motion Detector
- Air Track Simulation from Tony Wayne

Elastic collision: 1 kg @ 4 m/s collides with 1 kg @ rest

8 J of E_{k }–> 8 J of E_{k}

Inelastic collision: 1 kg @ 4 m/s collides with 1 kg @ rest

8 J of E_{k} –> 4 J of E_{k }+ 4 J of ΔE_{th}

Inelastic head-on collision: 1 kg @ 4 m/s collides with 1 kg @ -4 m/s

16 J of E_{k} –> 16 J of ΔE_{th}

Kinetic energy not always constant before/after. Outcomes ranged from all kinetic transferred to none transferred.

YET — there seems to be a pattern. In the inelastic collision, the speed drops by half. In the inelastic head on collision, the speeds “cancel out.”

Students naturally asked what happens if we change the mass of the carts. So we demoed a few examples in the remaining time:

- What happens in head on inelastic collision between a light cart and a heavy cart going the same speed? (Goes slower in direction of heavy cart.)
- How might we get them to stop after collision? (Make the lighter cart travel faster.)

TODAY

Explored a careful sequence of collisions where students had to draw before/after pictures, bar charts, and look for what remained the same (based on a similar progression from Etkina). Again, we used the Red and Blue Pasco carts and tracks to see the collision and used the Air Track Simulation to collect quantitative data. To get a feel for how the conversation flowed, it’ll be helpful if you read a post from 2 years ago called Inventing Momentum.

What’s new this year is that I’ve created a worksheet to help students keep organized notes for the discussion (snapshots below).

Here’s the progression of collisions:

*A 1-kg red cart moving right at 4 m/s collides elastically with a 1-kg blue cart at rest. *We draw speed bar charts and we see that speed is constant before and after.

*A 1-kg red cart moving right at 4 m/s collides inelastically with a 1-kg blue cart at rest.* We draw speed bar charts, but see that **total speed** is constant before and after. Does this new pattern still work with the previous scenario?

*A 1-kg red cart moving right at 4 m/s collides inelastically with a 1-kg blue cart moving left at 4 m/s*. Total speed is NOT constant, but **total velocity** is constant. So now our bar charts become velocity bar charts. We draw the negative velocity bars downward. Does this new pattern still work with the two previous scenarios?

*A 2-kg red cart moving right at 2 m/s collides inelastically with a 1-kg blue cart moving left at 4 m/s.* Total velocity is NOT constant. But the total “mass-velocity blocks” are constant before and after (see Inventing Momentum). So now our bar charts become mass-velocity bar charts. Does this new pattern still work with the all the previous scenarios?

*A 2-kg red cart moving right at 3 m/s collides inelastically with a 1-kg blue cart moving left at 3 m/s.* Total “mass-velocity blocks” are constant before and after.

*A 2-kg red cart moving right at 3 m/s collides elastically with a 1-kg blue cart moving left at 3 m/s. *Total “mass-velocity blocks” are constant before and after.

You can download a Word version of the worksheet: MomentumFindAPattern 2014

##MTPM

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Also played with VPython program showing charged particle moving in B-Field:

- What determines the force on the charge?
- changing B (magnitude, direction, parallel, perpendicular)
- changing q (magnitude, sign)
- changing v (magnitude, direction)

- Cross product & Right Hand Rule to determine direction of force.

The VPython program (and others) are available on the Matter and Interactions website page E&M Lecture Demo Programs.

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*College-Prep Physics*: This is our first time doing video analysis and I was only able to get the computer lab for 1 class period. So I made the activity very structured. We used a pre-made video from Live Photo Physics and I gave detailed instructions on the mechanics of video analysis using Logger Pro.

You can download the instructions here: Projectile Motion Video Analysis DIRECTIONS 2014

NOTE: I can’t seem to find the video on the Live Photo Physics website, so I’ve upload it here: Ball_Toss_12.mov If anyone knows the original location of the video, please let me know.

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*College-Prep Physics:*** **Using only a stopwatch…

1. Determine the launch velocity and maximum height of a toy popper.

2. Determine the height of the stairs and impact speed of a dropped ball.

Some sample work:

*Student A*

*Student B*

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*College-Prep Physics:* On whiteboards, students were asked to predict the model for the force and motion of a dropped ball soccer ball (m = 0.4 kg):

- Draw a motion diagram, a position-time graph, a velocity-time graph, and a force diagram.
- Determine the ball’s acceleration.

Then, as a class, we tested our predictions using Logger Pro and a motion detector (red graph above).

Next, I asked them to determine the acceleration for a ball with twice the mass. Most groups immediately said it would still be -9.8 m/s/s. Some referred to prior knowledge that all objects fall at the same rate. Others referred to the math they just did on their whiteboards — doubling the mass doubles both the gravitational force on the ball and its mass, so the acceleration will remain the same.

Gravitational acceleration = 9.8 m/s/s for all objects. Why? Why not? *(Sometimes, always, never)*

Show hammer and feather dropped on moon.

Now predict the model for the force and motion of a tossed ball rising and falling — just after leaving hand to just before catch.

- Motion diagram, position-time graph, velocity-time graph, force diagram.
- Determine the ball’s acceleration.

What’s the same as before? What’s different than before? Why?

Then, as a class, we tested our predictions using Logger Pro and a motion detector (blue graph above).

Because students had already done forces, Newton’s Laws, and dynamics, these free fall scenarios were just natural extensions.

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**DO ANY TWO **(in order of complexity)

1. Determine the starting and stopping acceleration of the elevator:

2. Determine the coefficient of kinetic friction between any two surfaces using only a meter stick, stopwatch, and a balance.

3. Determine the force of the slap shot:

Students were required to use the dynamics problem solving template. Sample work for each problem below:

##UBFPM

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*College-Prep Physics*: So this wasn’t on the agenda today, but the fire syringe had been left out from another class and students wanted to know what it was. How could I say no?

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*College-Prep Physics:* Students have been working on designing experiments to determine if the 3 myths above are always true, sometimes true, or never true. And Veritasium’s newest video about numbers was the perfect introduction!

##UBFPM

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Then place the electron sea on top of the atomic cores to represent a neutral conductor. Notice it’s black.

The electron sea shift slightly in the presence of a charged object (slide the blue filter), causing one side to become positively charged and the other side negatively charged.

I like this because it shows that the conductor as a whole is still neutral. It also refutes the misconception that lots of electrons all move to one side. In reality, it’s just a slight shift in the sea of electrons.

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*College-Prep Physics: *Introduced students to this problem solving template for multiple-step dynamics problems. Linking force concepts and motion concepts together can be tricky. I hope this sheet will help students organize their information.

You can get a Word version here: FMA Problem Template 2014

My template is influenced by similar templates from…

Knight (5 Easy Lessons)

and Van Heuvelen (ALPS Kit):

##UBFPM

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