Day 131: Discovering Momentum Conservation

College-Prep Physics: This year, I taught energy before momentum for two reasons…

  • 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–> 8 J of Ek

Inelastic collision: 1 kg @ 4 m/s collides with 1 kg @ rest
8 J of Ek –> 4 J of E+ 4 J of ΔEth

Inelastic head-on collision: 1 kg @ 4 m/s collides with 1 kg @ -4 m/s
16 J of Ek –> 16 J of ΔEth

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.

New Doc 42_1

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?

New Doc 42_2

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?

New Doc 42_3

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?

New Doc 42_4

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.

New Doc 42_5

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.

New Doc 42_6

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

##MTPM

Day 131: Moving Charge in a Magnetic Field

AP Physics C: Intro to Magnetic force on moving charge (shown without sound):

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

MagneticForceVPython

  • 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.

Day 108: Intro to Projectile Motion and Video Analysis

LoggerProProjectile

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.

Day 107: Real-World Problem Solving (Free Fall)

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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

March 12, 2014 41335 PM EDT

Student B

New Doc 26_2

Day 106: Why I Teach Free Fall AFTER Forces

IMG_20140312_121804

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.

Day 105: Real-World Problem Solving (Dynamics)

College-Prep Physics: 

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:

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New Doc 24_2

New Doc 24_1

##UBFPM

Day 104: Fire Syringe

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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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