Friday, October 12, 2018

Banked Turns

In AP Physics C students deal with forces in two dimensions, on inclines, acting in circles and more. Inevitably during the unit students will ask the following question in fear:
"Will we ever have to deal with turns on an incline?"

Oh yes kids, but lets build up slowly.

I created this worksheet that referred back to sample and back-of-chapter problems in the textbook. Students worked on increasingly difficult problems with a partner before we reviewed. Here are a key for the worksheet and a key for the textbook problems.

To introduce the concept I delved into the cabinets left to me by my predecessor and found the toys I needed. I raised the whole demo on a wood stand to raise it up. I found a double lane flat track (in yellow) and a banked Hot Wheels track (in orange). Amazingly the Hot Wheels track fit into the inner lane of the flat track. For my first period I used clay and ring stands to hold up straight track to feed cars into each lane. By the next period I added a third straight track to feed one car straight to the wood support, with no turn. By the last period I added color coded signs ...

When I demonstrated this for students I ask students what will happen to the car that goes on the "no turn" track. They correctly guess that it will continue straight so I ask why it doesn't turn. It may take a second but they realized, "There was no force to push it into a circle!"

So then we drop the second car down the "flat turn" track and the initial ramp is high enough that the car rides the edge of the track through the whole turn. I ask students which force kept the car going in a circle and they realize that it isn't the force of friction but the force from the wall in this case. We talked about how that wouldn't be good for "real cars" and that instead we prefer a force of friction to keep our cars going around a turn.

The final car goes down the banked turn and while it may briefly touch the wall it doesn't ride the wall like the flat turn. They notice the banked orange track is about as smooth as the flat yellow track so I wasn't sneaky and just adding friction. Then I asked them what force caused the car to go around a circle and they realize its a portion of the normal force. 

Here is a video of the three cars being sent down the ramps at the same time:

The radius and coefficient of friction for the two turns are not the same and I did not bother to match the masses of the Hot Wheels cars I grabbed. I did not introduce any quantities for students other than identifying which force was causing the motion. It helped for my students to see the differences in the types of turns and they loved being able to run the cars down the tracks themselves. For a quick set-up it did well to help show my students the differences for each type of turn they were going to work through.

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