Long Chain of Reasoning exercise 1: Momentum conservation
Conservation laws are beautiful. They are among the primary “big ideas’ I want my kids to leave my class understanding. And I want them to understand them at a level beyond . But the challenge in using conservation laws is knowing when to apply them. This is where I think my thoughts about following long chains of reasoning might come into play.
Here is a long chain of reasoning about a collision between two cars (A and B) on a level road.
- Car A and B experience a contact force between them.
- the change in momentum of A should be equal to the net force on A times the time of the collision.
- the change in momentum of B should be equal to the net force on B times the time of the collision.
- By N3, the force of A on B is opposite the force of B on A.
- Since the other forces are balanced (gravitational force and normal force) the net force on each object is this contact force.
- So the net forces are equal and opposite.
- Thus the change in momentum will be opposite.
- Thus the total change in momentum will be zero
- We conclude that the momentum is conserved (does not change) during the collision.
My thought is to start my students by having them construct the above chain of reasoning. Then, present them with a new situation: the collision takes place on the side of a hill, and ask them to use the chain of reasoning to see if momentum will be conserved in that case. Since I’ve been on leave for 2 weeks, I haven’t gotten a chance to test this out in the classroom, but I’ll let you know how it goes.