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12 April 2014

Multiple choice question: "evaluating claims" about impulse

John and Bob, both of mass 70 kg, each drop on to a scale from the same height. Which of the following explains why they both experience the same impulse in the collision?
(A) Both start at zero speed before they jump, and both end at zero speed after they jump, so both change momentum by the same amount.
(B) Both have the same mass, so both experience the same force; both were in the air for the same time; and impulse is force times time.
(C) Conservation of momentum says that the change in one object’s momentum is the same as the change in another object’s momentum in a collision.
(D) Since they dropped from the same height, they each have the same speed before hitting the scale; they both come to rest after hitting the scale; since their mass is also the same, they change their momentum by the same amount during the collision.

A good number of questions for the new AP Physics 1 and 2 exams will ask students to evaluate claims, to identify features of correct and incorrect physics reasoning.  Above is a question in the style of an AP Physics 1 multiple choice question.  But where did I get the idea for it?  And how do I use it in my class, other than just asking it on a test?

I've had my class do this "bent legs/straight legs" problem in several different incarnations.  You might know it as the airbag problem, or the catcher's mitt problem... when something comes to rest, it experiences less force when the time of collision increases.  This can be understood through kinematics and Newton's second law, or through the impulse-momentum theorem.  I prefer to use the latter approach, particularly when we're studying impulse and momentum.

In class, I walk students through the bent legs/straight legs problem in stages.  The first stage question is, "Which of the variables in J = Ft is the same no matter how your legs bend?"  That's a tough one in the first couple days of studying impulse...

The most common incorrect answer is "Force is the same either way" with some spewed non-physics baloney.  My response is to ask them to jump off a 10-foot wall and to land with straight legs.  "No, that would hurt," they say.  "No it won't!  You said that the force on your legs is the same however you land!"  But this is a mistake stemming from of a lack of understanding the problem, or of laziness of thought.  Since no real physics is involved, this is not a true physics misconception.

The misconceptions come when they try to justify why the impulse is the same in both the bent leg and straight leg case.  Consider each of the three incorrect choices (A), (B), and (C) in the problem above.

(A) Some correctly use the fact that impulse is change in momentum.  Problem is, they consider the change in momentum from when they begin their fall to when they finish the jump.  No!  The equation J = Ft should be used in a collision:   J is the change in momentum from the collision's start to the collision's end.  Sure, they dropped from rest to the ground before the collision, but that doesn't mean that the momentum immediately before collision is zero.

(B) Others try to use J = Ft to explain why the impulse remains the same.  Again, they conflate the collision with the time in the air before the collision.  The time of the fall is the same no matter how students land; the force of the earth on John and Bob is the same while they are in the air, because they have the same weight.  That means that the impulse on John and Bob is the same while they are in the air.  But the question asks about impulse in the collision.

(C) Aargh!  Conservation of momentum states that two objects have the same TOTAL momentum before and after they collide with each other.  John and Bob are not colliding with each other, they're colliding with the Earth in separate collisions.  Conservation of momentum means that any momentum lost by John in the collision is picked up by the Earth.  That doesn't help compare the impulse on John and Bob.

I gave this question on a test; most of my class got it right, because we had gone through this reasoning enough in class.  Those who got it wrong were asked to write a correction.  Most just restated the correct choice (D) in their own words.  I told them that's not good enough -- they had to explain why the answer they originally chose was incorrect.

So much of good physics teaching is about picking at every detail of a problem until students can not only come to the correct answer, but until they can articulate every bit of reasoning that goes into the solution.  And so much of the new AP Physics exams will be questions requiring just this sort of articulation.  You want to write a good AP Physics 1 question asking for an evaluation of a claim?  Write down three incorrect student responses on a conceptual homework problem, add in the correct response, and voila: Physics 1 multiple choice question.