Each day in 9th grade physics we begin with an 8-12 question quiz. I usually write these the night before -- I wait until I've had all my classes and graded all the problem sets before I decide what needs to go on the quiz. Sure, sometimes I'll reuse questions from previous years. But many of the questions are invented on the spot. They're targeted to bust a misconception, to make a point about a common mistake on a problem set, or to reinforce a discussion from class.
Below are the ten questions from tomorrow's quiz. I'll explain what led me to ask each one...
On today's problem set, I asked: "Momentum is conserved in a collision. So, how is it possible for a cart to collide with another cart and change its speed without changing its mass, too?" A whole bunch of folks gave answers that implied that speed was conserved in a collision. Others missed the point of the question entirely. So the first few questions on today's quiz are targeted toward understanding the conservation principle, that a single object can change momentum, but the total momentum must remain the same.
1. True or false: In a collision, the total momentum of two objects is conserved. My students all know this, virtually everyone will get this right; but they don't read carefully. I think they skim over the "total momentum" part, and read, "In a collision, blah blah blah conserved." Hence the next few questions.
2. True or false: In a collision, the total mass of two objects is conserved. This one is a "synthesis" question rather than a "recall" question. These other true-false questions can be answered with straightforward reference to facts I've handed out on a fact sheet or to discussions we've had in class. However, I've never explicitly discussed conservation of mass. Here I'm asking the students to apply their understanding of the word "conserved" to a different situation. I don't expect more than half the class to get this right. Why do I ask, then? The discussion of the general principle of a conservation law will be effective in the context of this quiz question. If I would instead say, "listen up while I talk about conservation laws," no one would pay attention.
3. True or false: In a collision between two objects, any speed lost by one object must be gained by the other. I have discussed how a consequence of the conservation of momentum in a collision is that both carts change their momentum by the same amount. As with question 1, I don't believe my students are reading or listening carefully: I think they are internalizing "anything lost by one is gained by the other." I'm checking in several different ways whether they recall that momentum, not speed, is conserved.
4. True or false: In a collision, the total speed of two objects is conserved. Same as #3, just with different language.
5. True or false: In a collision between two objects, any momentum lost by one object must be gained by the other. This is the alternate statement of momentum conservation that I've discussed repeatedly. Although this is a straightforward statement, recognizing it as true requires two minor steps of reasoning: (1) recognition that this is a restatement of "total momentum does not change in a collision" and then (2) recognition that it is total momentum, not speed, that remains unchanged.
6. True or false: In a collision between two objects, the amount of impulse on one object is the same as on the second object. And now I've added a third step from the reasoning in the previous question: Impulse is change in momentum, so this statement is a restatement of #5.
7. A 2 kg ball slows down from 3 m/s to 2 m/s. Calculate the impulse on the ball. When I give this quiz, we will have studied collisions for more than a week, but impulse for only a day. I know the students are still struggling with the idea of calculating a change in an object's momentum. They tend to simply calculate a momentum, and call it "impulse." Or, they subtract one object's momentum from another object's momentum and call that "impulse." I want to guide them to the habit of calculating a single object's initial momentum, its final momentum, and then subtracting to find the momentum change.
8. True or false: two identical objects that fall from the same height must experience the same force during the collision with the ground. Word for word what someone told me today on an in-class lab problem. The counterexample is to ask a student to jump from his desk with and without bending his knees. Since he didn't hurt himself with bent knees, if this statement were true he should be able to land stiff-legged without damage.
9. True or false: two identical objects that each collide with the ground for the same amount of time must experience the same force in the collision. Also word for word from a student. By this rationale, since a belly-flop onto a gym mat from six inches is safe, a belly-flop onto a gym mat from the roof should be equally safe.
10. A 4 kg object is moving 2 m/s when it collides with the ground, stopping after 0.05 s. Calculate the impulse experienced by the object in the collision with the ground. My students know that impulse is both change in momentum and force times time. The misconception here is that the "force" in the impulse-momentum theorem is just the weight of the object. No! The relevant force is the contact force between colliding objects. I know darned well that half the class will see the time interval, and grasp at straws to find a force: "Oh, 4 kg has a force of 40 N," they'll say. I'm using this problem to make the point that they can't make up forces. Rather, if J=Ft isn't useful, use impulse = change in momentum.
I'll give the class four minutes to do these ten questions; then I'll have them grade someone else's paper while I explain the answers. I doubt more than one student in each section gets all of them right. So what. This quiz, like all daily quizzes, isn't really, actually an evaluative quiz. Rather, it's a means for getting my students to articulate what they think about momentum concepts, so that a discussion about those concepts is meaningful, in-context, and memorable. While I can't guarantee that this quiz will lead to perfect understanding of momentum concepts, I can guarantee that going over this quiz is substantially more effective than a lecture or a reading.