Before spring break, we had two days to talk about work and energy in physics class. Today, we are talking about momentum. For their online pre-class reading quiz, I decided to throw in the following question:
Explain what you think the major difference is between energy and momentum. Why do you think we need both concepts?
Here is a sample of student responses.
Momentum deals with mass and velocity, while energy deals with the work done over a period of time.
Momentum measures the ability of an object to continue moving in the same direction with the same speed, while energy measures the amount of force which an object has due to its mass and velocity.
Energy does not involve a collision specifically, it can be potential or kinetic. while momentum does involve a collision.
Energy is what it takes for something to move and momentum is how fast something is moving when it hits something else.
Energy is the capable of work and momentum is a mass in a motion. we need them both because without the work of energy we can not move a object and with out momentum we do not have enough force to keep the object from going fast or to slow down.
Energy is a transferable unit which can be stored and changed into other forms where as momentum is the directional energy that an object has due to its motion.
Energy is a scalor, and momentum is a vector. Energy is measured in foot pounds while momentum is in Joules. We need both concepts in order to find all possible answers for a problem
Momentum is needed to make energy and vice versa. Conservation of energy when collision. Momentum of energy during movement.
Energy is a scalar quantity only expressing magnitude, momentum is a vector quantity and has a magnitude and direction. We need both because they represent different values in the same way that speed and velocity are not the same.
Momentum is a vector and energy is not. Energy can be converted in other forms of energy, while linear momentum can be converted only in linear momentum.
Energy is length times force while momentum is mass times velocity. We need to know both concepts to figure out things we do daily in life.
Teach. Brian. Teach. 
Ugh. And yet I find myself having almost the same problems if I try to come up with a formula free explanation that is suitable for introductory students.
Sometimes you need both constraints to make a prediction because just using momentum or just using energy you find an infinite set of possible answers. And amazingly, those two infinite sets of answers only overlap in one place.
But then sometimes it’s just really convenient to use one or the other (like momentum if you know a lot about the motion and masses before and after something happens but not a lot about whatever messy thing happens in between).
I’m having trouble imagining the “ideal” post-instruction answer.
This one is pretty awesome: “Energy is a transferable unit which can be stored and changed into other forms where as momentum is the directional energy that an object has due to its motion.”
This is kind of honest: “We need both concepts in order to find all possible answers for a problem.”
Yeah, there was no “ideal” answer I was looking for. Mostly, I wanted to draw their attention to the fact that there are these two concepts, both very similar in some respects. They are both “conserved” and relate to mass and velocity. Today in class, I have to model sample problems and they have to work through problems that involve conservation of energy for some parts, and conversation of momentum for other parts. That’s rough, considering we haven’t even talked about conservation of momentum.
ask them which one causes pain. That led to a great discussion in my mechanics class last year.
I certainly would fall toward the ‘usefulness for problem solving’ focus. Momentum is great for simple mechanical systems, energy is great for more complex systems that may not be entirely ‘mechanical’. Sometimes you can measure interaction time more easily; other times distance is easier. It’s a great question, but I don’t think you should be too disappointed that they weren’t able to come up with profound answers. I would guess that most undergrad physics majors couldn’t do much better.
So, I wouldn’t say I’m disappointed. Not at all. That’s not the point of posting these. I post these kinds of thing because they provide windows into how students might make sense of content we teach. Also, to me, how students think, talk, write about physics is just interesting. They give us all an opportunity to notice and react to student thinking. And yes, I would love to see how physics majors respond to these questions. I’ll post that this weekend.
I agree that the “ideal answer” meme is a red herring.
There’s no way you can read this set of answers and go teach the lesson you thought you were going to teach before you read them, right? As the resident physics-outsider here, I have no idea what kernels of truth there are in these responses. But I appreciate the depth of knowledge you’ll gain from reading these and I know it puts you in a position to plan effective instruction. Fun stuff.
Absolutely, Chris. The purpose is two-fold— getting them to just begin thinking about the question that there are two different things, and helping me to find out before hand what differences they are and aren’t noticing. These quizzes are graded on engagement with question, not on correctness.
This year, I explained the difference to my students this way: Use momentum strategies when looking at two different snapshots of time. Collisions and explosions were my only classroom examples. Use Energy strategies when looking at changes as an object moves from one location to a different location. I have students set up the conservation laws in the following ways:
Total momentum of the system (before something happens) = Total momentum of the system (after something happens)
Total mechanical energy of the system (at location A) = Total mechanical energy of the system (at location B)
This seems to go hand in hand with Impulse (change in momentum) being an integral of Force with respect to Time; and Work (change in kinetic energy) being an integral Force with respect to Position.
The concept seemed so clear to me that I assumed they got it. I’m motivated to pose your questions to my students and see what reasoning they write back to me.
Let me know how it goes it you do ask. I agree–I think about it that way, too…. In mechanics, energy is something we invented to track motion because it accumulates nicely over distances; where as momentum accumulates nicely over distances… outside mechanics, energy story gets more complicated… (and more historically accurate in its development).