One of my impulse-momentum theorem exercises is to predict which applies more force to a person: jumping off a chair and landing knees-bent, or jumping off the chair and landing knees-locked. Each student makes and justifies the prediction, then jumps onto a force place to experimentally verify the prediction.
To guide the students through the prediction, I start by asking which variable in the impulse-momentum theorem is the same for both cases. That's actually a tough one. Even though I've already explained that the point of the exercise is to determine which case delivers more force, a bunch of students tell me the force term is the same for each.*
* My response is to ask them to keep their legs locked as they jump off an 8-foot high fence. After all, the force on your legs should be the same either way... [student retreats sheepishly]
The more common and more understandable mistake is for students to tell me that the time of collision is the same. Usually, this stems from a misconception of what the t term in J=Ft means -- they correctly state that the time for the person to fall from the chair to the force plate is the same regardless of how the person lands. Sure... but the t term isn't just any old time, t represents the time of the collision. Anything that happens before the collision isn't exactly relevant to the impulse-momentum theorem.
But I do have a number of students who consider the collision, and state to me earnestly that they believe that the time of collision doesn't change either way -- it's the same surface, the same person, the same speed before collision. I need to address this incorrect reasoning without appealing to my authority as teacher.
We recently downloaded the "Coach's Eye" app on some ipads, and we had used this app in class a while back. So I asked a couple students who were struggling with the time of collision issue to make two videos of Trevor jumping onto the force plate -- one with knees-bent, one with knees-locked. They managed to record these videos in about three minutes. (Wow, I love modern technology.)
The app allowed me to run the video frame-by-frame with a stopwatch superimposed. All the rest of the day, whenever a student struggled with the idea that the knees-bent case resulted in a longer collision time, I showed him the video. I had him advance the frames to show that the knees-locked Trevor took about 0.10 s to land, and the knees-bent Trevor took more like 0.40 s to land. That ended the argument about whether the time of collision was or wasn't the same... then I could visually show the instants before and after collision to help the students understand why the impulse -- i.e. the momentum change -- must be the same for both Trevors.