I have noticed a big difference in student comprehension when the problems become real to them. Simple visuals can have a big impact on the students "getting it." I can't count the number of times I've tossed a tennis ball around to make a point. Somehow holding the tennis ball at different heights or just tossing it up to catch it again can lead to "Oooh now I see what's happening!" So I have several simple demos that help students visualize their problems, a block or two hanging from the ceiling with spring scales, a stuffed toy in a bucket, etc.
When we studied springs I found a Pasco spring demo set with five springs all of the same length but different spring constants. The first stage was to hang a 20 g mass from the red spring and see it barely settle above the table. I asked students what would happen if I were to hang a 500 g mass then from the green (which they assumed was identical). They were surprised at its shorter elongation and when I asked why they all said "it has a larger spring constant."
For the next stage I set up two large ring stands with another bar clamped horizontally between them. I dramatically assure students it is level with the springs hanging at their relaxed length. Then I hang a 500 g mass from each and they can see the slight differences in elongation. Then the 500 g masses are switched out for 1 kg and the difference between them becomes more pronounced (left). Applying this to Hooke's Law they could all calculate the spring constant for each spring. But this made it way more interesting than five given forces and elongation lengths to calculate the spring constant from a word problem.
When my AP Physics C class started center of mass, many could calculate the center of mass with equations but had a hard time visualizing what that actually meant. A common problem involves materials of different densities stuck together, for example a piece of aluminum and a piece of iron. To make a real life version I found a piece of Styrofoam that was the same thickness as a piece of scrap wood. I drilled three holes in the wood, stuck three dowels into the holes and stuck the dowels into the Styrofoam. I wrapped the whole thing in paper to make it appear uniform but I did tell students it was made of two different materials. I showed it to students and asked what information they would need to solve for the center of mass. Of course I play with them a bit and after each response I say, "Ok, now you can solve it right?" to which they predictably respond, "No, we need XYZ too!" Eventually, I give them the dimensions of the whole thing and let them solve for it. The dimensions are listed on the paper below (the "total mass" includes the paper in case they ask).
They are not surprised that the center of mass is closer to the wood side but they are surprised that for this particular arrangement it's actually on the wood. It's a simple practice problem but once they're done I can balance the piece on my hand at (almost) the exact position they predicted, about 5 cm in from the wood side. Students that struggle with this homework problem were successful with this in-class practice problem.
Another simple one my colleague Jessie Chen shared with me can be done by every student in your class on the cheap. Like less than $1 cheap. Most dollar stores sell packs of cards for $1, or even a double pack if you're lucky. Each student will need one plastic playing card (or index card) folded at a right angle along the length of the card. Place it on the corner of the table with one corner hanging off the edge of the table. Place two pennies on the card so that one is on the portion on the table and one is on the portion hanging off the table. You can use a pen or pencil to press on the card so that when it moves it pivots around that point. Flick the vertical part of the card on the side that is hanging off the table. This causes the card to move so that it is no longer supporting the penny hanging off the table and it will fall straight down due to gravity. On the other side the vertical portion of the card will push forward, applying a horizontal velocity to the penny and making it shoot off the table in a half a parabola shape. You can hear (and see) the two pennies hitting the ground at the same time. Many of us have a fancy machine that demos this for us, sometimes called a "Drop/shot" or a Newton's Second Law machine, and those work great, don't get me wrong. But to be able to hand these to my students and have them try it, nothing can be better than that!
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