This table [not pictured] lists the coefficients of friction for four materials sliding over steel. A 10 kg block of each of the materials in the table is pulled horizontally across a steel floor at constant speed. Which block would require the smallest applied force to keep it moving at constant speed?
Virtually all of my students will recognize to use the equation Ff = μFn. They've also been well trained in using such an equation to first identify and justify which variable is the same for each of the blocks.
Most students recognize that the normal force Fn is the unchanged variable. The question is, how should they justify that the normal force is the same for each block? Consider some incomplete answers:
1. The normal force is the same for each because they both weigh 100 N. No, sorry... Consider one 10 kg block hanging from a string in midair, and another on the floor. These blocks experience different normal forces, because the hanging block experiences no normal force whatsoever.
We have to get to the idea that the up forces equal the down forces, so the normal force equals the block's weight. Why is that?
2. The normal force is the same for each because neither block moves vertically. Still not quite there -- it's not motion that relates to forces, it's acceleration. Try again.
3. The normal force is the same for each because neither block is changing speed vertically, so both experience zero vertical acceleration. This makes the vertical net force zero for each, meaning up forces equal down forces. Both blocks thus experience a normal force equal to their weight; since they weigh the same, they experience the same normal force. Now we're cooking with ethanol.*
*True story: during my senior summer research, my nerd friends and I tried to grill, but we were out of lighter fluid. No problem, 'cause the chemists had a ready supply of ethanol from the lab. Two hours and zero flames later, we ordered pizza.
Point is, even though I've moved on from explicitly discussing the difference between movement and acceleration, I've gotta be vigilant that we never slip into the "acceleration = motion" habit. And, even on a problem so straightforward, it's important for students to write out the reasoning to justify determining the normal force. Otherwise, they fall into the habit of "normal force ALWAYS equals weight", which we know to be bogus.