These are not necessarily comprehensive. I don't know how many I'll have time to post.

1) You want to open a trap door in the floor, just a little. The door is hinged on one side, and the handle by which you will lift it is on the other side. If the door weighs 100 pounds, how much force will you have to apply in order to lift it by the handle?

2) Earlier in the course we encountered the idea that mass scales (approximately) with the third power of height, but that the strength of a bone scales as its cross-sectional area. If no proportions were changed, a bone's strength would scale only as the second power of its length, and bigger animals couldn't support their own weight. So, bigger animals have thicker bones, scaled so that the cross-sectional area is proportional to the animal's mass, and therefore to its height cubed. Now we learn that the bigger animal is still not so well supported as the smaller one. (a) Why is that? (b) Nature apparently gives up on this one, and doesn't make the bones even thicker. Why not? (Sure, you've gotta guess on that one, but then, this is only a sample problem.)

3) We have a road bicycyle, with skinny tires, and we're supposed to inflate those tires to a pressure of 100 pounds/square inch. By contrast, I'm supposed to keep the pressure in my car tires to only 30 psi. The rubber walls of my car tires are much thicker than the walls of the bike tire, but I'm pretty sure the car tire would explode if I inflated it to 100 psi. Is the rubber of the bicycle tires soooo much tougher, or stiffer, or whatever?