"A crate is sitting in the center of the back of a flatbed truck. As the truck accelerates to the east, the crate moves with it, not sliding on the bed of the truck. In what direction is the friction force exerted the truck on the crate?"
The answer is "east". My question is, if the friction force didn't exist, which way would the crate move towards? Would it go west with respect to the flatbed and fall off? If so, is that the reason why the friction force has to go east? Because it opposes the relative motion? What if the crate actually moved east instead of falling off? Is that possible? Would the necessary friction force in that case go west? And ultimately, what determines the direction the crate would move towards? Since the acceleration is eastwards, wouldn't the crate naturally tend to move eastwards, and then the friction force should have to go west?
EDIT: I think when I first asked this I was getting lost by confusing the scenario presented in the question with other possible scenarios. In the question, what happens is the crate moves with the truck, which, if I was in the truck next to the crate, would seem like the crate didn't move at all, as if it was always at rest, right? Even though it is moving. But to be clearer, the question now is: What would need to happen in a situation where the truck accelerates East and the crate slides off? What would the forces acting on the crate be? And what would happen in a scenario where the truck accelerates East but the crate doesn't "move with it" but rather moves like this:
Number one represent the position it's in before the truck accelerates East and number two represents where it would be after the truck has accelerated. To the person in the truck next to the crate, it will appear to have moved. This is the situation I was imagining when I asked "What if the crate actually moved east instead of falling off? Is that possible? Would the necessary friction force in that case go west?" In fact, this is what I was originally imagining when reading the question. And wondering what forces would be needed to act on the crate in this case.