It's still near the beginning of the semester for most introductory physics courses—so it's not too late to give some physics advice. I know it might be hard to believe—at least it is for me—but I have been a physics educator in one form or another for over 20 years. In all that time, I see students make mistakes, often the same ones, year after year. Oh, sure, me describing them won't necessarily make a huge impact on the learning of physics, but it can still be interesting to look the most common missteps. And just identifying faulty thinking is the first step to changing it.
Many people will often call these mistakes "physics misconceptions." I don't think that term is incorrect, but it can be a little misleading. Yes, students can have wrong ideas, but they aren't crazy wrong. All of these problems that students have in physics are based on some element of understanding. If students just had ideas that didn't at least make sense in some manner, they would just be crazy.
So here are the some of the biggest ideas that cause trouble in the first semester of physics.
What happens when you have a constant force on an object? A very common student answer is that a constant force on an object will make it move at a constant speed—which is wrong, but it sort of makes sense.
Imagine you're in your house and you want move a couch. It's one of those hide-a-bed versions and no one ever wants to pick it up, so you're just going to push and slide it across the room. If you want to move it as fast as possible, you are going to have to push much harder than if you wanted to move it slow. It just seems like a greater force—your pushing—makes it go faster. More force equals more speed.
But it's not true. There are two problems with this example. First, your push isn't the only force acting on the couch. The gravitational force pulling down, and the floor pushes up. Those forces are relatively small, but there is one more force that really matters—the frictional force. This is a force that opposes the push such that in many cases the total force will be very close to zero. Zero net force means that there is zero change in velocity but since you only think of the force from the push, it seems like this force makes it move at a constant speed.
The second issue is with changes in speed. The frictional force is pretty much constant no matter how fast the couch is sliding. If you push harder the net force should no longer be zero and the couch should speed up—and it does. The problem is that over a short distance, it is very difficult for humans to distinguish between changing speed and high speed—see this awesome video from Veritasium. In general, humans have evolved to detect motion—any motion. The basic idea is that if it moves, maybe we could eat it.
This isn't technically a physics problem, it's a math problem. However, vectors are so important in introductory physics that if you don't use them correctly, you are going to have a problem. If you want a quick review of vectors, here is a start.
Now for an example that shows the problems people have. Many floors have square tiles. In our building these are 12 inch squares and they are very useful for roughly measuring distances. So suppose I move 3 squares and then I move 2 squares. How far did I move? You can try this on your own if you have tile floors. Do you have an answer? Did you travel a total distance of 5 squares? That is indeed a possible answer (and the most common). But you could also end up at a distance of 1 square. Yes, if you move three squares and then back two squares you end up one square away.
What if you move three squares and then turn 90 degrees to move two squares? You would end up somewhere between 1 and 5 squares away. The reason that you can get a variety of answers for the total distance is that the displacement is a vector. This means that it's not just the distance in each move that matters but also the direction for each move. Displacement is a vector and you have to add them as vectors. Oh, force is also a vector and so is acceleration and velocity. You have to treat these things as vectors.
Notice that this is the second idea that depends on change? Yes, changes are important in physics. In this case, the main idea deals with the work-energy principle. This says that the work done on a system is equal to the change in total energy. Work is the product of force and displacement, but it's the energy I want to talk about.
Again, I will start with an example. Imagine that you have a 1 kg ball and you hold it 2 meters above the floor. If you release it from rest, how fast will it be moving when it is 1 meter above the ground? A common method in solving this problem is to first calculate the gravitational potential energy. This might seem like a good idea (and you can indeed get the correct result this way) but the potential energy isn't important.
It is only the change in potential energy that matters. Consider the following definition of gravitational potential energy: U = mgy (where m is the mass, g is the gravitational field, and y is the vertical height). But where is y measured from? Is it from the floor? Actually, it doesn't matter. You could pick the location of y to be where ever you want because it doesn't matter. What does matter is the change in gravitational potential energy since that is what shows up in the work-energy principle.
Yes, we all know that a graph isn't actually a picture but still this is a problem. Let's look at this graph of position vs. time (in one dimension) for the motion of some object. Note: This graph is actually a Python program because it's sometimes easier to calculate something than it is to just draw it.
If you had to describe the motion of this object, what would you say it is doing? A very common answer would be that this is the motion of a car that speeds up, travels at a constant speed and then slows down. That answer is wrong. Another answer might be that this is for a car going up a hill and then down a steeper hill (again, wrong).
The best way to think of a graph is as a series of points—because that's what it is. Let's take that first point at t=0 and x=1. That gives the position of the object at the first time. A little bit later, the x-position is increasing and the amount of increase is the same for the beginning part of the graph. This means the object is moving with a constant velocity. At the top flat part of the graph, the x-position doesn't change at all such that the velocity is zero. Finally, the x-position starts to decrease to give it a negative velocity in the x-direction.
Don't let your mind convince you that the graph is a picture but instead focus on the points.
OK, those are just some of the common mistakes I have seen in the introductory physics. Remember, it's OK to make these mistakes. The problem is if you continue to make them. Learning is all about being wrong and then changing to something not wrong. Of course you will never make a change without practice—so be sure to do all your physics homework!
