In our work on elevators, we measured the forces that were responsible for changes in motion. In summary, we found that an extra force (“net force”) is necessary only if there’s a change in motion. This is Newton’s 2nd Law of Motion.

Now we’ll look at measurements from a slightly different angle. Instead of considering the forces and how they vary, we’ll analyze the motion due to these forces — and then think about the forces after the fact. In this case, we can look at the upward and downward motion of a ball tossed straight up into the air. We’ll use iPads and a program called “Video Physics” by Vernier, but you have a collection of additional options that you can look into yourself, including:

• Video Physics (Vernier Software) for iOS — This is what we typically use in class
• iTrack Motion lite and iTrack Motion for iOS
• VidAnalysis free and VidAnalysis for Android
• Logger Pro (Vernier Software) for Mac and Windows. (You may have access to a site license for this as a student.)
• Tracker (Open Source) for Mac and Windows.

With any of these pieces of software, the idea is that you can take your own video, identify a specific object or a piece of an object (like a tennis ball, or a point on someone’s shirt) and trace it frame by frame. You simply locate the position of an object for each frame of the video, and then the software will take care of showing what happens to that object’s position and velocity over time.

Of course, the point of a lab like this is to actually do this and see how these things go. What I’m writing here is a description of something you are probably already working on. If you haven’t done this already, go download yourself some software, have a friend toss a tennis ball up in the air (or, someone could jump, or something else entirely) and track the motion of that object with the software. Go ahead. I’ll wait.

An object that has been thrown up into the air or has jumped from the ground has a vertical (y) position versus time plot that could look like so:

This is for someone jumping, tracing out a spot in the middle of a striped t-shirt. We can see the position on the shirt go down for the first 0.4 seconds, and then there’s a sudden upward motion that peaks and falls back down until a landing at about 1.2 seconds. There’s lots to appreciate here. For our purposes, we’re really interested in that smooth arching pattern that takes place while the jumper (or tennis ball) is in the air. We can tell where the object is going upward (the slope is positive), where it reaches its highest height (the slope is zero, or the graph flattens out), and when the object is falling downward (the slope is negative). And, we get a sense for how this velocity is changing. Our software package probably shows us this velocity as it changes. It’s not new information, but it’s useful to display the values for the velocities:

This graph shows velocities. At 0.5 seconds, we see there’s a maximum upwards velocity, and at about 1.1 seconds, there’s a maximum downwards velocity. At about 0.8 seconds, there’s actually a zero velocity. This is also communicated by the position graph, but in a different way.

NONE OF THIS IS OBVIOUS. Go ahead and stare and ponder and pull on your hair. Undoubtedly, we talk about and analyze and agonize about this in class, but it took physics about 2000 years to make these connections and see these patterns. You should spend at least another 20 minutes on it.

The most beautiful and important part about this is that the velocity is continually changing in a very consistent way while the object is in the air. This is what we call freefall. It happens when the object is falling down, but also when the object is on its way upwards. Continually, the change in an object’s velocity is always negative, always getting less, always showing that negative slope. This change in velocity is, as you’ll remember, due to a force. Since there’s only one consistent change to the velocity, there must be only one force — and that’s what gravity is. We’ve discovered that an object moving up or down is only subject to one continual force, that of gravity.

Now, if something like a bowling ball that we rolled earlier in the class were analyzed in the same manner, we’d see a position versus time graph look like this:

This is an object that is continually moving at the same (or close to the same) velocity. It’s making the same progress in position which each moment of time, a constant velocity. It is not accelerating in this direction.

The graph above is actually taken from someone leaping across a video frame. This is just one dimension, from left to right. But we know that she’s also in “freefall,” so we’d expect the graphs of her up-and-down, vertical velocity to look just like what we’d had before:

This is perfectly allowable. An object can move left to right with a constant velocity, but be falling in the vertical direction. We see this all the time; and you’re used to those kinds of arch-like patterns as something flies through the air. You can probably think of a few.

Here’s the thing. What if you saw vertical motion graphs that looked like these?

Where there are a lot of similarities to our original graphs, but in these cases something happens right in the middle. There’s a leveling off in the position graph, and you see that we have almost zero up-and-down velocity. It’s as though someone is levitating, not moving up or down. That’s weird, right? It’s as though someone turned gravity off!

But this isn’t really possible. You know, based on the patterns and your analysis of them, that there must be something else going on. That’s the point of patterns: You now know what to expect, and when something doesn’t match the expected pattern, you know that something else strange happened. There must be another factor to consider.

In this case, the person who was leaping did something like this. You can imagine that as this dancer jumped and lifted up her legs into this leap, the mass of her legs made up for or compensated for the rest of her mass. If we were just tracing the top of her head as she raised her legs into the splits, we’d miss what the mass of her legs was doing in the overall motion. Her “center of mass” is rising with her legs, allowing her head to stay level. This makes the dancer look as if she’s levitating, momentarily. It creates a plateau in the graph and a horizontal, levitating motion in her leap. We see this aesthetic in both the graph and in the dance.