Pendulums, ramps, levers, towers - what better place to see physics in action than a playground? It's a veritable mechanics laboratory!
This playground is nearby in Walnut Hills Park so I threw my pack of gadgets on and headed out to do some light demonstrations of motion and how to measure it using a smartphone.
[Playground at Walnut Hills Park]
First, I hiked up Davies Street to Yosemite. I needed an approach to the playground, not to make a grand entrance, but to measure linear motion on the trail. I have several apps on my phone to do that, but I chose the AllTrails and Science Journal apps. AllTrails uses GPS information to record a lot of information about a hike, and the Science Journal taps the phone's accelerometers to measure...well, acceleration.
The path through Walnut Hills Park and, consequently, the Little Dry Creek Trail begins at Yosemite Street between Davies Street and Briarwood Street. I started there, recording my progress downhill to the playground.
In physics, there are three fundamental measurements - position, time, and number (count). Everything else: force, temperature, voltage, current, illumination, ultimately boils down to those three.
Distance is established by two points. It has direction and time might also (have direction, that is.) You establish direction by setting up an arbitrary frame of reference. It can be any frame of reference, but the best is the most convenient. When you're working with geographic positions and distances, the most convenient is usually the longitude-latitude system used by mariners and surveyors.
Here are some pictures.
Science Journal uses the sensors in my phone to record things. Here, it's recording my motion as I walk down the trail. Note! It's not recording distance, and it's not recording speed. It's recording acceleration. It's limited to the sensors available in the phone and it can receive signals from a Bluetooth instrument like my Arduino, Bluetooth multimeter, or camera shutter release. What it has to record motion is the accelerometers in my phone. Accelerometers measure acceleration...period.
Some phones have gyroscopes to measure motion - mine doesn't.
Acceleration is the rate at which velocity changes. Say you're traveling at 30 miles per hour in a car down a city street. 30 miles per hour is your speed. In one hour, you'll have traveled 30 miles (assuming your speed doesn't change). 30 miles per hour north, north west is a velocity. Velocity is a vector quantity which means that there's two things to keep up with - speed and direction. If you change speed from 30 miles an hour to 40 miles and hour, you have accelerated. Acceleration is measured as distance per time (velocity) per time. If you keep a speed of 30 miles per hour but you turn a corner and at now going due north, you have still accelerated. Direction matters.
You might have heard of nanotechnology, machines that you have to use a powerful microscope to see? Well, phone accelerometers are nanotechnology. But they work the same way you feel a change in speed or direction in a car. When the phone's motion changes, a tiny weighted arm in the accelerometer leans a little, just like you do, and the electronics can pick up that tilt and translate it into a measurement of how big a change there was.
There are three accelerometers in a phone. They measure acceleration in three directions. They're used to tell the phone if you're holding it right side up, sideways, or upside down.
The accelerometers are usually labeled x, y, and z. Do you remember high school algebra and all those graphs you had to draw? That can help you remember which accelerometer is which. Picture a graph on the face of your phone. The x accelerometer measures motion in the direction along the x axis. The y accelerometer measures direction along the y axis. And the z accelerometer measures directions at a right angle to the face of the phone..
I had my phone in the front breast pocket of my overalls so x was left-right, y was up-down, and z was forward-backward. I just show the output of the y and z accelerometers here because x is boring. I just went straight ahead.
Scientists (and the Science Journal) measures acceleration in meters per second per second (meters per second squared or m/s2). That means that, if I'm walking a meter per second (a decent clip) and I speed up in a second to two meters per second, I will have accelerated one meter per second squared.
My smallest acceleration in the y direction on the walk was -5.7 m/s2. That's -5.7 m/s2 downward. My maximum y acceleration was 39 m/s2 . That jolt will be explained in a minute. My average acceleration was 8.9 m/s2 . Why was I moving up and down at all?
Let's spread out the tracing and see what it looks like.
That's the up and down motion of my steps. Those double blips are the profiles of my steps and they are how pedometer apps can count my steps to figure out how far I've walked.
My forward and backward motion ranged from -12 to 18 m/s2 . Those spikes in the middle of the tracings (and in the y direction) was when I started walking backwards and then started walking forward again. See acceleration is directional!
Otherwise, I kept my velocity pretty constant. My average acceleration was only 2.7 m/s2 .
A nice thing about the Science Journal recording is that I can go back to it and do things like move my stylus along the tracing to see exactly what the measurement was at any particular time in the recording.
The AllTrails app recorded my distance, the time of the walk, and the elevation. How did it do that!? The phone can keep track of time, certainly. It has a clock, like all computers, but distance?
Some phones have a barometer built in that keeps up with atmospheric pressure (for weather measurements) and because pressure decreases predictably as altitude increases, it can measure altitude. My phone doesn't have a barometer, but it can receive signals from the Global Positioning System satellites orbiting the Earth - the same satellites that send signals to the GPS system in some cars. It can pinpoint the position of the phone to within a few feet. Altitude is a little less accurate, but okay for my purposes.
I walked 0.3 mile in 5 minutes and 23 seconds for a speed of about 0.05 miles a minute or 3.3 miles an hour almost due west (see the mountains below? In Denver, the mountains are west.). That's a fast walk. I usually walk 2 or 3 miles/hour. I had an altitude loss of about 40 feet. Those are 40 foot contours on the map. The elevation profile shows a loss of 50 feet. There's an error of about 10 feet.
After arriving at the playground, I measured the height of a tree, crashed a cart on a spiral slide, and swang on a swing. What fun! To be continued!
If you have a cellphone, you probably have accelerometers and the Science Journal is a free download developed by the folks at Google. There are also free pedometer apps online. AllTrails cost (not much) but it also gives you descriptions of trails you might want to hike and puts you in touch with other hikers.