Determining Scale and Measurements

Before delving into the analysis, establishing a scale from the video is essential. If we can identify the real size of a known object within the scene, we can extract position and time data for all visible elements.

One potential method is to find the dimensions of the laundry basket used in the video. Alternatively, we could analyze the vertical acceleration of the person after they leave the treadmill, assuming this scenario occurs on Earth with a constant gravitational pull.

For this analysis, I will focus on the treadmill’s speed readings. Assuming the treadmill displays an accurate speed of “1 mph” (approximately 0.447 m/s), we can proceed.

Next, I will import the video into Tracker Video Analysis—a free and incredibly useful tool. I plan to use the diagonal length of the basket holes as my scale reference, denoting this distance as “1 b” (with “b” standing for basket).

After adjusting for camera motion by setting the origin and axes in each frame, I can track the basket’s position throughout the video. Notably, the slope of the position-time graph fluctuates initially—something that I will discuss further.

The average velocity in the x-direction is depicted as the slope of the x vs. t graph. Using Tracker’s linear fit function, I calculated a slope of 1.413 b/s, which allows me to establish a relationship between the basket and meter units, ultimately discovering that 1 basket equals approximately 0.316 meters. Voilà! We have our distance scale.

Analyzing Velocity Variations

Now, let's dive into why the velocity isn't consistent throughout the experiment. This scenario resembles a classic physics question:

• A box is dropped onto a moving conveyor belt with speed v. Given the kinetic friction coefficient μk, how far does the box slide before matching the belt's speed? (Assuming the belt maintains its speed.)

To illustrate this, I’ve created a simple diagram. The box experiences three forces: gravitational force downwards, normal force upwards from the belt, and frictional force opposing motion.

Applying standard frictional force models, we recognize that the box’s vertical acceleration remains zero, indicating that the normal force equals its weight. Thus, we can derive the box's acceleration in the x-direction as -μk*g.

Using this acceleration, I can determine how far the box travels before achieving the belt's speed. The same principles apply to the girl in the basket. It would be fascinating to measure her distance traveled before reaching treadmill speed, potentially even estimating the coefficient of friction from this data.

As a fun challenge, consider how long a treadmill would need to be for her to reach a speed of 10 mph, assuming she remains upright.

Exploring Tipping Dynamics

Let's examine why tipping occurs at higher speeds. I’ll start with a force diagram at the moment she makes contact with the treadmill. For simplicity, I’ll represent the basket and rider as a single box.

Previously, I depicted all forces acting at the box's center. However, real objects have dimensions, so we must consider the application point of each force. The frictional force acts at the base, while I can separate the normal force into components acting in various directions.

The net torque on a rigid object matters just as much as the net force. Torque can be thought of as a rotational force, determined by both the force magnitude and the distance from the pivot point.

In equilibrium, both net force and net torque should balance to zero. When the box lands on the belt, the negative net torque causes a clockwise rotation, leading to the amusing tipping of the basket-rider.

But would the torque be consistent across different speeds? Yes, the frictional force remains unchanged irrespective of speed. However, at lower speeds like 1 mph, the time to reach final speed is minimal, preventing the basket from adjusting its rotational motion. At higher speeds like 10 mph, the longer duration allows for tipping to occur.

Projectile Motion Analysis

Now, let’s discuss the moment when the rider leaves the treadmill and becomes airborne. At this point, she is a projectile, subject solely to gravitational force. This means her horizontal motion maintains a constant velocity, while vertical motion experiences constant acceleration—an essential concept in understanding projectile dynamics.

I won’t solve this particular problem for you, but it certainly poses a physics challenge!

Homework

The effort put into setting up this treadmill next to the pool deserves recognition. Here are some physics questions to ponder:

1. Measure the time it takes for the person to hit the water at 7 mph. Use this to calculate the vertical height of the treadmill above the pool, utilizing the basket-to-meter conversion factor.
2. Measure the vertical acceleration after leaving the treadmill to verify the video’s scale.
3. Analyze the basket’s acceleration at 7 mph to estimate the coefficient of kinetic friction.
4. Using the coefficient of friction, measure the basket's rotational acceleration to estimate the moment of inertia of the system (skip if unfamiliar with moment of inertia).
5. Calculate the necessary treadmill length to achieve 10 mph.
6. If the treadmill launched the basket at 15 mph, how far would it travel before hitting the water?
7. Record the final speed for all treadmill settings using video analysis. Graph the measured speed (in baskets/second) against the listed speed (in m/s). Is the relationship linear? If so, use it to derive the basket-meter conversion ratio.

And that’s a wrap! Thank you, Internet, for the continual flow of fascinating content.

The video titled "The Story of Stuff" explores the interconnectedness of various elements in our world, showcasing how they influence one another. It's a thought-provoking piece that adds depth to our understanding of physics in everyday life.