*Rolling Resistance Introduction*

Rolling resistance is a force that opposes the motion when an object rolls along a surface. There are many examples of objects experiencing rolling resistance: car or bicycle tires on pavement, skateboard wheels on a half pipe ramp, steel wheels on a railroad track, ball bearings in a pulley, bowling balls on a bowling lane, and carts rolling on a dynamics track, just to mention a few. Many factors can affect the magnitude of the forces associated with rolling resistance. These include the wheel substance, the surface on which it is rolling, pressure created by the load it may be carrying, bearings holding the wheel to its axle, surface adhesion, and wheel diameter.

In this experiment a coasting PocketLab Mini HotRod on a HotWheels track gradually slows down and stops due to rolling resistance, as shown in Figure 1. The figure shows Voyager and the HotRod loaded with an additional 160 g of mass. A white cardboard at the end of the track serves as the reference plane for Voyager's IR rangefinder. Significant energy is lost from two main sources as the HotRod moves down the track: friction in the wheel bearings and friction between the wheels and track. The purpose of this experiment is three-fold: (1) to determine the deceleration of the HotRod while slowing down on the track, (2) to study the effect of the mass of the Mini HotRod on deceleration, and (3) to learn what is meant by the concept of *coefficient of rolling resistance*.

*The Dynamics of Rolling Resistance*

Figure 2 shows the free-body diagram of the cart as it slows down from rolling resistance. The normal and gravitational forces are equal in magnitude but opposite in direction as the cart rolls on the level plane of the surface. From Newton's second law, the net force, *ma*, is therefore equal to the force of rolling resistance. The coefficient of *rolling resistance* is * defined* by the equation shown in the diagram as the

*ratio of the force of rolling resistance to the normal force*. The coefficient of rolling resistance is, therefore, a

*dimensionless quantity*that can be thought of as

*the force per unit weight required to keep it moving at a constant speed on a level surface, assuming negligible air resistance*.

*Example Data and Video*

Figure 3 shows an example snapshot of combined data/video as soon as the HotRod has come to rest. The graph is rangefinder position vs. time. The HotRod was moving from left to right. The total mass is the mass of HotRod/Voyager (70 g) plus an additional 40 gm in the form of two 20 g slotted masses. The slotted masses are attached to Voyager with strong Velcro sticky back tape. The region from roughly 3 to 5.5 s contains data collected while the HotRod slows down. The HotRod comes to rest at about 5.5 s where it is 0.11 m from the cardboard. If one were to do a curve fit on the region from 3 to 5.5 s, a polynomial of order 2 (quadratic) would turn out to be an excellent fit, as intuitively suggested by the parabolic shape of the curve. The coefficient of t-squared would then represent one-half the acceleration. If we doubled this coefficient, we could quickly determine the acceleration (or deceleration in this case) of the card. For simplicity, we'll simply use the magnitude of the acceleration.

Here is the combined data/video of the trial discussed above. It is probably best to push the HotRod in such a way that it comes to rest before impacting the white cardboard. The result will then more clearly show students the parabolic nature of the curve.

*Preparing a CloudLab Lab Report for the Rolling Resistance Experiment*

If you are not familiar with CloudLab, it is strongly suggested that you read the short article "The CloudLab Model" before proceeding. It will give you an overview of the structure of CloudLab.

We now take you on a tour of CloudLab via a series of screenshots taken *after our experiment was completed*. Each screen shot is accompanied by a short discussion explaining the screenshot.

The top of Figure 4 shows the title of our Lab Report. Our experiment consisted of 5 runs. Each of the runs was given a name representing the mass of the HotRod. Each of the runs consisted of five trials. You can see that it is quite easy to add additional runs by clicking the green "Add Another Run" button. If we click on the down-arrow to the far right of the "Car mass = 70 gm" run, we can then see the details of that run.

Figure 5 shows a summary of the first three of five trials for the "Car mass = 70 gm" run. The "Trial Results" are the acceleration values of the car. At the far right of each trial are three icons. The pencil icon allows the student to enter the trial result. The middle icon opens up the graph of the data recorded by Voyager for that run. The trash can icon lets you discard a faulty trial.

Let's now look at the graph of the data recorded in Trial 1 of the "Mass - 70 gm" run, as shown in Figure 6. The graph is rangefinder position versus time. The shaded region represents the time during which the the HotRod was slowing down on the track.

After dragging the highlighted region, we obtain a zoomed in graph of just that highlighted region, as shown in Figure 7. We click on the "Data Analysis" button and select the polynomial option for curve fitting. We see that the coefficient of x^2 is 0.11. Since this is one-half of the acceleration, we know that the acceleration is 0.22 m/s/s. We key in 0.22 as the "Trial Result".

This process is repeated for each of the five trials in each of the five runs. After this we are ready to set up the Results Table.

Figure 8 shows the results table in the Data Analysis Toolkit. The independent variable is keyed in as *Cart Mass (gm)*. The values 70, 110, 150, 190, and 230 are then keyed in for the car masses for each of the runs. The dependent variable is keyed in as *Acceleration (m/s/s)*. In this experiment, rather than using Manual Entry for the dependent variable, we click the radio button for "Trial Mean". For each of the five runs, CloudLab then calculates the mean value for the five trial results in each run and fills in those values *automatically* for us.

We can then work with the Results Graph, shown in Figure 9. A Bar graph will display by default, but we click on "Line" since we want a line graph. It is seen that the axes are automatically numbered and labeled in accordance with the Results Table of Figure 8. It appears that there is some kind of an inverse power relationship between acceleration and mass of the car.

We are now ready for the data analysis of the results graph of Figure 9, so we click on "Data Analysis" in the lower left corner of the figure. Upon clicking the "Data Analysis" button, we select *power* curve fitting and obtain what is shown in Figure 10. We see that the power -0.45 provides a fit with an r-squared value very close to 1. This power is very close to an inverse square root relationship, with acceleration inversely proportional to the square root of the mass. Different student groups are likely to get somewhat different powers but all should be inverse power relationships.

Finally, we add a "Section" to our Lab Report for which we give the title "Conclusion", as shown in Figure 11. We see that in any section, we can also add a YouTube video and an image. The ability to include links is also being planned.

*Additional Lessons on Rolling Resistance*

For a rolling resistance experiment using a cylindrical can and Velocity lab, click here. For another similar experiment click here. For information on the original larger PocketLab HotRod, click this link.