# A Velocity Lab Experiment on Rolling Resistance

Rolling resistance is a force that opposes the motion when an object rolls along a surface.  In this experiment a coasting cylinder on a carpet gradually slows down and stops due to rolling resistance.  The primary factor affecting rolling resistance here is deformation of the carpet as the cylinder rolls.  Not all of the energy needed to deform the carpet is recovered when the pressure from the cylinder is removed.  In other words, the effect is non-elastic.  The purpose of this experiment is two-fold:  (1) to determine the force of rolling resistance and (2) to determine the coefficient of rolling resistance between the cylinder and the carpet.

The cylinder in this experiment is an unopened can of jellied cranberry sauce.  The author used this as it is reasonably heavy and there seemed to be little if any sloshing of the sauce in the can as it rolled.  The photo below shows the can resting on the carpet with PocketLab Velcro'd to the end of the can in such a way that the z-axis is the desired axis of rotation when used with the VelocityLab app.  The white arrow shows the direction of the initial push on the can.  After the initial push, the can eventually slows down and stops moving.  This is due primarily to rolling resistance, and using the can means that there is no friction in an axle that would also consume some energy.

The video below shows a typical run of the experiment.  Graphs of position, velocity, and acceleration versus time are synced with the video. As can be seen, the experiment is easy to set up, and the data is obtained quickly for analysis by student lab groups.

The figure below shows the free-body diagram of the cylinder as it slows down from rolling resistance.  The normal and gravitational force are equal in magnitude as the cylinder rolls on the level plane of the carpet.  From Newton's second law, the net force, ma, is 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.

The position, velocity and acceleration graphs in the figure shown below were obtained using Microsoft Excel from the VelocityLab.csv file produced by the VelocityLab app.  The acceleration of the cylinder can be obtained in two ways: (1) from the slope of the region of the velocity vs. time graph where the can is slowing down, and (2) by averaging the data points in the acceleration vs. time graph in the region where the can is slowing down.  Both methods give an acceleration of -0.363 m/s/s.  With the acceleration known, students can then address the two-fold purpose of the experiment.  (Note that the mass of the cylinder plus PocketLab, obtained from a balance, is 0.479 kg.)  First, the force of rolling resistance is ma = (0.479 kg)(-0.363 m/s/s) = 0.174 N.  Secondly, the coefficient of rolling friction = a/g = (-0.363 m/s/s)/(-9.81 m/s/s) = 0.0177.

An interesting optional exercise for the student lab groups would be to repeat the experiment with the can rolling on, say, a school hallway or on a gymnasium floor.  What are their predictions on the value of the coefficient of rolling friction in this case?  Does experiment verify their predictions?

Note that the VelocityLab.csv file used by the author is included as one of the attachments.  At the writing of this lesson, it should be noted that the acceleration in the VelocityLab.csv file is given in units of g's.  A column needs to be added giving acceleration in m/s/s by multiplying g's by 9.81.

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