Rolling Friction. Two bicycle tires are set rolling with the...

Rolling Friction. Two bicycle tires are set rolling with the same initial speed of 3.50 $\mathrm{m} / \mathrm{s}$ on a long, straight road, and the distance each travels before its speed is reduced by half is measured. One tire is inflated to a pressure of 40 psi and goes 18.1 $\mathrm{m}$ ; the other is at 105 psi and goes 92.9 $\mathrm{m}$ . What is the coefficient of rolling friction $\mu_{r}$ for each? Assume that the net horizontal force is due to rolling friction only.

Key Concepts

Kinematics of Deceleration

The study of motion under deceleration involves understanding how an initial speed decreases due to a constant resistive force, such as rolling friction. By analyzing the change in kinetic energy and relating it to the work done by the friction force over a known distance, one can derive important quantities like the coefficient of rolling friction. This approach integrates concepts from both energy and kinematics to bridge the force applied and the resulting change in motion.

Rolling Friction

Rolling friction (or rolling resistance) is the force that opposes the motion of a rolling object due to deformations in both the tire and the surface it rolls on. It is usually quantified by a dimensionless coefficient, ?r, which relates the resistive force to the normal force. Unlike sliding friction, rolling friction is often much smaller, but it plays a significant role in energy loss during rolling motion.

Work-Energy Principle

The work-energy principle states that the net work done on an object is equal to its change in kinetic energy. When a rolling object decelerates due to the force of rolling friction, the work done by this frictional force over the distance traveled is equal to the reduction in the object’s kinetic energy. This principle is key in linking the measurable distance of deceleration to the frictional force and hence to the coefficient of rolling friction.

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