### Mathematical modeling 0 Comment

Rolling resistance is the force that resists the rolling of a wheel or other circular object along a surface caused by deformations in the object and/or surface. Generally the force of rolling resistance is less than that associated with kinetic friction. (Silliman. 1891) Rolling resistance is the force that resists the rolling of a wheel or other circular object along a surface caused by deformations in the object and/or surface. Generally the force of rolling resistance is less than that associated with kinetic friction.

Typical values for the coefficient of rolling resistance are 0. 001. One of the most common examples of rolling resistance is the movement of motor vehicle tires on a road, a process which generates heat and sound as by-products. (Silliman. 1891) The bicycle has tires made out of rubber i. e. the bicycle has pneumatic tires. The primary cause of rolling resistance in the pneumatic is hysteresis . Hysteresis is a property that is unique to all the elastic products in which energy is lost during the recovery of the elastic from the stress it is put under.

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When the cycle rolls down the ramp it loses energy due to hysteresis property of the pneumatic tires. Since the bicycle loses energy because of hysteresis , less work has to be done by the cycle . But the bicycle has to travel the same distance , which means that the there is a reduction in force that is required by the bicycle to do the work . This reduction in the force is caused by the rolling resistance. The theory stated above involves the rolling resistance faced by a bicycle on all surfaces .

When we talk about the rolling resistance the tire faces on sand , it is important to remember that sand is a loose surface and the tire has the ability to sink in the sand . If a tire sinks in more than its usual sinkage depth . The tire needs to do more work inoder to overcome the rut it has sunk in the opposite direction of the force . Since the force is constant , this work done by tire acts counter-effective to the work that needs to be done in order to cover the distance , and hence the force is degraded .

The degradation in the force is caused by the increased rolling resistance due to the sinkage depth . As the tire roates under the weight of the vehicle , the tire experiences continuous cycles of deformation and recovery . As the tires recovers from the deformation , energy is lost in the tires due to hysteris. In the diagram above R refers to the rolling resistance acting on the wheel , r is the radius of the wheel , W is the force acting on the wheel , F is the towering force applied on the axle in this case it is the force due to the acceleration due to gravity .

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