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# Friction force

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Hello, I have a question about friction force aktiong on the back wheels on a car. The car is gliding backwards but the backwheels has spunn loose. Is the force acting to stop the car, A: the cars engine force times the friction coefficient or, B: the cars engine force times the friction coefficient plus a friction force that would be the same as when the backwheels are locked ? /Niklas

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Your question is difficult to follow, but I think you''re asking, in effect: If a tire is spinning without grip on pavement, what is the friction force?

Normally, at the contact point between the tire and the pavement, the two surfaces are mutually at rest. The tire is not sliding over the pavement, but rather it rolls over the surface.

In this case, the friction is controlled by the engine force, weight of the car and the coefficient of static friction of the tire-pavement interface. Basically, the force is equal to the force produced by the engine on that tire due to torque and such, however the force is limited by the normal force (weight on the tire) and coefficient of static friction.

maxFriction = staticCoeff * weight
(direction opposite engine force / tire rotation)

If the engine force exceeds that force limit, the tire loses its grip on the road, and the car begings to skid. If by this means, or some other way, the car skids, the tire-pavement interface is no longer at mutual rest. The surfaces of the tire and pavement slide over eachother.

In this case, the friction is somewhat more complicated, however it would be simply modelled as a dynamic friction between the two surfaces. The friction is no longer determined by the force of the engine, but rather is determined solely by the weight of the car and a new coefficient of friction, the dynamic friction coefficient. This coefficient applies when two surfaces are sliding over eachother (as opposed to being at rest as above). The dynamic friction coefficient is generally less than the static coefficient. The direction of the friction is also different. Above, the direction of friction force was directly opposite the force applied by the engine. Now the force is in the direction opposite to the relative motion of the two surfaces, which, if the tire is skidding, may be only partially related to the direction the tire is facing. The speed of the tire''s rotation, in the purely linear motion case, is not really relevant (though this is a simplification, and may not be really accurate). More detailed physics is probably available online somewhere.... or perhaps someone else will comment here?

actualFriction = dynamicCoeff * weight
(direction opposite relative motion of surfaces)

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Geoff,

GOOD explanation!

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

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the pacejka formula.

I''m no specialist in that stuff, but this formula is usually used a lot for resolving the contact forces on tires, either turning, transmitting power or rolling.

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