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Assuming proper operation of the brakes on the vehicle, the minimum stopping distance for a vehicle is determined by the effective coefficient of friction between the tires and the road, and the driver's reaction time in a braking situation. The friction force of the road must do enough work on the car to reduce its kinetic energy to zero. If the wheels of the car continue to turn while braking, then static friction is operating, while if the wheels are locked and sliding over the road surface, the braking force is a kinetic friction force only.
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http://www.csgnetwork.com/astp1.gif
To reduce the kinetic energy to zero:
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http://www.csgnetwork.com/astp2.gif
so the stopping distance is
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http://www.csgnetwork.com/astp3.gif
Note that this implies a stopping distance independent of vehicle mass, and in this case, driver reaction time. It also implies a quadrupling of stopping distance with a doubling of vehicle speed.
For calculating minimum stopping distance, a value of 0.8 is a nominal value for the coefficient of static friction between good tires and a good road surface. Almost always, coefficients of kinetic friction are less, and are dramatically less for wet, icy, slick, sandy, dirty very smooth or oily surfaces. For many newer high performance tires with good tread, the coefficient of kinetic friction on a dry road surface may approach 0.8 if the braking is not so prolonged as to cause tire melting. You may wish to plug in a smaller value such as .7 or .6 for a vehicle with normally driven and worn tires. Poor condition tires might yield .5 or .4 for a closer representation of friction.
圖片參考:
http://www.csgnetwork.com/astp1.gif
The stopping distance is given by:
圖片參考:
http://www.csgnetwork.com/astp3.gif
2007-05-06 04:12:57 補充:
somehow the images did not show up, click the link to see the diagrams and formula