When a car skids, kinetic energy is converted to heat by friction, and rubber is left on the road. The work done by fiction, the force-distance integral, (FDI), is equal to the kinetic energy lost. Since the friction force is the same at all speeds the FDI can be calculated as fD where f is the friction force and D is the skid distance. If the car comes to rest at D the integral fD is equal to the initial kinetic energy.
1 Toy cars with their wheels locked, are lined up along a meter stick. The stick is pivoted at the left hand end. The right hand end is jerked forward to propel the cars down the table. The initial velocity, (u), of each car, is proportional to its distance from the pivot. The initial velocity squared, (u2), of each car, is proportional to the skid distance.
The cars skid down the table and come to rest again on a curve. Fitting a parabola to the photograph shows that the skid distance D is proportional to the initial velocity squared as expected. Within errors the curve is a parabola. The fit is all the more remarkable, since one of the vehicles was loaded with lead, and was three times the mass of the others.
 The truck is carrying twice its mass in lead. |
Since the friction force is proportional to the normal force (the weight mg)....
.... and the skid distance is independent of the mass.
Since the friction force is also independent of the area in contact with the 'road', neither the mass, nor the total number of wheels, affects the skid distance. The only significant determiner of skid length is the coefficient of kinetic friction between the two surfaces. Approximate coefficients are listed below.
Table 1
The findings have immediate consequences....
1 Fully loaded trucks can stop in the same distance as cars. It is not particularly dangerous to travel at speed in front of a truck, provided the brakes and tires are in good condition.
2 A fully loaded car can be stopped in the same distance as the car with only the driver. It is not correct to assume that, because you are by yourself, it is safe to travel faster.
3 Stopping distance depends on the velocity squared. Traveling twice as fast lengthens your skid by four times.
4 The length of a skid-mark indicates the initial speed of the vehicle. That is why you see police with tape measures at the scene of a road accident. The length of a skid mark is enough to convict on a charge of dangerous driving. No eye witness is required.
5 The stopping distance depends on the coefficient of sliding friction. Water lowers the coefficient. Wet roads are dangerous. That is why you see flashing 40 km/h speed limit signs on the Bangkok motorways during thunderstorms.
Death Valley, California, USA
Believe it or not, 300-kilogram stones end up near the middle of the a large flat surface, having been driven by high winds, after rain made the flat level surface temporarily very slippery (reduced the coefficient of friction to near zero).