When you skid to a stop on your bike, you can significantly heat the small patch of tire that rubs against the road surface. Suppose a person skids to a stop by hitting the brake on his back tire, which supports half the 90 kg combined mass of the bike and rider, leaving a skid mark that is 40 cm long. Assume a coefficient of kinetic friction of 0.80. How much thermal energy is deposited in the tire and the road surface?

In this case the kinetic energy of the bike is converted into the heat energy between the area of contact of tyre and the road. This happens due to the work done by the frictional force between the surface to stop the relative motion between the road and the tyre.

Given:

normal force on the rear tyre, [tex]N=45\ N[/tex]

(as given in the question that the rear tyre supports half the combined weight of the bike and the rider.)

distance dragged while stopping the tyre, [tex]s=0.4\ m[/tex]

coefficient of kinetic friction between the surfaces, [tex]\mu=0.8[/tex]

Now, frictional force between the surfaces:

[tex]f=\mu.N[/tex]

[tex]f=0.8\times 45[/tex]

[tex]f=36\ N[/tex]

Now, the work done by the kinetic friction:

[tex]W=f.s[/tex]

[tex]W=36\times 0.4[/tex]

[tex]W=14.4\ J[/tex]

According to the energy conservation this amount of energy is converted into thermal energy between the surfaces in contact, i.e. road and the tyre.