Question

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 36 cm long. Assume a coefficient of kinetic friction of 0.80.

How much thermal energy is deposited in the tire and the road surface?

Answer 1

Gravitational acceleration = g = 9.81 m/s²

Mass of the bike and rider = m = 90 kg

Normal force on the back tire = N

The back tire supports half the weight of the bike and rider.

N = mg/2

Coefficient of kinetic friction = = 0.8

Friction force on the tire = f

f = N

f = (mg/2)

f = mg/2

Length of the skid mark = L = 36 cm = 0.36 m

Thermal energy deposited in the tire and the road surface = E

The thermal energy deposited in the tire and the road surface is equal to the work done by friction.

E = fL

E = (mg/2)L

E = mgL/2

E = (0.8)(90)(9.81)(0.36)/2

E = 127.14 J

Thermal energy deposited in the tire and the road surface = 127.14 J