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 48 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

E = 169.34 J

Step-by-step explanation:

First, we need to find the frictional force between the back tire and the road. For that purpose, we use the following formula:

f = μR = μW

f = μmg

where,

f = frictional force = ?

μ = coefficient of friction between tire and road = 0.8

g = 9.8 m/s²

m = mass supported by back tire = (0.5)(90 kg) = 45 kg

Therefore,

f = (0.8)(45 kg)(9.8 m/s²)

f = 352.8 N

Now, for the heat energy we use the formula of work. Because, thermal energy will be equal to work done by frictional force:

E = W = fd

where,

E = Thermal Energy = ?

f = frictional force = 352.8 N

d = displacement = 48 cm = 0.48 m

Therefore,

E = (352.8 N)(0.48 m)

E = 169.34 J