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15 August, 02:14

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?

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  1. 15 August, 03:28
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    E = 169.34 J

    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
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