To find the fraction of the total kinetic energy of the bicycle that is due to the rotational kinetic energy of the wheels, we first need to calculate the total kinetic energy of the bicycle.
The total kinetic energy (KE) of an object is given by the formula:
KE = (1/2)mv^2
where m is the mass of the object and v is its speed. In this case, the total mass of the bicycle, including the wheels and the rider, is 79 kg.
Next, we need to calculate the rotational kinetic energy (Kerot) of the wheels. The formula for the rotational kinetic energy is:
Kerot = (1/2)Iω^2
where I is the rotational inertia of the wheels and ω is the angular velocity of the wheels. The rotational inertia of each wheel is given as 0.080 kg•m^2.
Since the bicycle is coasting at constant speed, the linear speed of the bicycle is the same as the speed of the rider. However, since the wheels are rotating, their angular velocity is related to the linear speed by the equation:
v = ωr
where r is the radius of the wheel. In this case, the radius of the wheel is given as 0.32 m.
To find the angular velocity of the wheels (ω), we rearrange the equation:
ω = v / r
Now we can substitute the given values into the formulas to calculate the total kinetic energy of the bicycle (KE) and the rotational kinetic energy of the wheels (Kerot).
KE = (1/2)mv^2
Kerot = (1/2)Iω^2
Finally, we can find the fraction of the total kinetic energy that is due to the rotational kinetic energy of the wheels by dividing the rotational kinetic energy by the total kinetic energy:
Fraction = Kerot / KE
By following these steps and substituting the given values, we can find the desired fraction.