Final answer:
To find the smallest radius of an unbanked track around which a bicyclist can travel, use the equation R = v² / (g tan(θ) - μ), where v is the velocity, R is the radius, g is the acceleration due to gravity, θ is the angle of the curve, and μ is the coefficient of static friction.
Step-by-step explanation:
To find the smallest radius of an unbanked (flat) track around which a bicyclist can travel, we need to consider the maximum velocity at which the bicyclist can traverse the curve without slipping.
The maximum velocity can be calculated using the equation:
v = √(Rg tan(θ))
Where v is the velocity, R is the radius of the curve, g is the acceleration due to gravity (approximately 9.8 m/s²), and θ is the angle of the curve.
In this case, the velocity is given as 27 km/h, which needs to be converted to m/s. The coefficient of static friction is given as 0.35. Plugging in these values and rearranging the equation to solve for the radius R, we get:
R = v² / (g tan(θ) - μ)
Substituting the given values, we can calculate the smallest radius of the track around which the bicyclist can travel.