Final answer:
To determine the minimum coefficient of static friction, we use the equation for the centripetal force and the equation for friction. By rearranging the equation and plugging in the appropriate values, we find that the minimum coefficient of static friction between the bike tires and the ground is approximately 1.14.
Step-by-step explanation:
To determine the minimum possible coefficient of static friction between the bike tires and the ground, we can use the equation for the centripetal force. The centripetal force is equal to the mass of the cyclist multiplied by the square of their velocity, divided by the radius of the curve. This force is provided by the frictional force between the tires and the ground. So, we can solve for the coefficient of static friction using the equation F_friction = μ_s * N, where N is the normal force equal to the weight of the cyclist.
First, we need to convert the velocity from m/s to km/h. The cyclist's velocity is 11 m/s converted to km/h by multiplying by 3.6, resulting in 39.6 km/h.
Now we can solve for the centripetal force using the equation F_c = m * v^2 / r. The mass of the cyclist is not given, so we assume it to be 60 kg (an average value for an adult). The radius of the curve is given as 22 m. Plugging in these values, we get:
F_c = (60 kg) * (39.6 km/h)^2 / (22 m)
Simplifying this equation, we get F_c = 8372.73 N.
The centripetal force is provided by the frictional force, so we have F_friction = 8372.73 N.
Finally, we can solve for the coefficient of static friction by rearranging the equation F_friction = μ_s * N. Since the coefficient of static friction is the minimum value that allows the cyclist to negotiate the curve without slipping, the equation becomes:
μ_s * N = 8372.73 N.
The normal force (N) is equal to the weight of the cyclist (mg), where g is the acceleration due to gravity (approximately 9.8 m/s^2). Plugging in the values, we get:
μ_s * (60 kg)(9.8 m/s^2) = 8372.73 N.
Simplifying this equation, we get:
μ_s = 1.1396.
So, the minimum possible coefficient of static friction between the bike tires and the ground is approximately 1.14.