Final answer:
The frictional force that acts on the tires of a cyclist as they round a curve can be found using centripetal force equations and trigonometry, based on the cyclist's speed, mass, angle of lean, and gravitational force.The correct option is option c .
Step-by-step explanation:
The subject is a physics problem that involves finding the force of friction acting at the point of contact between the tires and the road surface as a cyclist rounds a curved path. We can solve this by using circular motion and friction concepts.
To calculate the frictional force, we must first understand that the frictional force provides the necessary centripetal force to keep the cyclist moving in a circular path. The equation for centripetal force (Fc) is Fc = (m*v2)/r, where m is the mass of the object, v is the velocity, and r is the radius of the curve.
In this case, the cyclist is leaning at an angle θ such that tan(θ) = 0.50. Using trigonometry, we find the radius r using the relationship tan(θ) = v2/(r*g). We solve for r and then use it to find Fc.
Since Fc is provided by the frictional force, then frictional force = Fc. By substituting the numerical values given (m=80 kg, v=20 m/s, g=10 m/s2, and tan(θ) = 0.50), we can find the frictional force.