Final answer:
To find the coefficient of kinetic friction between the bowling ball and the lane in a game of rayuela, you need to calculate the acceleration of the ball first. Once you have the acceleration, you can use equations of motion to determine the time required for the ball to stop sliding and the distance to the point where it is rolling without slipping.
Step-by-step explanation:
To determine the coefficient of kinetic friction between the bowling ball and the bowling lane, we need to find the acceleration of the ball first. The net force acting on the ball is the force due to friction. Using Newton's second law (F = ma), we can calculate the net force. The force of friction is given by the coefficient of kinetic friction multiplied by the normal force (Ff = μN). The normal force is equal to the weight of the ball (N = mg). Substituting these values into the equation, we can solve for the coefficient of kinetic friction.
Given: radius (r) = 8.5 cm = 0.085 m, initial speed (v) = 9.0 m/s, coefficient of kinetic friction (μ) = 0.3.
The time required for the ball to stop sliding is given by the equation: v = at. Since the initial speed is not zero, the ball will take some time to reach the point where it is rolling without slipping. The distance (d) to this point can be calculated using the equation: d = vt + (1/2)at^2. Substitute the known values into these equations to find the time and distance.