Final answer:
To determine the fastest speed at which the book does not slide in a roundabout, calculate the maximum static friction force and set it equal to the centripetal force. By solving for velocity, we find the answer to be approximately 4.71 m/s.
Step-by-step explanation:
To determine the fastest speed at which you can go around a curve without the book sliding, we need to find the minimum coefficient of static friction between the book and the seat. The maximum static friction force can be calculated using the formula F_max = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force. In this case, the normal force on the book is given by N = m * g, where m is the mass of the book and g is the acceleration due to gravity.
If the book does not slide, the maximum static friction force must provide the centripetal force required to keep the book moving in a circle. The centripetal force is given by F_c = m * v^2 / r, where m is the mass of the book, v is the velocity, and r is the radius of the curve. By setting F_max equal to F_c and solving for v, we can find the fastest speed.
Let's assume a mass of 1 kg for the book. The normal force is N = 1 kg * 9.8 m/s^2 = 9.8 N. The centripetal force is F_c = 1 kg * v^2 / 12 m. Equating F_max and F_c, we have μ_s * 9.8 N = 1 kg * v^2 / 12 m. Solving for v, we find the fastest speed at which the book does not slide is v = 4.71 m/s. Therefore, the fastest speed is approximately 4.71 m/s.