This question requires a visual representation of the track, which is not possible in this text-based format. However, I can provide you with the relevant equations and steps to solve the problem.
A) To determine the velocity of the block at point B, we can use conservation of energy. The initial potential energy at A is equal to the final kinetic energy at B.
Initial potential energy at A = mgh = (1.0 kg)(9.81 m/s^2)(2.0 m) = 19.62 J
Final kinetic energy at B = (1/2)mv^2
Since the section AB is frictionless, all of the initial potential energy is converted to kinetic energy at point B.
19.62 J = (1/2)(1.0 kg)v^2
v = sqrt(39.24) = 6.27 m/s
Therefore, the velocity of the block at point B is 6.27 m/s.
B) To determine the thermal energy produced as the block slides from B to C, we can use the work-energy principle. The work done by friction is equal to the change in kinetic energy.
Work done by friction = force of friction x distance = μkmgd
where μk is the coefficient of kinetic friction, m is the mass of the block, g is the acceleration due to gravity, and d is the distance from B to C.
Work done by friction = (0.20)(1.0 kg)(9.81 m/s^2)(2.8 m) = 5.48 J
Change in kinetic energy = (1/2)mv^2 - 0
where v is the velocity of the block at point B.
Change in kinetic energy = (1/2)(1.0 kg)(6.27 m/s)^2 - 0 = 19.62 J
Therefore, the thermal energy produced as the block slides from B to C is 5.48 J.
C) To determine the velocity of the block at point C, we can use conservation of energy again. The final potential energy at C is equal to the initial kinetic energy at C.
Final potential energy at C = (1/2)kx^2
where k is the stiffness constant of the spring and x is the compression of the spring.
Final potential energy at C = (1/2)k(0.15 m)^2
Initial kinetic energy at C = (1/2)mv^2