IPHO 2014 theoretical problem1 PartA

Solution

  Assume a_x is the horizontal acceleration on the puck, N is the normal force acting on the puck, F_x is the horizontal component of N. Analyzing the puck:

  Assume F_x' is the inverse F_x acting on the cylinder, f is the friction force acting on the cylinder, u is the linear acceleration of the cylinder, alpha is the angular acceleration of the cylinder. Analyzing the cylinder:

  Assume w is the angular velocity of the cylinder when the puck reaches the lowest point, W_f is the work the total work friction done in the whole process. The connection between the puck and cylinder can be obtained by using the conservation of energy:

  Then find the relative velocity of the puck compared to the cylinder and use that to find the force between them.