Final answer:
To find the distance the bag moves before coming to rest with respect to the belt, use the equation d = μ*tan(theta). The work done by all forces can be found by adding up the work done by the force of friction and the work done by the force of gravity. The energy dissipated in the process is equal to the work done by the force of friction.
Step-by-step explanation:
To solve this problem, we need to consider the forces acting on the bag and the work done by each force.
(a) The bag will come to rest when the force of friction equals the force of gravity along the incline. The force of friction, in this case, is equal to the coefficient of friction multiplied by the normal force, which is mg*cos(theta), where m is the mass of the bag and g is the acceleration due to gravity. So we can set up the equation: μmg*cos(theta) = mg*sin(theta). Solving for d, the distance the bag moves before coming to rest, we get: d = μ*tan(theta).
(b) If the bag reaches the top after moving a distance 2d, it means that the work done by the forces is equal to zero. The work done by the force of friction is -μmg*d, and the work done by the force of gravity is -mg*sin(theta)*2d. Adding up these two works, we get the total work done by all forces.
(c) The energy dissipated in the process is equal to the work done by the force of friction, since friction is the only force involved in dissipating energy. So the energy dissipated is equal to -μmg*d.