A drop test is a conceptually simple method to measure adhesion force. Consider the following scenario: a number of particles of different sizes adhere to a plate facing down, the plate is allowed to free-fall from a height, and it is stopped abruptly at the bottom of the test rig, dislodging some of the particles. Use m to denote particle mass, u impact speed, t stopping time and f adhesion force, and ignoring effect of particle weight and influence of air, use the concepts of momentum and momentum conservation to answer the following questions: (a) Write expression of momentum of a particle of known mass (m) and speed (u). (b) (c) Assume the momentum is used to overcome the adhesion force (f) over the time of impact (t), for a particle to dislodge, what is the relationship between mu and ft? Assume adhesion force is proportional to particle size. After the impact, if you examine the plate, do you expect to see more small particles or large particles still on the plate, and why?