AAPT UNITEDSTATES PHYSICS TEAM AIP 2007 Semi-Final Exam Part B B1.A certain mechanical oscillator can be modeled as an ideal massless spring connected to a moveable plate on an incline.The spring has spring constant k,the plate has mass m,and the incline makes an angle 0 with the horizontal.When the system is operating correctly,the plate oscillates between points A4 and B in the figure,located a distance L apart.When the plate reaches point 4 it has zero kinetic energy,but then trips a small lever that instantaneously loads a block of mass Monto the plate.The block and plate then move down the incline to point B, where the force from the spring stops the plate.At this point,the block falls through a hole in the incline,allowing the plate to move back up under the force of the spring.Upon returning to point 4 it collects another block,and the cycle repeats.Both the plate and the block have a coefficient of friction u with the incline for both kinetic and static friction.It is reasonable that the motion in either direction is simple harmonic in nature. blocks load here moving plate B blocks fall here (10 pts)a.Let u be the critical value of the coefficient of friction where the block will just start to slide under the force of gravity on an incline(without the spring acting on it).Then let Findin terms ofg,the acceleration of free fall,and any 2 or all of the following variables:and M. Copyright 2007,American Association of Physics TeachersCopyright © 2007, American Association of Physics Teachers Semi-Final Exam Part B B1. A certain mechanical oscillator can be modeled as an ideal massless spring connected to a moveable plate on an incline. The spring has spring constant k, the plate has mass m, and the incline makes an angle θ with the horizontal. When the system is operating correctly, the plate oscillates between points A and B in the figure, located a distance L apart. When the plate reaches point A it has zero kinetic energy, but then trips a small lever that instantaneously loads a block of mass M onto the plate. The block and plate then move down the incline to point B, where the force from the spring stops the plate. At this point, the block falls through a hole in the incline, allowing the plate to move back up under the force of the spring. Upon returning to point A it collects another block, and the cycle repeats. Both the plate and the block have a coefficient of friction μ with the incline for both kinetic and static friction. It is reasonable that the motion in either direction is simple harmonic in nature. (10 pts) a. Let μc be the critical value of the coefficient of friction where the block will just start to slide under the force of gravity on an incline (without the spring acting on it). Then let 2 μc μ = . Find μ in terms of g, the acceleration of free fall, and any or all of the following variables: θ and M