Instructions Click 'start' in the following Active Figure depicting static and kinetic frictional forces with a given appliedforce to a trash can to complete the exercise.EXPLOREA trash can with a mass of 11 kghas a coefficient of static frictionof Ms= 0.88 and a coefficient ofkinetic friction of μk = 0.40. (TheActive Figure applies to a similarsituation, but the values of themass, coefficient of static frictionand coefficient of kinetic frictionmay be different. So the values itgives may not be the samevalues you obtain from yourcalculations.)(A) What is the maximumhorizontal force F that can beexerted without moving the trashcan?(B) Suppose this force is justbarely exceeded. Determine theacceleration of the trash can as itmoves.CONCEPTUALIZEThe trash can is being pushednear its base but the appliedforce is balanced by the force of static friction. The maximum force of static friction is determined by the coefficientof static friction and the normal force that the ground exerts on the trash can.Display in a New WindowCATEGORIZEWe seek the largest horizontal force F that can be applied without moving the trash can. Examine when it is possibleto balance the forces to have no acceleration; this is a problem of balanced forces and equilibrium. ANALYZE(A) What is the maximum horizontal force F that can be exerted without moving the trash can?The surfaces are extremely rough, and only a fraction of the surfaces is in close contact, but we make theassumption that the relation between the friction force and normal force applies.The maximum possible force of static friction is= μsnFs, maxwhere n is the magnitude of the normal force exerted by one surface on the other. For an applied force that is toosmall to move the trash can, the force of static friction balances the applied force and both have the same magnitudewhich, because n = mg, is equal toF = Fs, max = μçmgwhereMsis the coefficient of static friction. This givesF = Fs, max=(B) Determine the acceleration of the trash can as it moves.N.For a force F that is just slightly larger than Fs, max, the trash can accelerates. The applied force can still be taken asthe same, but the friction force is given by the coefficient of kinetic friction μk times the normal force n instead of thecoefficient of static friction μ times the normal force n:FK = μkmg.The net force that gives the mass times the acceleration is the difference of the applied and kinetic friction forces:μkmg = μsmg - μkmg = (μs - μk)mg= max.ΣΕ= Fs, maxXThis can be solved to give the acceleration:ax(Ms - Mk)g==m/s².FINALIZEIf the applied force is suddenly removed from the moving trash can, the force of kinetic friction continues to act withno applied force as long as the trash can is moving. Consider how this affects the motion of the trash can.

Name: Instructions Click 'start' in the following Active Figure depicting s
Uploaded: 2024-03-20T06:57:57.000Z
Channel: Bartleby
Description: Instructions Click 'start' in the following Active Figure depicting static and kinetic frictional forces with a given appliedforce to a trash can to complete the exercise.EXPLOREA trash can with a mass of 11 kghas a coefficient of static frictionof