A box of mass m on the floor is connected to a horizontal spring of force consta

Question

A box of mass m on the floor is connected to a horizontal spring of force constant k. The coefficient of kinetic friction between the box and the floor is ?k. The other end of the spring is connected to a wall. The spring is initially unstressed. If the box is pulled away from the wall a distance d0 and released, the box slides toward the wall. Assume the box does not slide so far that the coils of the spring touch. (Use any variable or symbol stated above along with the following as necessary: g.) (a) Obtain an expression for the distance d1 the box slides before it first comes to a stop. d1 = (b) Assuming d1 > d0, obtain an expression for the speed of the box when it has slid a distance d0 following the release. v0 = (c) Obtain the special value of ?k such that d1 = d0. ?k =

Explanation / Answer

a)given that do is the distance pulled        then the block makes to and fro motion about the mean position       if F=mg the force on the block then         mg=k*x         x=mg/k      if µ is the coefficient of friction            and d1 is the distance travelled by the block before coming to rest     d1=2do-2µ(mg/k)    b) kd02/2 = mv2/2 +µkmgd0
   ?v =v[(kd0 -2µkmg)d0/m]

   c) 2d0 - 2µkmg/k = d0
     ?µk = kd0/(2mg)    b) kd02/2 = mv2/2 +µkmgd0
   ?v =v[(kd0 -2µkmg)d0/m]

   c) 2d0 - 2µkmg/k = d0
     ?µk = kd0/(2mg)

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