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https:// session. masteringphysics.com next Copy of Homework assignments for General College Physics I HW Set 7 Problem 8.98 Problem 8.98 Part A In the figure(Figure 1) a 1.5 kg block is held at rest Find d such that the block's speed after crossing the rough patch is 2.0 m/s against a spring with a force constant k 710 N/m Express your answer using two significant figures. Initially, the spring is compressed a distance d. When the block is released it slides across a surface that is frictionless except for a rough patch of width 5.0 cm tha has a coefficient of kinetic friction uk E 0.43. Submit My Answers Give Up of 1 Figure 1 Equilibrium position Rough patch 5.0 cm Signed in as fahad alkaltham I Help I close previous l 5 of 10 l next Provide Feedback Continue

Explanation / Answer

   given

mass of the block 1.5 kg
spring constant k = 710 N/m
rought patch width 5 cm, coefficient of kinetic friction = 0.43
       velocity v = 2m/s
  

   the potential ednerfy of the spring converts in to kinetic energy

while crossing the rough patch surface frictional force will do work

   so work done = change in energy

       1/2 (k*d^2) -1/2 (mv^2) = muek * mg *s
          

       => 1/2 kd^2 = 1/2 mv^2 + muek * mg *s

       ==> 1/2*710*d^2 = 1/2 *1.5*2.0^2 + 0.43* 1.5*9.8*0.05

                    d = 0.09664 m = 9.664 cm

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