A mass of 349g is on a horizontal surfacewith mu_k=0.150, and is in contact with

Question

A mass of 349g is on a horizontal surfacewith mu_k=0.150, and is in contact with a lightweight spring with aspring constant of 694N/m which is compressed. When the spring isreleased, it does 1.25J of work on the mass while returning to itsequilibrium position. Calculate the distance the spring wascompressed. A mass of 349g is on a horizontal surfacewith mu_k=0.150, and is in contact with a lightweight spring with aspring constant of 694N/m which is compressed. When the spring isreleased, it does 1.25J of work on the mass while returning to itsequilibrium position. Calculate the distance the spring wascompressed.

Explanation / Answer

                Given that the mass of body is m = 349 g = 0.349kg                  Thecoefficent of kinetic friction is k = 0.15                  Thespring constant is K = 694 N/m                  The work done is W = 1.25 J ----------------------------------------------------------------------------             The work done due to all force is W = (1/2)kx2 +work done due to friction                                                            1.25J = (1/2)kx2 -mg*x                                                             2.5J = (694 N/m)x2-(0.15)(0.349kg)(9.8m/s2)x                                                    x2 -0.00073x- 0.0036 J = 0                                    Then we get x = 0.06 m          This is thecompressed distance of the spring .                                                                                                                                 

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